S WVVP 6 1 This paper is prepared for staffuse and is not for publication.The views expressed are those of.the author and not neoessarilythose of the B .

INTERNATIoNAL BANK FOR RECONSTRUCTION AND DZVIOFPMDNT

INTERNATIONAL DEVEIPMENT ASSOCIATION

Economics Department Wcrking Paper No. 61

Transport Network Model

February 23, 1.970

This paper is one of a series of papers from the Transport PlanningModels Study under the direction of Mr. Jan de Weille and Mr. Leon H. Miller.The overall objective of the Study is the continuing investigation ofmathematical modela developed for uge in transport planning. The) Studywill analyze existing transport models, revise and extend the models wherepractical, and develop new models where needed. An evaluation of the modelswill include their application in transport planning studies and a criticalreview of the methodology.

This paper is based on Chapter 4 of the Harvard UnivetsityiTranxportResearch Program report "An Analysis of Investmuent Alternatives in theColombian Transport System", by Paul 0. Roberts, David T. Kresge and John R.Meyer, (Cambridge, Massachusetts, September, 1968). The member of the BankStudy working on this portion of the study was Leon H. Miller. A sampleof the computer outputs has been added to the Harvard presentation alongwith a listing of the data requirements. Also editorial and other changesin the text have been made to improve the presentation.

The transportation model is designed to simulate the traffic flows ina country taking the transportation system and shipping requirements as inputs.The output of the model is the system network link utilisation with itsassociated costs and performance measures.

This paper is expository in nature; no attempt has been made tocritically evaluate the model. A critique will be covered in a subsequentpaper. Bank staff members are invited to make comments and suggestionsfor improvement of the model.

Sector and Projects Studies Division

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TABLE OF CONTENTS

Page No.

The Scope of the Model 1Supply and Demand 2Disaggre-. ton 5Supply Disaggregation 5Deriand Disaggregation 6Conputation of Flows on the Transport Network 9Network Definition 9Modal Choice and Routing 12Commodity Distribution and Assignment 19Cost Performance Submodels 24Highway Model 25Rail Model 26Transfer Model 28Unsophisticated Modal Submodels 30Transport Price Determination 31System Performance Measures 32

Appendices

Appendix A - Summary Tables 49Appendix B - Data Requirements 60Appendix C - Network Data Requirements 61Appendix D - Transport Dictionary 63

Figures

Page No.

Figure 1 Location of the Transport System Model in the Total Model 3figure 2 Diagrammatic Representation of a Typical Breakdown of

Supply and Demand by Industry and Region 4Figure 3 Disaggregation Factor Table 10Figure 4 Network Representation of the Transport System and its

Coding in the Network Link File 13Figure 5 Minimum Path Tree 18Figure 6 Fixed Charge Aspect of Transfer Links 20Figure 7 Mode and Rate Table Input To The Pricing Example 33Figure 8 Some Tables Relating Cost and Flow 38Figure 9 Results of Disaggregation Process 42Figure 10 Perceived Cost of Each Link As Seen By Shippers of Banano 43Figure 11 Decision Costs Per Ton For Banano 44Figure 12 Decision Cost/$100 Good For Banano 45Figure 13 Flow In Tons Per Day For Banano 46Figure 14 Ton-Miles Per Day (00) For Banano 47Figure 15 Flow Per Season ($1000) For Banano 48

Charts

Chart 1 Dollar Value of Vehicle Depreciation 52Chart 2 Old Vehicles Scrapped From The Fleet 52Chart 3 Total Vehicle-Hour Requirements For This Year 52Chart 4 Total Vehicle-Hour Availability For This Year 53Chart 5 Ratio of Vehicle Requirements To Availabilities 53Chart 6 Total Vehicle Deficit (Desired - Actual, (_) Surplus 53Chart 7 Vehicle Deficit in Number of Vehicles 53Chart 8 New Vehicles Added To The Fleet 54Chart 9 (VEHCLS) Number of Vehicles By Class - Blk, Gen, Spc, CC, PP 54Chart 10 Dollar Value of Good I Transported From Region N to Region N 55

TRANSPORT NETWORK MODEL

The Scope of the Model

The transportation model is designed to simulate the traffic flows ina country taking the transportation system and shipping requirements as inputs.The output of the model is the system network link utilization with itsassociated costs and performance measures.

The transport model has been designed to use the basic production andconsumption data furnished by the macro-economic model for the commoditysupplies and demands. However, the transport model can also be used alonewhen these supplies and demands are specified exogenously. There may betimes when the situation does not warrant the use ofthe full macroeconomicmodel or when the detailed data required for its use simply do not exist butwhere sufficient flow or prodtction data are available to allow the transportmodel to be used separately.

Since the principal purpose of the transport model is the prediction ofnetwork link flows, a number of inputs are required pertaining to the system.These include the following:

1. Regional supply of each commodity2. Regional demand for each commodity3. Regional unit production costs by industry4. Information on the intraregional distribution and

product mix of each industry5. Topology and characteristics of the transport network6. Transport preference weightings associated with

each commodity7. Operating characteristics and costing for each

transport mode8. Transport pricing policy in the form of a rate

structure for each mode and class of vehicle.

The first three categories of input normally come to the transportmodel through the forward coupling mechanism linking the transport and themacroeconomic models. Intraregional distribution and commodity mix aresupplied via the disaggregation process. Network topology and linkcharacteristics are specified each year in the process of updating thecurrent transport network. Information on transport preferences, necessaryfor determining modal choice and routing, modal operating characteristics andtransport pricing policy must be supplied for each study conducted.

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The transport model is most easily described in terms of thecomputational steps which must be performed using the input above.The steps are: a) 'commodity disaggregation and link edit, b) computationof flows, c) modal cost-performance determination, d) transport pricedetermination, and e) summary of the system performance measures. Figure 1depicts this computational sequence.

3upply and Demand

Perhaps the most important input to the transport model is thesupply of the product of each industry in each region and the demandfor the output of each industry in each of the regions. Without thisinformation there is no model. The use of a macroeconomic model toreproduce a complete and consistent set of these inputs appears highlydesirable. A diagram showing a jUical breakdown of supply and demand byindustry and region is shown in Figure 2. The supply of the output ofindustry I in region M is represented by means of the elements of thetwo-dimensional array, SUPPLY (I,M). The demand by industry J or sector Iin region M for the output of industry I is represented by each of theelements of a three-dimensional array, DEMAND (I,M,J). Thus, each industryin each region has a single supply quantity and a vector of demands.

The outside world is merely another region but imports and exportsare treated as separate industries. Naturally the import sectors arestrictly supply sectors which do not generate demands for any commodities.This is shown in Figure 2 by shading in the boxes which cannot logicallyhave any entries. Similarly, the export sector only provides a demandfor domestic commodities and does not supply anything. The transportindustry and final consumption are two other sectors which supply notran:portable outputs. The boxes indicating the demand for transportare also shaded in because there is no direct demand for transport.Transport demand is a derived demand generated by the need to movecommodities from one location to another. Determining the derived demandfor transport is, in fact, one of the important functions of the transportmodel.

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MAROECONOM/%IC MWODE L

F/OR?WARD COUPLINGINDUSTRY SUPPLIES, PEiANDS ANDPRO DUCTION COSTS, BY ITEGIO

- - -- -TH E TRN l5PORr MODE L _

DISAGGEGATIOk t INtR zGfO,.jAL DISMIElTIOUDJ

CO/YMODIlY SUPPLIlES AND ANDO COMMAOPITr

IDEMAiNDS BY fJODS -AK-vP

I .-UPDAtE NETWlORK TO <- - rOKI< TOPOL^oGVe

CURRENT YEAR 8eDuZoam

I DErERMINE MODAL CHO(CG mRSoRr P¢fEI'

A D RTG OVER NErWOr( - IvB ComMOoiry

I DErERMIKIE PATrERtI OF DISTRI BUMJONI j_AND ASSIGU F]OWS TO NErWORK

I JUSE MODAL SUOMODELS FOR . O

DETERMIlNlG LIAKCOSTS < T-n MOog

ANlD PE-RF0MMJCF-5

I SuMMAY OF T'ANSPORt

SYSTEM PERFOSMANCE MeASUKJES Lptci rf o

5AcKWAKt) COUPULJIGILJD S1R'Y TKANSPORTr COSTS Br

fE.G 10 14

FIGURE 1

FUNCTIONS OF THE TRANSPORT MODEL

SUPPLY OF DEANPRODOCTS___

B IN BY IN ___

INDUS. REGION OVAUrITY INDL)!. REGIONJ QvA,Mn.TY

Mt3 M__0_3

_ _ M=4 AA_A,_

ML=3 M__-

Ji33___1I3

_____ -Me44'_ // X

M: 1

_ _ M z _ _ _ _ _ _

M 3 M1 _3 _

',M=4 1 Mi

1,7 14A-51-7M=

Iva 1-8 M -

!-a9 ?Aw5 19M

1'Wo M:5 -0MS

II M:5

5UPPLx (1,M) DEMAND (I,M J)

Figure 2

Diagrammatic Representation of a Typical Breakdownof Supply and Demand by Industry and Region

-5-

DISAOQREGUTIf(

The industry supplies and demiinds serve as direct inputs to thetransport model. However, these maoroeconomic estimates are usuallytoo aggregative for direct use in the transport model. The state ofavailable data in most developing countries makes it difficult tootbtain input-output tables and supporting economic data for more thana small number of sectors. Disaggregation into sub-commodity types,each with a definable set of transport requirements must be accomplishedtio provide the additional detail. From the viewpoint of the transportsector, the finer -ue commodity breakdown, the more easily transportconsequences such as number and type of vehicles, travel times andnetwork distribution can be determined, and the more realistic the finalsimulation will be.

The supply and demand for the products of a specific industrycan be disaggregated by the specification of percentage factors withineach region. If, for example, one knows that seventy per cent of theagricultural production of a given region is rice, ten per cent is fruit,and twenty per cent is some other agricultural product, then one has ineffect disaggregated agricultural supply for that region. It is necessaryto formulise this procedure and to relate the quantities produced tospecific nodes of the network in order to make it usable.

Supply Disaggregation

The subcommodity supply disaggregation is-performed as follows:

SUBSUP(K,NODE) = SUPPLY (I,M)*SUBCdM(K,NODE) (1)

where K and NODE are subscripts for subcommodity and point of production andI and M denote industry and region. The meaning of the variables is asfollowss

SUBSUP (K,NODE) supply of subcomodity K produced at NODESUPPLY (I,M) aggregated supply of the output of industry

I in region MSUBCOM(K,NODE) the proportion of the regional production

of industry I which is due to the productionof subcommodity K at location NODS (anexogenously supplied subcommodity dis-aggregation factor).

-6-

Note that the subscripts K and NODE also imply industry I inregion M since each K belongs to a specific industry and each NODEis located in a particular region. Thus, supply disaggregation isperformed within the model using SUPPLY (IM,) from the macroeconomicdata and by using the subcommodity disaggregation factors suppliedexogenously from an input form.

Demand Disaggregation

Disaggregation of demand for transportable products is somewhatmore difficult than supply disaggregation since it is necessary tomaintain consistency. Within the model, "supply" must equal "demand"in each time period. Since regional demand for a particular commodityis the sum of the demands for all of the component subcommodities, theexternal specification of a region's demands by subcommodity mayover-constrain the system, in which case there would be no feasiblesolution. This makes it impossible to specify exogenous disaggregationfactors for both demand and supply. Instead, the demand disaggregationis carried out on the basis of information contained within the model.

To specify the demand disaggregation procedure, the followingdefinitions are useful.

DEMAND (I,M,J) = aggregate demand for commodity I in regionM by sector J.

SUBDEM (K,NODE) = the demand for subcommodity K at locationNODE.

The disaggregation proceeds in two distinct steps: first, the demandis disaggregated from a regional to a nodal basis and, second, it isdisaggregated from a commodity to a sub-commodity basis. In the firststep, it is assumed that the demand generated by a particular industryis geographically distributed in the same fashion as the productionof that industry. Thus, the demand for commodity I at location NODE(which is a node within region M) from;subsector K2 (which is acomponent of industry J) is given as

DEMAND (I,M,J)-SuJBCOM (K2,NODE) (2)

This relation says, for example, that the demand for inputs to the steelindustry will be located at the same nodes as is the production of steel.It should be noted that relation (2) merely allocates demand among nodes

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within a given region; it does not determine the interregional distributionof demand. Regional demands, it .will be recalled, are endogenouslydetermined by the macroeconomic modal or may be input from another source.

If relation (2) is summed over aUl demanding sectors located atNODE, the result is an estimate of the total demand for coiodity I atlocation NODE. This is denoted as fo-lows:

< DEMAND(I,M,J).SUBCCK (K2, NODE) (3)K2

where K2 again denotes a subsector of the aggregate demanding sector J.

The remaining step involves the disaggregation of relation (3) intoa demand for subcommodity K which is a component of aggregate commodity I.Here it is astsumed that the demand at each node can be split into subcommoditiesin the same proportions as the national demand. In the aggregate, sub-commodity K makes up the following fraction of the total demand forcommodity I.

tE SUBSUP(K,NODE)NODE (4)

XE DEMANDtI,M,J)J

The numerator in relation (4) is the total supply of subcommodity K but,in the aggregate, this must equal the demand for subcommodity K.

An estimate of the demand at location NODE for subcommodity K isnow obtained by multiplying the fraction in relation (4) times the demandgiven by relation (3).

-<~ SUBSUP (K,NODE)SUBDEM(K,NODE) e NODE (5)

E5 DEKAND (I,M,J)M J

. . DEMAND (I,M,J)*SUBCOM(K2,NODE)K2

- 8 -

By disaggregating supply and demand, the ability of the transportmodel to capture the details of the pro'duction and consumption processwithin each region is greatly enhanced. Without disaggregation, theutility of the entire transport model would be diminished. Thealternative of developing a large input-output table would be extremelydifficult and it would be computationally difficult to use even withlarge computers. Furthermore, if the regional breakdowns of the varioussubcommodities making up the industries change over time, this can beincorporated in the model by changing the make-up of the disaggregationtable. If, on the other hand, growth occurs proportionally between thesubcommodities making up an industry, it will not be necessary tomake any changes at all. With the national input-output table andthe subcommodity disaggregation factor table, a great deal of detailand flexibility can be incorporated into the model.

There are important instances of substantial seasonal fluctuationsin demands and supplies. Sometimes this causes seasonal peaking problemsin the transport network. The logical structure of the transport modelactually includes the capability of handling seasonal disaggregation.Unfortunately, computer limitations have made it infeasible to putthis capability into operation at this time.

In practice, supply and demand disaggregation are specified byfilling out a table of disaggregation factors based on a study ofcommodities and the production characteristics of each industry in eachregion. Figure 3 illustrates the manner in which input is prepared fora four region, eleven-industry economy. All of the required informationcan be specified on a single input form of disaggregation factors.Because of the length of the complete table, only selected portions of itare shown here. The four columns on the right of the table indicate how,in principle, seasonal disaggregation has been put into the model. Theyear is split into four seasons and four seasonal disaggregation factorsare specified for each subcommodity being produced at each node. Thesefactors specify the proportion of the annual output that is producedduring each season. Note that SUBCOM sums vertically to 1.00 over eachregion and that the seasonal factors for each subcommodity sum to 1.00horizontally. For those sectors that have demands but not transportablesupplies, such as the consumption sector, the specification of a supplydisaggregation factor merely designates the distribution of demand withinthe region.

-9-

The final result of the disaggregation computation for eachsubcommodity is:

1. a list of supply nodes for the subcommodity2. a list of supply quantities for each node above3. a list of regional unit production costs for

the subcommodity for each node above4. a list of demand nodes for the subcommodity and5. a list of demanded quantities for each node above.

These vectors are used as inputs to the distribution flow process whichfollows.

Computation of Flows on the Transport Network

Network Definition

It is assumed that all economic activity takes place within citiesor villages rather than being continuously distributed over space andthe transport is confined to routes between these cities. The spatialaspects aof the transportation process are represented by means of anetwork composed of links and nodes. The links correspond to transportroutes, and nodes represent cities'or producing regions. Each commodityis produced at one or more'supply nodes'and demands for these commoditiesexist at other nodes within the network. Commodities are shipped fromsupply nodes to demand nodes over the links,of the network. 'Thisrepresentation'of the transport network will be 'used as the basis for 8

description of the problem and the computational scheme.

Links are classified within the model by modal type. This includestransfer points which are represented as links belonging to the transfermode. All of the modes commonly found in a transport network can berepresented. The most common modes will, of course, be highway, rail,waterway,pipeline and air with the appropriate transfer links connectingone mode to another. All modes are represented on a single network,facilitating the computational problem, particularly in the determinationof modal choice and routing.

- 10 -

SEASONREGION SUB-C"OM0DIT _ NODE SUBCOM 1 2 3 4

Ku1 RICE 1 .75 0 .10 .50 .40H=1 K=2 WHEAT 2 .15 .70 .30 0 0

K-3 OIMER 2 .10 .50 .25 .25 0

K=- RICE 3 .05 0 .10 .50 .40M=2 Ks2 WHEAT 3 .80 .70 .30 0 0

K=3 OTHER 3 .15 .25 .25 .25 .25

K-1 RICE 5 .09 0 .10 .50 .40M=3 K=2 WHEAT 7 .50 .70 .30 0 0

KX2 WHEAT 6 .4C, .70 .30 0 0K-3 OTHER 6 .01 .40 .50 .10 0

K-1 RICE 8 .05 0 .10 .50 .40M=4 K=2 WHEAT 4 .05 .70 .30 0 0

K=3 OTHER 4 90 .50 .50 0 0

K-5 CANNED 1 .10 .25 .25 .25 .25M=1 K-6 OTHER 2 .90 .30 .10 .20 .40

B=5 CANNED 3 .50 .25 .25 .25 .25M=2 K-6 OTHER 3 .50 .30 .10 .20 .40

M=2 K-5 CANNED .25 .25 .25M=3 .30 .10

M=2 K=17 2 .50 - - -

K=17 5 .40 - - - _X=17 6 .40 - - - _K=17 7 .20 - - - _

M=3 KX17 3 1.00 - - -

KM1 14 .60 - - - -

M=4 K=17 8 .40 - - _ _M=1 K=18 1 .75 - _ -_

K=18 2 .25 _ _ _ _M=2 K=18 3 1.00 _ _ _

K=18 5 .10M=3 K=18 6 .30 _ _ _ _

K-18' 7 .60 o _ _ _K=18 14 .10 --

M=4 K=18 8 .90 g o _ _K=19 RICE 9 0 .90 .10 0 0

M=5 K=20 OTHER 9 .80 0 .10 .30 .60K=21 OTHER 9 .10

Figure 3 - Disaggregation Factor Table - Continued

.65 r25 .25 .25 .251=11 Ko28 X&CHo .25 .25 .25 .25 .25IMORT MANUFACTURING m5 o-29 ELTo 9 _ .10 .25 .25 .25 .25

T-10 IC=30 ENGR. 9 .20 .25 .25 .30 .20IMPORT K=31 CONSTRo 9 .70 .25 .25 .30 .20SERVICE;S _.10 .25 K=2.25 .25

I =11EXPORTS 1%5 KE33 ALL 9 1.00 - _ - -

Figure 3 -Dsaggregation. Factor Table. Continued.

- 12 -

The network is defined as a set of links. A separate link ispresented'for each direction, and the fully defined network is storedin the network link file, see Figure 4. The file* for each link ismade up of three parts labeled the "link characteristic vector"; the"link utilization vector" and the "link performance vector". The linkcharacteristic vector (LCV) defines the link by giving the nodenumbers at each end, its mode and those parameters which characterizeiws operation - grade, design speed,- etc. The link utilization vector(LUV) gives volume, both by tonnage-and number of vehicles flowing overthe link. The link performance vector (LPV) presents a summary oflink performance in terms of travel factors such as time, cost, etc.

The commodity flow is characterized by five classes, each of whichis represented by a typical vehicle. These five classes 'are'bulk,general, special, common carrier passenger and private passenger. Eachsubcommodity is assigned to a particular class of carrier. For example,coal traveling over a highway would travel by bulk truck and over rail bybulkrOrail vehicle. Volume of flow and cost-performance entries foreach of these classes of vehicles are carried in the network link file.

The network link file is originated and maintained by an editroutine within the transport model. The network is defined initiallyby specifying the origin node, the destination node,, the mode of eachlink, and -the link characteristi-c vector. The edit routine beginsthe initial n6twork link file by making -an approximation of flows foreach link 'to establish the initial flow volumes. These volumes and thelink characteristics are then used in the cost-performance models foreach mode to estimate initial values of the link performance vector. Thefile is updated each year to take account of changes, additions ordeletions in the network. The updating process is performed by the editroutine.

Modal Choice and Routing

The shippers choice of mode is typically not a simple choice ofwater, rail, highway or air transport but is a highly subjective selectionover a mix of modes, routes and schedules. The choice of mode and route

* The "file" is the computer terminology for the stored information anddata pertaining to the problem.

- 13 -

> ~~~~~~~~~~REGION 2

MODES10 TRANSFE5L

\ 20 zg=D HIGWAYTRANS PoRT NErwoRxS RAIL

40 , AIR

50 MAZINETIHE NeTwoRKLINK FILE

LCV LUV LPVI NODE JNObF MODE LINK Cb4RAcTERjSTIc vCEtiR. UNJ UrILIZArioN VECfroI UNK PERF1ZMANCE VECrOP

2 1 10 .. .. . .. * .. ..

* . . 4 . 0

I . 0 .

3 4 X 0 *....*....*.........*.*.*....*......*..*..... .. * ...4 3 t 0 . * * * * * . * * . * * * * * * 6 . 0 0 v

4 S 20 * * * * - * - v . * - . 0 . . . .

0 00

Figure h

Network Representation of the Transport Systemand its Coding in the Network Link File

- 14 -

is very much a function of the conditions which exist at any given timeon the network and it involves an evaluation of the alternatives availablein terms of their ability to satisfy the shipper's needs. For thepurposes of this discussion, modal choice and routing can be viewed asdecisions made by the shipper. It is assumed that the shippers of eachsubcommodity consider a number of important factors or costs which aremeaningful to them. Both direct and inidirect costs are included.For different commodities different factors will take'on greater orlesser importance. For any one commodity, the weights given to eachfactor will remain constant over the network and each link's ratingcan be determined on the basis of its'particular performance characteristics.Once links are rated, paths can be sought which maximize the shipper-'sutility rating (or minimize his costs).

Assigning ratings to links is referred to as the computation ofR-factors. An R-factor is the product of link performance factors andthe commodity preference ratings associated with each of'those factors..

As used in the model, the link performance vector, LPV, which isindividually specified for each link in the network, contains the followingfive elements:

C1 waiting time en route, in hours

c2 link travel time, in hours

LPV =.C time variability, in hours3,

c4 probability of' shipment loss

C5 transportation charge, in $/ton.

Waiting time here means normal delays due to arrival of vehicIes, switching,rest stops and so on. Waiting time for a transfer' link is primarily thetimde spent waiting for a vehicle in which to continue the journey. When the

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demand for vehicles over the network is great, waiting times willbe larger. Link travel time is the time required to traverse thelink in question, inc 1uM-d3 average delays due to weather' etc.For transfer links, travel time is a slight misnomer. The timereferred to here is that required for unloading from one vehicleand reloading onto another, including queuing time as required butexcluding time spent waiting for another vehicle which was-countedabove under waiting time. t-avel time variabilt is the averagespread in time for both traveling and waiting. Probability of

loss measures the frequency with which goods are lostdue to theftor mishandling, or to physical damage caused by accident.This factor is probably most pronounced in the case of transferlinks where loss due to theft is more frequent and where loadingand unloading damage can easily take place. Transport charge perton is not an inherent quality characteristic of a link, but ratherof the pricing scheme. It represents the out-of-pocket costs ofshipping over the link.

The commodity preference vector gives the cost, or disutility,associated with the corresponding element in the link performancevector.

w cost of waiting, including loss or damage due to1 waiting, in $/hr/ton

w cost of time spent traveling, including losses2 during travel, in $/hr/ton

CPV w cost due to uncertainty of arrival time, in (7)3 $/hr/ton

W4 cost or value, in $/ton of commodity

w5 commodity rate factor (usually 1.0)

- 16 - ,

A separate commodity preference vector is defined for each class.The cost for waiting includes the cost needed to cover time variantdamages such as spoilage or costs for late shipments. Travel- timevariability will include costs for warehousing due to early arrivalor costs due to loss of sale in.the case of late arrivals. Cost,or value of the commodity, multiplied by the probability of shipmentloss, gives the expected cost for damaged shipments. The.last itemin the commodity preference vector, the commodity rate factor, isa multiplier which can be used-to handle any special charges incurred'in shipping a particular subcommodity. In the usual-case, however,the rate factor would be set equal to unity.

The R-factor associated with shipping subcommodity K over li-nk L,RFAC(L,K), is computed as the product of the relevant link per-formancevector and commodity preference vector.

RFAC (L,K) = LPV(L) . CPV(K).

= a~C ci(L) . W (K) (8)i-l - i

The R-factor measures the total cost of shipping one- ton'of subcommodity.K over link L. It is important to note that this is- total perceivedcost, or disutility, as viewed by the shipper and is not:-merely,'theout-of-pocket. cost.

It.may be useful to undertake a- small Sample problem- to illustrate-the manner in which the items in the link performance.-vector-and comnodity-preference vectors are combined into a single R-factor. Suppose-there i's-a link where the waiting time is 3 hours, travel time is-0.3 hours,.variability of time is 1 hour-, the probability of' loss is- .001 and the;distance is 45 miles, which at a-rate of $.02 per ton-mile equalsi$.90/ton.The commodity preference vector is then defined with appropriate values--for the commodity being shipped, each-'item corresponding to the elements~in the-link performance vector as follows:

!3.0 hrsn wait time $.10/hr/ton 10.3 hzrs travel time ! .12/hr/ton

!LPV T l.0 hrs time variability CPV .1!_01/br/ton0.001 probability of loss 50./ton$.90/ton price to shipper l1.1

These two vectors are now multiplied to produce the result

R = / 3.0 x .10) + (.3 x .12) + (1.0 x .01) + (.001 x 50.)

+ (.90 x 1.1)_7 - 1.386 $/ton (9)

- 17 -

This computation is easily performed for all links in the network.The resulting R-factor for each link rates the link from the viewpointof the shipper of the subcommodity. All subcommodities are consideredsuccessively until a set of R-factors has been developed for eachlink in the network.

With all links in the network rated with an R-factor, it isrelatively simple to trace out paths over the network which minimizethe sum of the R-factors between each of the supply points of thesubcommodity and the points of demand. This is done using a minimumpath routine of the type advocated by Martin, based on an algorithm byDafltzig.2/ 2/ The algorithm can be stated as:

C 1R m uin

southt R(10)

where J is a chain made of links, i, which form a single path, out of theset of all possible paths, J. CUMR is the sum of the R-factors incurredin shipping from the supply point to the demand point.

The routine which performs this computation works with the networkdefined in list form as shown in Figure 5. Computati as proceed outwardfrom the "home" or origin node, indicated as node 1 in the figure. Theresult is a minimum path tree, also defined in list form, containing(NODES-1) entries (one for each node except the origin). See TME TABLEFigure 5. Tree Table shows the minimum network routing which will beused to minimize the sum of the R's in going from the origin to each ofthe other nodes in the network. The column labeled "Link No." in theTree Table refers to the "Link No." column of the Link File. The indexof the Tree Table is of course the node numbers shown in the "Node No."column of the Link File. The table entry of one file is the index tothe other and vice versa. This makes the assignment process extremelyrapid on the computer since everything is-direct addressing.

1/ Martin, B. V., "Minimum Path Routines for Transportation Planning,"M.I.T., Department of Civil Engineering, Research Report R-63-52, 1963.

2/ Dantzig, G. B., Linear Programming and Extensions, RAND CorporationResearch Study, Princeton University Press, Princeton, New Jersey, 1963.

- 18 -

NETWORK WITH TREE AND NODE POTENTIALS

LINK F1LE TREE TABLE7D sEr To usE

I NODE J NODE RFAC NODE NO LINK NO RSUM

1 1 2 3. 1 0 0.2 Z 1 4. 2 1 3.3 13 2.. 3 3 2.3 3 3 1. 4 11 3.5 4.5 13 4.6 4 I 4. 6 9 9.7 2 3 3. 7 ZT 9.a 3 2 2. 8 19 9.9 2 66.t0 6 2511 3 4 T.1z 4 3 1.13 3 5 214 5 32.15 S4 2.16 5 '4 1.17 5 6 7

6s 5 719 5 8 S.20 8 5 6 !21 572.2 7 5

0 0 o__

Figure 5

Minimum Path Tree

- 19 -

The manner in which minimum paths are computed requires thatthe total R-factors from the origin be monotAnically increasing.Thus, it is impossible for a point further out in the network tohave a lower R-factor than one close to the origin. This mayhappen in the real world because of the use of basing-point-pricing ora point-to-point statement o' fares.

A more usual problem, however, is the way in which low-costbulk modes, such as rail and barge, react when compared with faster,more expensive modes, such as truck or plane. Rail and barge typicallyhave verry low costs for long-distance bulk movement, whereas that fortrucks and planes may be much greater. Yet, on shorter hauls, trucksmay be less expensive. The feature within the model which producesthis kind of behavior is the cost of transfers. Transfer from truckto rail involves a fixed or "set-up" cost. Once the transfer isaccomplished, however, the unit costs per ton mile on rail are muchlower than those by truck. This is illustrated in Figure 6.

Commodity Distribution and. Assignment

The purpose of the commodity distribution procedure in the modelis to move commodi-ties between points of origin and destination insuch a fashion that they approximate real world flows. In approximatingthe buying and selling pattern of goods, two approaches come to mind.For homogeneous products, such as coal, rice, limestone, or sulfur, thebuyer's inclination is to purchase them as cheaply as possible. Ifproduction costs areererywhere identical, then they should be purchasedclose to their place of use in order to save on transport costs. Forthis case of completely homogeneous products, the linear programmingtransportation formulation or Hitchcock problem, as it is sometescalled, appears to approximate the behavioral assumptions well.YFor heterogeneous products or product groupings such as chemicals,foodstuffs, or manufactured consumer items the transport cost of theitems does play a role, but a much smaller one. For this case ofheterogeneous product groups, a form of gravity distribution model canbe used.

1/ Hitchcock, Frank L., "The Distribution of a Product from Several Sourcesto Numerous Localities," Journal of Mathematical Physics, Vol. 20,1941, pp. 224-230.

- 20 -

POINT OF ORGIN DESTINATION I DESTINATION 2

P%ErTWORIK

R- COST

POINT OF ORIGIN DESTINATION I DESTINATION 2

COST/DISTANCE RELArIONSHIP

HOME NODE DESTiNATnON t DESTINATION 2

MINIMUM PATH TREE

Figure 6

Fixed Charge Aspect of Transfer Links

- 21 -

The linear programming distribution seeks to minimize theoverall cost of shipping a product from several production pointsto several consumption points, while satisfying all demands. Onemay question the propriety of minimizing the overall costs since evenin most developing countries there is more than one supplier orproduction location. It has been demonstrated by a number ofresearchers that fully competitive industries will tend to act in thesame fashion under a condition of spatial price equilibrium.-/

The linear programming model can be stated mathematically asfollows:

minimize CCOT(M,N)$FLOW(MI,N) (U)M N

Subject to the constraints:

,g FLOW (M,N) SUPPLY(M) (for all M), (l1a)N

: FLOW(M,N) - DEMAND(N) (for all N), (llb)N

4 SUPPLY(M) = >DDAND(N) and where FLoW(M,N) >tO (lic) and (lld)

SUPPLY(M) is the supply of the subcommodity produced at node X, DEKAND(N)is the demand for the subcommodity at node N, C06T(M,N) is the cost oftransporting the subcommodity from M to N and FLOW(M,N) is the flowof the subcommodity from M to N.

For the case of highly aggregated freight flows, the gravity modeloffers a great deal of flexibility to adjust to a wide range of conditionsbut the underlying behavioral attributes are more difficult to isolate.The model is essentially a statistical one since it is correct only in anaverage sense and ideally its parameters should be fitted by regression.In mathematical terms, the gravity model determines the flow betweenregions M and N so that it satisfies the following conditions.

1/ Stevens, B. H., "Linear Progranming and Location Rent.," Journal of RegionalScience, 3, 1961, pp. 15-26.

- 22 -

SUPPLY(M)- DEMAND (N)

FLOW(M,N) = C06T(M-N) (12)<) DEMAND(N)

EXPN COST(M,N)

dFLOW(K,N) = DEMAND (N)(for all N), (12a)M

4 FLOW(M,N) = SUPPLY (M) (for all M), (12b)

! SUPPLY(M) = DEMAND (N), and (12c)M N

FLOW (M,N) O.>. 0. (12d)

where EXP is an empirically determined exponent. Although EXP is the onlyparameter to be determined others may be introduced if necessary.

In situations where there is only one demand point, or one supplypoint, the exponent can assume any positive value less than infinitywith no effect at al1 on the resultant distribution. As the number ofsupply and demand points increases, the exponent begins to have an effect.A large value of the exponent forces demands to be satisfied as closeto the demand point as possible, while a small one teyds to let goodsmove over greater distances. In the extreme, a zero exponent would causesupplies at each point to be distributed in direct proportion to thedistribution of demands. Transport coste would, in this extreme case,have no effect on commodity flows. This suggests that low values of theexponent ought to be used for highly aggregated and high value itemswhile larger exponents are appropriate for low value items.

Since transport is by definition a"non-transportable" industry,there is no supply vector for transportation. There is, however, a finalconsumption demand for transportation in each region which can be thoughtof as the demand for passenger transport in each region. Because of thenature of passenger transportation, the "supply" of transport may bethought of as equal to the "demand" for transport in each region. Byusing the demand vector as the supply vector, passenger travel can betreated as another subcommod'ty. Supplies are disaggregated into

- 23 -

subcommodities and assigned to nodes according to the disaggregatlanfactor table. Demands are assigned to nodes by means of the finalconsumption part of the table. The supply and demand points andquantities are then reversed to represent return trips. By appropriateselection of the constants employed (such as travel impedance exponents),the model can be calibrated. Justification for such a simplifiedtreatment of passenger flows lies in their limited importance in most(though not all) less developed countries. Where passenger flows arethe principal movements, as they are in the United States, more elaboratemodels are justified.

Flows can be assigned to the network as soon as the flow volumeshave been calculated in the distribution process. Up to this pointflows have been carried in terms of dollars per year. Flows are nowconverted to tons per day by dividing by the value per ton and by thenumber of days per year. The minimum paths determined during the treebuilding process are now retraced and flows in tons are placed on eachlink. Later, flows expressed in tons per day will be divided byvehicular payloads to produce vehicular volumes. Once all assignmentshave been made for all subcommodities, the network link file is updatedto reflect the flow volumes in tons and number of vehicles moving overeach link. The oily remaining step in the computation of network flowsis the determination of the number of vehicles which must be returnedempty in order to secure another load.

There are a number of ways in which backhaul could be explicitlyincorporated into the model. The approach employed here is probablythe simplest. It is assumed that all vehicles are routed on thebackhaul trip exactly as they were on the forehaul. If there areforehaul goods to be carried, they carry them; if not, they returnempty. This allows backhaul to be computed by simply determiningthe number of forehaul vehicles required to handle flows in each directionand selecting the larger number. The difference between the two figuresis then the number of vehicles which must be backhauled.

In developing countries, the assumptions required to compute backhaulby this scheme are probably satisfactory. Neither road nor rail networksare well articulated, and trips tend to be forward and back rather thancirculating over the network. Large rail systems may in some instancestend to exhibit a sort of random movement with respect to box cars butthe limited extent of the network in developing countries tends to inhibitthis.

- 2 -

Cost Performance Submodels

The most importiant thing about a transport system is the way inwhich it performs. The various costs incurred in shipping a productfrom point of supply to point of demand are of direct concern to theshipper. They depend, in turn, on the situation encountered by thetransporter in operating his vehicles over the route and the way inwhich he passes his costs on to the shipper in the form of transportcharges. The purpose of the cost-performance submodels is to estimatefor each link the cost incurred both by the shipper and by thetransporter.

There are two inputs to the submodels for each link. Theseconsist of 1) the link characteristic vector, which gives the physicalcharacteristics of the link, and other information relative to capacityand operating conditions and 2) the link utilization vector whichgives link volumes in both tonnage and vehicular flow units. Outputfrom the models can be divided into two general categories, linkperformance and vehicle performance. The first type of informationis stored in the link performance vector and is used as feedback tothe model in future time periods. The vehicle performance vectorstores the operational information about the vehicles using the link.By changing the design of the link, the operating conditions will bechanged and the vehicle performance consequently altered.

There are two classes of modal submodels. In order to distinguishbetween them, they are designated as sophisticated and unsophisticatedmodal submodels with the former model being more complex resultingin a more realistic representation of the system. The unsophisticatedmodel, as is now used in the pipeline mode, consists of simplerelationships such as dollar/ton-mile of commodity shipped.

Sophisticated cost models are presently available for three modes--highway, rail and transfer. These cost models are based on internallydefined relationships, using the physical characteristics describing thefacility in the link characteristic vector as input. They can, therefore,be as complete and as detailed as is necessary to properly estimate thevalues for both link and vehicle performance. The transport model isdesigned in a modular fashion so that as more sophisticated cost modelsbecome available, they can be readily incorporated in the transport model.Each of these models will be described briefly here. For a more comprehensivereview of the cost-performance models, refer to the individual write-ups.

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Highway Model

The highway cost-performance model simulates the operation of afleet of highway vehicles moving in both directions along a specifiedroadway. The roadway, defined as two opposing links, is of uniformcharacteristics throughout. The characteristics defining the linkfnclude the distance in mi'.les, surface type, design speed, the rateof rise and fall, lane width, the number of lanes and seasonal delayfactiors.

Traffic volumes on the link are given-by specifying directionaltonnages for each of the five volume classes. Tonnages are dividedby vehicular payload to'obtain the total number of vehieles needed ineach direction. The direction with the largest number determines thedaily volume of vehicles' actually operating on the roadway since vehiclesare assumed to be backhauled empty if loads cannot be found for them.Each volume class uses a single representative vehicle type. Thisvehicle type is defined using a vehicle.characteristics table thatcontains the weight, payload,' horsepower, number of tires, lifetimemileage and crew size for each of the repre'sentative-vehicles. Relevantcost information, including the initial cost of the vehicle, tire cost,crew wages, mechanics wages, fuel coat and oil cost is also defined.

Computations begin with the determination of the free speed foreach vehicle. Free speed in this instance is the speed attainable bythe vehicle traveling on an empty roadway. Speeds are estimated usingthe regression equations obtained by Carl Saal of the Bureau of PublicRoads in his 1960 study of truck performance on the Pennsylvania Turnpike.In this study, truck speed is related to gross vehicle weight and horsepowerfor different rates of rise and fall of the roadway. Once free speedsare obtained, truck volumes are aggregated and inflated to account fortruck performance'on the traffic stream. The set of truck equivalencefactors obtained is then used to make adjustments to overall speeds.

Before speeds are adjusted, a representative distribution of hourlytraffic volumes must be determined, since not all hours are equallycongested. A probability mass function, analogous to the binomialdistribution, is used to obtain a distribution of equivalent hourly flows.Once the number of vehicles traveling in a given hour is available, it ispossible to estimate the speed conditions that will prevail on the roadway.Standard volume-delay curves are used to do this based upon capacity measuresreflecting the number of lanes and road surface type.

- 26 -

The components of vehicle operating cost are now computed.Fuel consumption in gallons per mile is estimated as a functionof roadway rise and fall, truck size and payload, again usingequations developed in the Pennsylvania study. Vehicle depreciationis in effect inversely proportional to vehicle speed since vehicleutilization generally improves, as speed increases. Interest chargesare computed for a typical vehicle at mid-life on the capital tied upin the vehicle purchase, using local interest rates. Tire wear isbased upon the speed of the vehicle and the road surface type.-Vehicle maintenance costs are expressed in hours of labor as wellas quantity of spare parts required to perform repairs. Estimatesare also made of road maintenance costs for various surface types,using a fixed and variable component for conditions typical of thecountry under study.

Measures of vehicle performance are output directly by thehighway model and include quantities of fuel, oil, tires, drivertime and so on, expended in traveling over the link followed by theirunit costs and total costs. It is possible, therefore, to distinguishthe makeup of vehicle operating costs as well as the overall cost permile. Link performance measures for waiting time, travel time, timevariability, probability of loss and cost are returned to the transportmodel for each class of vehicle via the link performance vector inthe network link file. From the standpoint of the transport model,these link performance measures are the result sought, since theyrepresent the final conBequences of this year's assignment of flows tothe highway network.

Rail Model

The rail model determines the manner in which a single railwaybetween two points in the real world will operate and the resultingcost-performance consequences. Railway operating policy is by naturemore controlled than the laissez faire operation which prevails onmost highways. Typical practice has generally been assumed. However,changes in operating rules may be incorporated into the model.

A railway line is represented within the rail model by means oftwo l allowing for flows in opposite directions. Input datadescribing the phytical characteristics of these links enter the model

- 27 -

through the link characteristic vector in the network link file. Dataincludes the length, the number of sidings, the ruling grade in eachdirection, the average gradient over the lihk, the nature of thesignal system, speed limits due to excessive curvature of the trackor other physical features which cause a train to travel at lessthan maximum possible speed, the number and type of locomotives andfinally the minimum number of trains per day. It is also necessaryto provide information concerning the physical characteristics ofthe equipment utilized: horsepower, weight and the cost for eachlocomotive type and the empty weight and payload of the rolling stockby vehicle class.

Flow of goods in tons per day by direction is given for eachclass of vehicle. Bulk commodities are assumed to move in open hopperor flat cars, general cargo by box car and special cargo by tank caror other specialized equipment. Rail passengers are assigned toordinary passrenger cars. Flous are specified in average daily tonnages.Using the average payload of each type of car, the. flows are convertedinto vehicles for each direction. To account for the backhaul of emptyvehicles, the assumption is made that the largest number of vehiclesused in either direction defines the total number of vehicles that will beused in both directions.

Computation to obtain train performance proceeds by determiningthe allowable tonnage per train given the locomotive power and rulinggrade on the link. Then using the characteristic of the cars haulingeach commodity and the capacity of the train, the number of trainsrequired daily is determined by dividing the average daily tonnage bythe load capacity of a single train. For a single train, the averagerunning speed is calculated by determining the speed at which thetractive effort developed by the locomotive just equals the rollingand grade resistances encountered on the average grade. Average runningtime over the link is then adjusted to account for delays en route.These delays depend upon the number of daily trains on the link, thenumber of sidings and the type of signal system. Rolling stock require-ments are calculated on the basis of adjusted running times and terminalturnaround times.

- 28 -

Operating cost calculations are broken down into the followingcategories: (1) depreciation of rolling stock, (2) rolling -stockmaintenance cost, (3) maintenance-of way and.structures, (4) trainoperating costs and (5) transportation and overhead costs. Operatingstatistics such as train miles, train hours and car miles aresummarized for the link and output in a list of train performancemeasures. Total costs for operation, maintenance, and depreciationare then summarized.

Train performance output includes information on the makeup-ofeach train, its running speed, the loads of each car type.and thesummary of operating costs by type of expenditure. Information tobe returned to the transport model is summarized by class i-n thelink performance vectors. The above computations are repeated to obtaina set of link performance measures for each rail link in the inetwork.

Transfer Model

The purpose of the transfer model is the simulation of the ttansferof goods and passengers from -eo mode of transport to another. .Itappears that-overall trip performance may be largely dependent upontransfer operations. Although no distance is tiaversed, there is alapse of time and an element of cost associated-with a transter.Consequently, the transfer process is handled here precisely -as ifit were another mode of travel.

A transfer facility appears in the model as two opposing-linkswhich can be made-to.represent any-form.of inter-modal.trans-fer, r.oadto rail, rail to ship, ship to pipeline and so on. There is a largerange of possible technologies that can be employed at.a tr,ansfer terminal,each with an associated set of cost and performance characteristics.Operating times and cost data describing each of -these unloading technologiesare described in a table known,as the IRATE table and input to the modelseparately for each operating environment. The IRATE table con-tainsinformation on the unloading and loading -rates in tons per hour, -the

norr;_l -rorking hours of the facility per day, the maximum number of workersemployed at each loading or unloading berth, the average basic wage of thelabor force per hour, the fixed operating cost for the facility per dayand the variable opprating cost for the facility per hour, the wage

2ltiplier fo- computing over-time.-wages and the probability of lossassociated with handling cargo by means.of this technology.

- 29 -

The input to the model of the link characteristics requires theclass of the technology to be employed and the number of berthsavailable. The technology is described by giving its line number inthe IRAIE table. The assumption is made that bulk, general, specialand passenger operations are carried on independentl. Trafficflows which were determined by the transport model between inbound andoutbound nodes are presented to the transfer model by the linkutilization vector of the network link file. Flows are described bygiving the tonnages over the link as well as the number of vehiclesin and out.

Computations to obtain link performance are broken into fivestages. The stages correspond to the operations to which a typicalload might be subjected during the transfer operation. These fivestages are: (1) time spent waiting for a berth, (2) unloading time,(3) time spent waiting for a departure vehicle to arrive, (4) timespent waiting for the departure vehicle to dock and (5) loading time.

The time spent waiting for a vehicle to dock is modeled byusing an M-server queueing model with random arrivals and exponentialservice times. Each berth corresponds to a server. From this, theprobability of zero vehicles in the queue can be computed as well asthe average length of the waiting line and the average time spentwaiting.. Unloading time is computed using the vehicle payloads and thetechnology to be employed. Where the unloading time at the facilityexceeds the normal number of working hours, overtime wages are computedup to the maximum number of hours allowed.

The time spent waiting for the arrival of a departure vehicle iscomputed from the known number of vehicle arrivals and departures atthe terminal and the requirements to availability ratio for the systemas a whole. Where the quantity of flow by mode coming into a terminalis greater than the flow going away, it is assumed that there is nodifficulty in obtaining a vehicle in which to leave. However, when thenumber of vehicles of a particular mode arriving at the terminal isless than those leaving, delays may be experienced in obtaining empty

- 30 -

vehicles. A set of algebraic equations which determine the rateof arrival and departure is used in computing the amount of timere(quired for this operation.

Since the time spent waiting for an outbound dock is thesame as the time spent waiting for a similar dock inbound, computationsfor only one direction must be made. Therefore, the time spent waitingfor a departure vehicle to dock and for it to load are secured fromsimilar computations involved in the inbound flows.

Output from the transfer model takes the same two forms as in theother cost-performance-models. Facility performance measures ,are outputdirectly by the transfer model showing (lueue lengths, queueing timesand waiting times as well as statistics on facility operation, such asnumber-of man hours, and cost of loading and unloading. The-secondform of output is the link performance vector required by the transportmodel. As with the other models, waiting time, travel time, timevariability, probability of loss and cost of providing the serviceare transmitted back to the trgsport model via the link performancevector.

Unsophisticated Modal Submodels

The unsophisticated models for all modes work similarly. Theyall employ what can be referred to as a typical unit link performancevector. This typical vector has entries on a "consequence per ton-mile"basis. These figures are then adjusted by the modal cost submodel forlength and for vehicular payload, in order to reflect the appropriateamount of backhaul. They may, in;addition, be4adjusted for seasonaldelay or for other- link characteristics which are obvious determinants oflink performance. It should be noted ,that the computations are-performedtwo links (both directions) -at a time. This is necessary in-order -thatbi-directional interdependencies, such as the amount of backhaul, can beaccounted for.

Typical link performance vectors can -be changed easily. This allowsnew modc-.s to be developed to handle special conditions. If, for example,

a model is to be constructed representing a new mode, then typical valuesper ton mile for waiting and traveling would be inserted into the typilcallink perf°ormance vector, along with an estimate of the time variability,the typical probability of loss (probably from theft) and fiinally theunit operating cost for the vehicles operating -at their maximum,payload.The results are then adjusted internally using the length of -the particularlink in the link characteristic -vector.

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The results can also be adjusted to reflect seasonal travelconditions such as flooding rivers or muddy roads. To do this,the travel times are multiplied by a delay factor which is codedinto the link characteristic vector. Where detailed vehicularperformance results are not required, the unsophisticated cost modelsenable a wide variety of different types of modes and differenttravel conditions to be modeled.

Transport Price Determiration

The use of pricing policy as a conscious tool of public planningis frequently neglected. It is, however, another dimension of controlwhich the planner can exert on the system to make it perform properly.This model through its use of a pricing policy routine contains theelements necessary to test alternative pricing policies. Either cost-based or rate-based schemes may be simulated. Cost-based policiesare those for which the price of a transport service is a linearfunction of the cost of providing that service and rate-based policiesare those in which an exogenously specified rate is given per ton-mileor by link.

The scheme for incorporating pricing policies into the transportmodel is quite simple. Within the input parameters defining the modesis a table in which each modal subsystem is defined by a single linein the table with a unique mode number. Corresponding to each mode numberare all the modal inputs for that mode. Mode numbers are two-digitnumbers as coded on the links in the network, but only the first digitis used in the selection of modal cost-performance submodels. The seconddigit can be used to identify a modal subsystem within the model. Forexample, it may be desirable to identify regional highway subsystems.This could be done by using numbers in the twenties to represent the highwaymode. Mode 21 would then correspond to the highway subsystem in region 1.Mode 22 would identify highway links in region 2, etc. Modal input forthis situation is shown in Figure 7.

A rate table is input corresponding to the subsystems. The ratesgiven for each class of commodity correspond to the mode number. Thus,the rates for a given modal subsystem are determined for each commodityclass. Rates are multiplied by distance to obtain changes per ton forshipping over the link. Separate modal subsystems may be defined inorder to get special rates on particular links.

When it is desired to use cost based pricing, the price for shippingover the link is given by the cost of transport, determined from the modalcost-performance models, multiplied times the absolute value of thefactor in the table to include profit.

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The manner in which the table operates is.easily illustratedby means of a simple example. When a negative value appears. in thetable, cost-based pricing will be used; otherwise, the values..willbe considered as the pricing rate in $/ton-mile. Figure 7 furnishesthe input for a situation in which there are three bas1c modes,transfer, highway, and rail, with three highway subsystems. Thetransfer mode is identified by mode 10. It employs a cost-basedpricing policy. -Modes 21, 22, and 23 are the three highway regicnalsubsystems. Each uses different pricing policy. Mode 21 and'thebulk class of Mode 23 are taken from the rate table, while the othersuse prices based on the costs developed in their respective cost-performance submodels. Rail, mode 30, is entirely rate-based. Allthe links-in the network would correspond to each of the five-.modesin the mode and Rate Table. A link with the mode number 21 isautomatically identified as.a highway link because of "2" in the firstdigit and the highway cost-performance model will be used. :T.hepricepolicy employed is that of mode 21 in the mode table. The CommodityPreference Vector is handled correspondingly.

System Performance Measures

The transport model produces a number of intermediate and final,oiitputs which may be used as system,performance measures. wTwo sets ofthese have already been discussed with the Cost Performance Submodels,namely, the vehicle.and the.link.performance measures.

Vehicle performance measures-include--a variety of physical andcost consequences which result from..the operation-of specific..vehicles overa particular link. These outputs could presumably be useful to the transportoperator at the microeconomic level in,;selecting new equipment. Similarly,the project planner can use these;.outputs in evaluating and designing newlinks to determine the effects of.proposed changes on the vehicle operatingcosts.

The use of link performance measures, given by the LPV, for theselection or mode and routing has-already been described. Alternative pathsmay be coipared through their LPV'.s. In,addition to this use, they serveas a valuable source of information about the conditions and costs whichprevail on the transport system at.a given point in time. These individualL?Vt s may be summarized to reflect.the total.transportation system performancemeasures.

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Figure 7

MODE AND RATE TABLE INPUT TO THE PRICING EXAMPLE

RATTE TABLE

BULK GENERAL SPECIAL COMMON PRIVATEMODE ICLAS 1 ICLAS - 2 ICLAS = 3 ICLAS 4 ICLAS = 5

10 -1.05 -1 .05 -1.05 -1.05 -1.05

21 .05 .10 .08 .20 .30

22 -1.07 -1.07 -1.07 -1.07 -1.09

23 .07 -1.07 -1.07 -1.07 -1.09

30 .02 .05 .03 .30 .30

- 34 -

System performance measures have not been previously mentioned.They are, however, the principal summary statistics for each systemby mode and vehicle class. They include the following:

WAIT (MODE, ICLAS) = total system waiting time in hours

TRAVEL (MODE, ICLAS) - total system time spent traveling

TRNSFR (MODE, ICLAS) = total system time which vehicles spendin loading and unloading at transfernodes

VEHMI (MODE, ICLAS) = total sys em vehicle miles

TONMI (MODE, ICLAS) - total number of ton miles carried

COSTS (MODE, ICLAS) - total cost

REVNUE (MODE, ICLAS) = total revenue

TERlNL (MODE, ICLAS) - total time spent in loading and unloadingvehicles at origin and destination

The systems performance measures shown here are of primary interestto the transporter. Some of them may also be useful to the governmentin setting rates, computing taxes and so forth. Ton-miles and vehicle-miles given for each modal system provide some indication of the relativeuse pattern of the various modes. Transfer time and terminal time,when compared with travel and waiting time, allow something to be saidabout the relative importance of terminal operations.

Vehicle availabilities and requirements deserve to be discussedin more detail because of the role they play in the computation ofvehicle waiting times at transfer nodes. The number of vehicles in thesystem and their utilization determines the ease with which a vehicle-can be obtained. If there is a large supply of available vehicles andvery few requirements for their use, the result is instant service. If,on the other hand, there are few available vehicles and many requirementsfor their time, poor service and long waiting times may be encountered.As noted previously, the points at which the waiting occurs are typicallyat those points of trip origin or transfer where the number of vehiclescoming into the node is less than the number that shippers require.Waiting times are a function of vehicle requirerents and availability.

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The availability of vehicles of a particular mode and class inthe system can be stated simply as:

NSWSAVATOT(YiOD,ICGLAS) = SZ VTH.CLS(MODE,ICLA3) DAYS - (IS) (13)

1=1 HRPDAY (YMDE)

where:

AVATOT (MODE, ICLAS) = the number of vehicle hours available,

VEHCLS (MODE, ICLAS) = the number of vehicles of this mode andclass in the system,

DAYS (IS) G the number of days in a season

HRPDAY(MODE) the hours worked each day by vehicles of thismode

Availability can be increased by changing the number of vehicles inthe system (i.e., buying new vehicles), by increasing the time worked(by means of overtime), or by shifting the demand to another mode.

Vehicle requirements are computed by summing the demands forvehicle time. Since there.are a number of demands, only the major onesare included here. The miscellaneous demands may be accounted for byreducing the number of hours or vehicles available. Requirements aredetermined by:

NSEZNSREQTOT (MODE, ICLAS) = Zj AAIT (MODE,ICLAS) + TRAVEL (MODE,ICLAS)

1=1 + TRANSFR (MODE, ICLAS) + TERMNL (MODE,ICLAS )J DAYS (IS) (14)

where:

REQTOT (MODE, ICLAS) = total vehicle hours required to accomplishthe goods movement undertaken by thesystem

WAIT (MODE, ICLAS) - total time which the vehicles of this modeand class spend waiting while switching,changing drivers, encountering delays incities, and so on,

- 36 -

TRAVEL (MODE, ICLAS) = total time which the vehicles in thismode and class spend traveling, includingseasonal delays in route,

TRNSFR (MODE, ICLAS) =total time which the vehicles in thismode and class spend loading and unloadingat transfer links and

TEINNL (MDDE, ICLAS) -total time which vehicles in this modeand class spend loading and unloadingat origin and destination nodes.

These values are determined by summing them over all links in the networkfrom the items in the respective link performance vectors. jTo obtaintransfer times, for example, the following summation is performed:

___

TRNSFR (MODE, ICLAS) = e TRAVEL(J,ICLAS) (15)Ji MODE

The ratio of requirements to availability can now be formed.

RATIO (MODE, ICLAS) REQ TOT (MODE,ICLAS) (16)AVATOT (MODE, ICLAS)

As the ratio goes up, relative waiting time on the system can be expectedto increase. This ratio is used in the transfer submodel to determinewaiting times on the transfer links. It also serves as one measure ofoverall system perforhance.

A number of other performance measures can also be obtained fromthe data computed by the transport model. The tables of cumulativeR-factors for each commodity, for example, give the cost of moving goodsfrom each of the regions of production to each of the regions ofconsumption, see Figure 8. The flow matrix contains the quantity of theproduct which is flowing between each supply point and each of the demandpoints. The result produced by multiplying corresponding elements ofthese two matrices is a matrix showing the transport cost to each regionalproducer. When the elements of this matrix are summed row by row, theyproduce a vector of transport costa to each producer. A comparison ofthese figures for alternative transport systems gives one a measure ofthe overall desirability of the system from the standpoint of thecommodity producer.

- 37 -

A similar operation can be performed for each region for theconsumers of products. Although this may not be important whenviewed commodity by commodity, it may be quite useful when summedover all products for each region. It is, in fact, the transportbill paid by the consumers at each node. One might also view itas a cost accessibility measuro of that node with respect to therest of the world. If the two are added together--that is, theproducer's costs for shipping the final product and the transportbill on intermediate and consumption goods brought in--still anothermeasure of regional performance is obtained. Although it doesadmittedly involve some double counting, it appears to be useful inrepresenting the regional viewpoint.

In the final set of computations in the transport model, theresults of the trarsport model are summarized to provide the necessaryfeedback to the macroeconomic model when it is used in conjunctionwith the Transportation Model. Estimates passed back to the macro-economic model include 1) the transport bill for each industry andinterregional flow 2) summary costs to the transport industry itselffor use in modifying the transport column of the input-output table,and the coefficients within the transport row which are modifiedusing the summary of real transport costs incurred by each producingindustry.

Needless to say, not all of the performance measures which areavailable within the model will be applicable to all situations. Thepurpose here has been merely to point out what seem to be some of themost useful of these variables. The model does provide many effective-ness measures to facilitate the analysis of transport planning. For awide range of system problems, the model supplies much itformation on theprobable outcome of a specified transport plan.

-38 -

TABLE OF CUMULATIVE a-FACTORS TABLE OF INTERREGIONAL FLOWS

E: OEMAND NODES ] E DLMAND NODES j

45U Rn i, R - Fo Fla F1p b

: CUMULATIVE : FLOWo R-FACTORS '

Rrks ~£ Fn 1 . Fn mn

UNIT COSY OF FLOWING BETWEEN QUANTITY FLOWING BETWEEN POINTSPOINTS Of SUPPLY AND DEMAND OF SUPPLY AND DEMAND

TABLF. OF REGIONAL TRANSPORT COSTS VECTOR OFDEMAND NODOS 3 TOTALS

eII R1a Fit 5 2 i

O REGIONWLA COSTSN~~~~~~~~~~~~~~~~~

s ntn ---. * p1 I R

TOTAL AMOUNT SPENT BY PRODUCER IN SHIPMETS PRODUCERS TRANSPOPTTo EACH REGION COSTS FOR FINISHED

PRODUCT

Figure 8

Some Tables Relating Cost and Flow

- 39 -

PROGRAM OUTPUT

The output of the model can be very large when all of theprinting switches are initiated in the program. However, provisionsare contained in the program to by-pass certain output when it isnot needed for analysis purposes. These options are discussed indetail in the computer program instructions. This section is devotedto giving the sample output from the model.

The output from the disaggregation and distribution models, asdescribed here, are,repeated for each of the subcommodities. Forillustration purposes, only the subcommodity BANANO will be shown here.

Figure 9 gives the output results from the disaggregation processas described in the text pages 5. The heading lists:

Subcommodity - Name and numberSector - NumberNo. of Supply NodesNo. of Demand NodesValue per tonType of transport requiredType of Distribution Model to be utilized in

determining the product shipments with theappropriate coefficients and exponents.

All entries in this heading are inputs to the program except the numberof supply and demand nodes.

The remaining portion of the output is calculated:

SUPPLY NODE - Calculated from the SUPPLY nodes in the DISAGGREGATION TABLE$/SEASON (000) - it I of n1 "ICOST/$ - From MACROECON(MIC Model

TONS/DAY - $/SEASONVALUE ($/TON) 365 DAYS/SEASON

COST/TON - VALUE ($/TON) C CpST/$DEMAND NODE - Determined as described in the DISAOGREGATION SECTION$/SEASoN - if iI it I n n

TONS/DAY - $/SEASONVALUE ($/ToN) * 365 (DAYS/SEASON)

- 4o -

2. DISTRIBUTION MODEL OUTPUT

Figure 10 presents the PERCEIVED COST OF EACH IINK AS SEEN BYSHIPPER OF * . These costs are calculated in the Link PerformanceModels reflecting the total of the direct and indirect shipping costsresulting from the product of the Link Performance Vector (LPV)and the Commodity Preference Vector (CPV) as described in equation 8.A R-factor is computed for each link in the system for each subcommodity.The column headings:

INODE - Beginning nodeJNODE - End nodeMODE - Mode of the linkR-FACTOR - R-Factor cost computed.

Occasionally there are some very high costs shown for a particularsubcommodity over a particular link. Such as BANANO'S over a pipeline.This is the models method of not allowing certain classes of commoditiesto be transported over certain links.

Figure 11 gives the DECISICN COST PER TON FOR * . This is theoutput from the Minimum Path Routine utilizing the orrgins and destinationsas shown in the disaggregation process. These elements are the minimumpath R-factors for moving one ton of the subcommodity from an origin toa destination. (The summation column and row are meaningless here. Thereis a standard print routine to print such matrices as this and in thiscase the sWs are not of benefit.)

Figure 12 gives the DECISION COST/$100 GOOD FOR *. This matrixdepicts the R-factor cost to move $100 of the subc between theorigins and destinations and costs from the figure 11.

Figure 13 gives the FLW IN TONS PER DAY FOR *. Thi is theoutput from the distribution model assigning the flows of commoditiesfrom the origins to destinations. Again the Gravity Model is used toassign flows of non-homogeneous products and the L.P. model is used toassign flows for homogenous products. The right-hand "SUMS" columngives tii;e total for each demand point and the bottom "SUKS" row givesthe tcotal of the columns which the subcommodity availability at each origin.

* Commodity name is supplied by the program.

- 41 -

A characteristic of the flow assignments by LP is that therewill be very few assignments in the matrix. That is, if an assignmentis least cost, the algoritbh will assign as much as possible tothat origin-destination. On the other hand, with the Gravity Model,assignments tend to include all origin-destination pairs and theassignment will have few, if any, non-zero elements.

Figure 14 gives the TON-MILES PER DAY (1000) FOR *e Thismatrix gives the ton-miles per day involved in shipping=eii particularsubcommodity between the assigned origin-destination.

Figure 15 gives the FLOW PER SEASON ($1000) FOR * . This figureis similar to figure 13, however, these are dollar flows per season ascompared to Tons/day in figure 13.

* Commodity name is supplied by the program.

RESULTS OF DISA3GREGATION PROCESS

S EASON JiM&NANU, suHcnmmHonITV NUMqER IA%4 INL)O STR'Y TN SECTOR to, wAS SUPPL!Efl AT 19 NOnES ANn [OEANDEn At 41 NODES. I.S V AL AT 2,. PES0.T PER TO'. ANJD UTIL! S tCLASS I TRANSPIIRT

tYOE 2 D1STRTHUIT(N MODEL wTT4 AN FjP0?ltNT OF 00, A',T,RA%JSPORT cIEFFrCTENT Or 1,00 ANn A wounGrNET-Ty COEFFICItE4T or 02. rs uiso

SUPPLY NOnE S/SEASON (000) cOST/S TONS/nAY COST/TON DEMA4n NnOE S/SFASON (000) TOWS/OAY

3 CARTG 45627. 0,8506 463.0 2.-29r- t MEnLN 17O91. n09525 173.4 2.572 1 S/4AR 424tt49 43,0 11 GAMAR 22803m-. 108721 73t14 7,355 2 RARRN 18171661 184.412 CUCTA 10223. 0)9190 103,? 2.481 3 CARTG 12282919 124e6

14 8/814J -12027. n,9190 1220 7e481 4 SINCL 64613099 65.6

15 BERIO 6729. 0.9525 68e3 2.572 5 MONTR 8402691 85.3

1.9 LAQQR 4 4169.4 ,8810 423.1 2*3T9 6 CAUCS 2791458, 28.3

20 HONDA 8839. 0*8956 89.7 2.418 7 MEOLN 62252756 631.722 VILC.A 24126. M.9172 244.8 2.476 8 FUNDN 740982 7.5

23 GIRAO 14803. 0.9428 150.2 2e546 9 VALOP 2861272# 29.0

28 ARMEN j9378, 0,8810 399.6 2.3r9 10 C4IRA 3426364s 34.8

30 8UGA 137489 0.8;52 139e5 2.417 It GAWAR 22845n6. 23#231_PQ_!py 2683. Q.8908 2 72 32- 244Q5 12 CUCT. 12794006 -- .129.L35 NEIVA 8839. ie8956 89.7 ?.418 13 RUCRM 14298439 145.1

36 FLORN 7261. (19172 73.7 2,476 14 B/8MJ 2 583496m 26.237 PASTO 268. 0,8908 2e. 2.405 15 RERtO 1914442 19*4

38 TUMAC 2147. 0.8908 21 . 2.405 16 RARBO 670422@ 6.8-

40 O/VTA 1.58109 0.8952 160,4 2.417 17 SOGAM 6774t13 68.7

_4 2 -FNR-_ It87. 28t21 307Q - 2,355 18 TU!NJA 7904120, -

19 LADOR 3701261 37,620 HnNDA 52730929 53,521 8OGTA 70659696 7T17O22 VILLA 7447071, 75.6 23 GIRAD 6300860 63*. 9?24 19QUc. 14T 5 1281 . .J4 9 _j25 MANIZ 13487717. 136.926 PERIA 11230499, 1t4,o.-27 CRTGO 61274979 62.226 ARMEN 96185s?e 97.629 URIBE 123550o 1.3*.Q.ftJs A _ . 715403?t Us. .

31 PALMR 6423262s 65,232 CALI 35607603* 361*913 SANTO j9733S5o 20,034 POPYN 7037540, 71.435 NEIVA 6976905, 91.13kf.LORN 493891 i 50 O37 PASTO 8912779, 90.438 TUmAC 110t7291, 11*240 B/YtA 2519?P8* 25*642 FM RR 596773, 6,180 WORLO 46692948* 473.8

44Z1390 453?.2 447139. 4537.2

Figure 9

Figure 10

PEQCEIVLO COST OF EACH LIN.c AS SEEN BY SHIPPERS OF RANaNiO

I NUIE j"nDE .4u1,E A.FArTOR 1INOOC JNnF~0 N4DE R.FACTOP INanE )NriDE NODE R-FACTIRI S/HAR 5 FAOn4 20 511.60 - 8 FumnO I s/MiR 20 13.55 2 BA*PN 3 CAR1'G 20 19.14 3 CARTG 2 gARRN 20 19.14 3 1CAQTr1 4 S1NCL 20 20.85 4 S14CL 3 CARTG 20 20.058 FuNON I CARTG 20 54.82 3 CAPVG 8 ruNO'4 21 54.82 £ SINCL 5 HoNTR 20 24.165 '04OTR 4 SINCL 20 24.16 4 .%INCL 6 CAUCS 20 39.81 6 CA;Ics 4 SINCL 20 39.cl S5 NONI R 6 CAUCS 20 2 3.4 9 8 CAUCS 5 ..0'fTR 20 2 3, 49 6 CAUCS 7 maE¶lLft 2073f7 M4EILN 6 CALIC S 20 7 3. 65 7 .'EDLN 1 9 LArOOR 20 * 8 ,35 1 9 LAnOR 7 mEOIN 20 45.851 '4EOLN 39 ANSER 20 38.50 39 ANSER 7 4EDL4 20 38 .50 4 VALOP 6 FUNflN 20 32.7 9 o8 FU40% 9 vALOP do 3749- 9 VALUP 1O C$41RA 20 30-011 10 CH4IRA 9 VALOP 20 3A.011 0 CHINA I I GAmAR 20 6 7.a54 1 1 GA.4&R I10 CHIRA 20 67 .54 1 1 GA.mAR 1? 2CUCT4 206 5612-CPUCIA It GA.4AR 20 6A.66 11 GAuAA 13 BUCRM 20 37.68 13 BUCRN It GA'4AR 20 31,60

12 CUCTA 11 9'JCRN 20 29.7? 13 BUCRNw 12 CUCTA 20 29.f? 12 ucOdA If S0rAN 20 63.1717 SOGAM 12 CUCTA 20 152.93 13 BUCAm 14 8/8'4J 20 35.46 14 a/smiJ 13 BUCRI( 20 35,4613 IIUCRN 16 BAR.3U 20 38.23 16 8ARB0 13 BUCRN 20 36.23 is 9EPi0 16 BARAD 20 37.37 16 NARSO 15 RPEIO 20 37.37 16 BARBO 18 TUKjA 20 16.2? 10 TU"jNA 16 BARBO 20 16.271 6 9ARFIr 2 1 8.1C T A 20 3 4 93 2 1 ROGTA 1 6 BARBO 20 3 8 .93 I I SOfi.4M 1 8TUNJA 20 1 0. 9016 rUNJA 1T SUGAM 20 10.90 28 TUNJA 21 BOGTA 20 25.55 21 SOfTA 18 TUNJA 20 25.55 19 LAOOR 20 HONDA 20 5.99 20 mONDA 19 LADOR .20 5.99 20 HONDA 21 90674 2t. 26.2921 SOOTA 20 HONDA 20 26.29 20 HONDA 24 ISOUE 20 21.19 24 lecUE 20 HONDA 20 21.1920 HONDA 25 M4ANIZ 20 27.52 25 .4ANIZ 20 HONDA 20 27.52 21 SOGTA 22 VILLA 20 30.16 22 VILLA 21 BUGTA 20 30.16 21 80G1A 23 GIRAD 20 22.01 23 GINADi 21 BOG.TA 20 22.0124 Ie9UE 23 GIRAD 20 10.87 23 GIRAD 24 IsoUE 20 10.8? 23 GIRAD 35 NEIVA 20 36.4235 NEIVA 23 GIRAD 20 36.4 2 24 BOQUE 26 ARMEN 20 24 .05 28 ARuEN 24 ISOIJE 20 2 4.05 2 5 MANIZ 26 PERIA 20 8.55 .26 PERIA 25 M4ANIL 20-. 6.55 .39 ANQER 25 H41N41Z 20 12.1225 NAN1Z 39 ANSER 20 12.12 26 PERIA 2? CRTGO 20 S.46 27 CRTGO 26 PERIA 20 5,4626 PERTA 26 ARMEN 20 11t. 43 26 ARMEN 26 PERIA 20 1 1 .43 27 CRTGO 29 UR19E 20 6.63 029 URIBE 21 CRTGO 20 6.83 39 ANSER 27 CRYGO 20 13.96 2? CRYGO 39 ANSER 20 13.9628 ARMEN 29 URBjE 20 13.85 29 UPIBE 26 ARME4 20 13.85 29 URIBE 30 RUJGA 20 7,4830 BUGA 29 URIRE 20 7.46 30 BUGA 31 PALmR 20 ?.O0 31 PALMP 30 8UG* 20 7.043[ E41.IR 32 C1.L! 1 5.08 32 CALI 31 P.ALMN 2 0,. 5.08 31 PALMR. 33 SANYO. 20 INA3?33 SA4Tn 31 PALmR 20 17.39 32 CALI 33 SANTn 20 9,54 33 SANTO 32 CAL! 20 9.5440 B/VTA 32 CALl 20 35.83 32 CALI 40 e/VTA 20 35.63 33 5A4TD 34 POPY'4 20 16.7l,34 POPYN 33 SANTD 20 16.11 35 NEIvA 34 POPYN 20 58,16 34 POPvN 35 NEIVA 20 58.2634 POPYN 3? PAsT0 20 58.95 37 PASTO 34 P0PY4 20 56.95 35 NETvA 36 FLORN 20 49.6336 FLORN 35 NiEIVA 20 49.63 38 YUH*AC 3r PASTO 20 63.40 37 PASTO 38 TU'4AC 20 63.4065 TURBO I mEDLN 20 216.23 7 M4EOLN 05 TURBO 20 216.23 41 SN RR 42 FM RR 32 20.7242 FN4 RR 41 SN RR 32 20.72 45 flU ARR 44 RR RR 32 24.0S 44 BR RR 45 qu RR 32 24.US47 MDO R 46 PR RR 33 40.13 46 PB RR 47 Pf0 RR 33 40.13 47 MD RR 56 CT RR 33 40.5456 CT RR 47 too Rif 33 40.54 ST PAR R 56 CT RB 33 11.5) 56 CT AtR 57 PR RR 3) 11.5)56 CT RR 60 UR RR 33 19.62 60 UR RR 56 CT RR 33 19.62 58 MZ2 RR 5y PR RR 33 17.75ST PR RR s8 Hi RR 33 17.75 SY PR RR 59 AR RR 33 21.59 S9 AR OR ST PR RR 33 21.5959.AR RR- 60 UR. PR 33 15.42 60 uP BR 59 AR RR 33 15.42 ..60 UR RR 61 PL RR 33 29,t161 PL RR 60 UP PA 33 29.11 61 PL RR 62 CA RR 33 17.27 62 CA RR 61 PL AR 33 17.2763 BV RNF 62 CA AR 33J 30.44 62 C A RR 63 DV PR 3 3 30. 4 62 C A RR 64 ST RR 332. .64 ST PR 62 CA AR 33 20.43 64 ST RB 65 PO AR 33 16.80 65 PO RR 64 ST RR 33 18.-3048 10 RR 53 GR RR 34 35.46 53 GR RR 48 LO RB 34 35.66 48 LD RR 49 RD RR 34 3',ST49 RO AR 48 LO RR 34 35.57 .54 19 PR 53 GR RR 34 16.33 53 GP PR 54 18 RR 34 ~ 35? ' 34 2.0 55 NV 'wQ 53 ro PR 34 76.30 SO TU PR 49 R0 RR 36 28.2049 90 RB 50 TO) RN J4 24.20 52 SG RB 50 TuARR 34 20.02 50 TU RR 52' SG PR 34 20.02S1 OR RR 49 eG RR 34 -3R.17 49 RD RR St BR RR 34 38.12 49 80 PP 53 GR Rp 34 31.50 5s GH RR 49 NO0 PB 34 31.50 84 84 81 PTD9Q 41 22.16 81 PTDBQ 84 84 41 22.1681 PTOBQ 69 RIVJT at 29.46 69 RIVJT 61 PTOBQ 41 29.46 69 RIVJT 82 PTOCR 41 37.0662 PTOCR 69 RIVJT 41 37.86 69 RIVUT 70 PTOGM 41 95.53 70 PTOIGN 69 RIVJT 4t 95.5370 P10GM 71 PTOISB 41 71.43 TI P1098 7U P T G14 41 4 4'.43 r1 PTnBB 72 PTOPO 68.4972 PTOPA 71t PTnRu 41 31.29 72 PTOPR 73 PTOLD) 41 147.94 73 PTOLD 72 PTOPB ' 41.1460 WORLD 90 PANAN 42 56.50 90 PAANA 60 WORLD 42 59.50 90 PANAN 74 74 42 253.06 Y

OECTSiON 'COSTS PER TOM FOR RAVA40

.......... ....... 0..4o ......... OR1414S ....... 0.............

I anne 'PA tool I A iA A ouroi in 0#40vu rt note 17, T,,v a 0- an ew De $Aft

3 MCPLN It CUCTA 14 RERID 19 MOMO� 22 OIRAO 2A RU4A' 34 4EIVA 36 PA$Tn 38 R/YYA 42 sumsI S/"AR 49o 183o 147* 214o 212* 73'4� 232o 235. 29f). 27()* 252. 25to 289e, 307o 3SA9 348a 4120 2999 24, 460602 OARRU 220 156. 146* 2'13* t9fle 207o 205o Ptlt 26A. 243. 225. 224o 262. 280* 3299 32tt 385o Me Sle,'4212o

0 3 CARTG 3. 137o 155o 72te, 19A. 188. 186. 192. 249. 2?4- 706. 70'5* 243. 261, 314* 302o 366o 253a 66. 39659E 4 St4CL 24- 10; 1?6* 242. 219 '. 167� 165. i?le 228. 203. 165. JP4- 222a 2409 2899 28to 345o 232q, 86o 3TIT,5 5 MONTR 48. 100* 260. 254o, 241, 151. t49. 155. 21t. 181's 166. 168p 206. 223o 273, 265. 328* 21-6. lit. 3657.t 6 CALICS. 459 719 2159 2JLs 214- 128* t23.o 131* 106. 16A* 145.- 14-Am 183. 200. 250. 242. 305a 192* 126a 3328jo1 1, HEOLM 13r- - 3* 165. 1579 145. 54a SP* 5do II&. 90, ?I. 71. 109e, 126. 176. 168o 231* 119* 200. 2246e,N 4 FU?4DM 58- tVo 133- 200t ?Of-* :f4 0 O' 2419 247o 270# 268, 260. 2�0. 298. .3 05 . 354. 357. 420. 3o8e Its &635�A 9 VALtIP 91. 225. tot. W. 174. 207e, 246. 240e, 244, 235o 2FO. 762. 330. 772. 32t. 389. 452. 340. 44. 4638,T to CmIPA 121. 221. Flo 1379 14�44 177i, 216o itoo 214. 205o 2409 262t 300, 262o 29is 359t 422, 3109 74. 42!4.1 It GAvAg 155. 153o .3a 709 7i. 110. 14Ro I'42t, 146. 134t t1`3. 194, 232. 174. 22h. 29t, 355o 242o 141. 3167's0 1 2- C U C T A � 22 1 eL IS? - 1`0. 3 o 6A. 106t 140o 1 j§#. 1 3.8s.- 130, 165 9-- 160i 225L 166ip 2 1 f- t. 20 3 9 347e 2 31's .2094 31976Ill 13 SUCRM 192. 128. 41. 33- 3R. 77. 110. iO4� iog. too- 135o 156* 195. 137o 186. 254, 317m, 2049 09. 2695aS 14 9/94J 72r- lflfv- ?6e, 6'3* l. 64a Io'5v lite, 144. 136o 06v 169# 207's 172. 222, 266q, 330a 20. 214. 299%

:S aER!D 188. 54. 114. 104. toi. 3a 74. 80. 104. 101. 116. 115. i54. 138. 187. 213. 276. 163o 25%o 254to16 BAR�O 226. .01. 77. 69. ?5. 40. ?4. 68o 776 64. 999 120o 159t 100, 150o 2ITe 20le 1609 215, 2366vIT SnfA,4 253. 118. 104. 66* 107. 660 i2o, 66o 70# 61. 96* IISo 156o 98. 148, 215. 21'S. l6be, 242# 24T6#1 -I.. 11P-1j4 242#_. JOB� 91. '7r, 9t. _5?e 610. 55& 59. 510 A5.. 1 07, 145. a?* 137m. 204a 247.o 1-55a 231 2311A19 LADIR t86. 52. 148. 135. 14A. 103. 34 Oa 65, 4to 54'. (tf. 105. 77. 127o 164t 226q, 115. 249:-2074s20 MO%')A 192a 58o 142. 09o 14M* i0e, 90 3o 59. 35. 48. 6le, 99* No 121, 222. 109o 255o 20117o21 EOSTA 213- 84� 116. 1030 Ile. 790 35# 29- 31. �5- 60. 01- 120- 61. til. 179. 2429 129o 254. ?(�74922 VILLA 249* 114. 1460 133. 144. 109. 65. 596 3. 55- 90- ttis 150. 92. 141. 209o 272a 1599 284a 2567s,23 GIRAD 224. 90. 131- 125c 1345, 101- i1e, 3S. $5. 3. 38. 59. 9A, 39, 80. 157. 220. 10?o 276. 20319Z4 V,1UE_ 2130 79t, It9o 131%t 14 7' , 1129 31)a 14 a. .66&. t4e,_ 2 7 ... 40. 8f. 50. 100, 146.. 209& 96. ZZA- 9 2 02-&-25 MA41Z JAB. 54. 170. 156. 161. JOS- 31'e, 310 87. so. 23. 339 72. 94. 144. 131* 194t Sit 2519 2074#26 PER14 194e, 600 1780 165* 176. 1050 45. 39o 96, 49. 140 25a 63. 86, 135, 122. 185. ?3# 257, MI#27 CITGO W. 54. 1640 tro. tol. 99. St- 450 1014 Ss. 20. 19. 58. 91. 1410 W. 1800 Slot 251. 2073o28 AR4EN 206. ?I* 173. 160. 171e, 116. 54e 48. 90, 36. 3. 24o 639 ?4. 1249 122o IOSs ?2e, 2669 2062e,29 UDIBE 19r- 63. 187. 1?3* 184. 108. 59. 53. 164. 52. 17. to. 49, Oa. t3a. 1080 tyle 58* 260. 2081.3o eUGA 205. N o 144e Jai. 192. 115- 61'. 61. It's 59. 24... 3. Al. 96. 145. 100. IL64. Ste, 2&3. 2148.31 PAL'4R 212. I'S. 20to We t9Q. t23. 74. 680 llpk. 66. 3t. to. 34. 42. 142. 93* tST. 440 275# 2205o32 CALI 217. 63. 20&. 193. 204. 128. 79. 13o 124o 1,10 36. 15. 29, 87'. 131`9 Sao 1529 39* 2609 2241a33 SANTO 221- 42. 216. 703* 214. 137. 88. 82o 133. Al. 46. 75. 2As 76. 127* ?9. 142. 48e, 289. 2321934 P3,Y4 743. 1099 232- 2199 230s 154o 105t 99* 150'e 980 63* 410 It 610 III� 62o 125. 6S* 305. 2477.35 NEIVA 76t. J26e, 174. 16t. IF2. 138. rT. ri. 920 39. T4. 96. 610 3e 511. 120"I 164. t23. JIZ. 2338.

FLORN 310- IrIl. 224o 2 14 t 222t fO F.; .1 2 121 c 141, 09o 124o f45jL III,, 5 3 a I 6 1704 2330 173, 36Zo 3182a37 PASTn 302. 164. 291- Plea- 780. 213. 164- 1,56. id'). IST- 172. too. 62. 12o. Ifo. 3e, 66. 124. 365. 336t.36 TUMAC �66. 23le, 355. 342- 353. 216o 2ig. 222- 2?2. i2O- 165- 16a. 125. 164a 233. 66o 30 -WIS 428. 4439,40 BiVTA 253. 117a 242. 229: 24n: ;��- 115,- 109# 00. 107. 72. 51. 65. 123, 173. 124- 187* 30 3ii. 2850.42 FN OR 66. Poo. 141. 20A 21i 48. 749, 255* 264. 2FA, 268. 248. 306. 312, 362a 365# 428# 316t 3. 4766t81-KOWLD 270. 404. 401. 467. 46f). 455. 453. 448. 499. 446. 411. 39t). 4(14. $62. 512. 409. 346o 343e, 263, 7843#

100 SU"IS 1`508- 49A4- '6693- 6993. 719A. 5?58- 4858- 475?- 600. 5004. 4960. 441M 61110. 6024o 1`960). 8268olO613a 6673,

Fipre _11

orelsiftm cftsy/tioo 4non roq RA4ANO

................................................ aqfGtfis -------------- I-----------------------------------------

CARTO T CAMAR 12 R/9WJ 15 LAonq 20 VILLA 73 ARmEN 30 popy" 35 FLOR4 3r. TUMAC 40 rm RR too

3 HEOLOO 11 CUCTA t4 RERTO 19 WONDA 22 GIRAD 26 OUGA 34 REIvA 36 PASTO 38 a/VTA 42...sumsI S/mAR 18e 64t 540 F90- ?40 are $6. 880 1010 100. 9i. 93. tOr. 114. 13i. 129-' 1�2'. tti's 9. IkO6,2 BARRN 8. sat 54# ?9. TM, pro ?.s. Fee 99. 900 a]. 83. 9r, IDA. 122. tig, 143. tOle 19. 1560oD 3 CARTG 1. 51. 5T. 820 71, ?O. 69. ?Io 97. 830 76. 16. 90. 97. 115. 117. t35- 940 24. 1468oE 4 SINCL 9. 43. 65- 9(. at. 62- 61. 63- 84. ri. 65, ha. 82. 89. ICT, 104. 125. See 32. 1390.S 5 SONTR In. 3F. Pa. ge. 9n. 56. 55. 5r. rho 69. 62. 62. 76. 83. 101. 98, 122- so* 41. 1354.

T 6AkMx_.?4- 28e. 80- a6t al. Ar. 4A, 49 . JO, 61. 54. '53, 64a -74, 9 2 e- 89. 113t 1�1 t 4Tm_ 123211I F MEDLN 51. to 6t- Ss. 54. 20. 19. 21- 42. 33. 26. 26. 40. 47. 65, 62. 66. 44, 74, 6!20R 8 FWIDN 21. ?19 49. 74, TA, 09. 890 910 1070 99. 96, 969 110. 113. 131. t32, 156. t149 4. Irtro'k 9 VALOP 34. 83. 3T- 62. 64. IF. 91. 69. 9n. 87. tOO. 108. 122. 10!. 10. 144- 168- 126. 16. 171doT 10 CWIRA 45. 82, 26. 510 53. 66. 800 Too 79, 16. 89, 9TO 111. 90. 1081 039 1560 1150 ??- IS61oI It GAMAR 5r. 51, 1. 26* 28. 41. 51s. 53. 54. 51* 64. 72. 86. 65. 81. 108. 131. 900 '52- 11?3#9- 12--Ul C I A_ 82z-- 54t-- 21te I a___ 25s 39 e. 5 2 t. 50v 5 t a IkS �_ _. 5? a - 03. 5.2 o -8')o 105. 12 8 ti -1 t .- I Le-a a4 13 EUCRM 71. 47. 115. 12# 140 28. 4is 39. 40. 37, 50. 58. 72. 51. 61;. 94. I"?. ?60 66. 998,S 14 2134J_ 84. . 4O'v__ 23-_ 25 9 I * 2 4 9 39, at. 53* 15 0 t So. 63o 17, 64. 67, 99, 122t 8 0 0. T9, 1116015 SER!O TO. 20. 420 39. 36. 1. 27. 30. 419 30. 43. 43.- 5r. 15!.- 69, 79. 102. -610 '�30 9410

16 CAROO 84. 34, 28. Z69 249 15. 27. 25. 27, 24. 3T. 45. 59. 37. 560 el# VI. 62o 00, 876#17 SJGAM 94. 44, 39o 25v 38. 25- 2F. 24. 26- 23. 36. 44, lie. 3-5. 55. 80. 103, 61. 909 925o_jj_jU 209- -229 19o -0 2-)�_-__._29.. 34, 21 2 3 9 _32L... -40.9 _54, 3Z. 51, T6, 6 6.56A1; LA'OR 69, 190 550 50. 54. 389 to 3. 24. 15. 20. 25- 39. 29. AT. 61. 64. 43* 92. ?68020 HO�OA 71. 21* 53* 43* S21 39. 3. 1. 22- 13. 18. 23. 37. 26. 45. 59. 82. 40# 94. 747 0 %A21 ?OGTA el* 310 43. 38 42. 290 13. tt- 12. 9. 22. 30. 44. 23. 410 66. 90, 480 94: 769*22 VILLA 929- 42* 54. _49:. �3t 41* 249 22o to 20'. 33* 4t. 55. 34, 52. ". toil 59t SOS 9531-23 GIIAD 839 33. 5to 46a 50. 38. Is* 13. 2n. 1. 14. 22. 36. is. 33. 51, 61. 409 102o 752o2 _ J§2.Q E 9 ___Z9 ___5 4 �L__ 4 2 Ito 9v__ 24.. St I0L__ I A c -32 5; 77, _L ._U2. 744i700 209 63* 5a, 14. �2- 30. 93. Fee.25 HANIZ 62. 39* 11- 32- 21. 9. 12. 27. 35. 53. 48.

26 PERIA 729 -. 22. 66o 619 65. 399 t?. 14. 3is is. S. 9, 23t 32. 500 45, 69, 27* 95. 766t2F CRTGO Too 200 66- 63. 67, 37. 190 16. V. 20. F. T. 21. 34. Sp. 43. 67. 25s 93. 769s23 ARMEN Fee 26, 64o -59, 630 43. 20. 18-- 33. 14* 1. 9* 23. 28. 46. 45. 69, 279. 99. T64*29 URIBE 73. 23o 69. 64. 6A. 40. 22. 20- 39. 19. 6. 4. to. 33. 51, 40. 63, 22. 96. Tri,�Q_DVGA !_�!t 26i 72. O-E t Tlp __ 4 3. 25& 23t 41o. 2?t U t le _5!'2 iL 9 fi t-.. . .I t _15, 35.c 54s. -3T,, -0 -3 -31 PALMR 79. 29- F4. .70. 74. 45. 27. 25o 44. 25, t2s 4, 13. 34. 53. 35. 58. 16, 1029 OlTo32 CALI 80. 31, The 71. 76. -. 47. 29, 2?- 4ii, 26, 13, 6, lie 32s 51, 33, 56. 144 104o 63os33 SANTD $4, 349 80. r5a 79. 51s 33o 31. 49, 30. 17, 9, 70 29. 4T. 29t 531. 18o 10r. 062o-34 POPYN. 90,_--40, 86._ at* 85, 5r. 39, V. 55, 36, 23t 15, 1. 239 4it 23t 46, 24c 113a 917935 HEIVA 970 47. 65. 60. 64. 510 29o 2&. 34. 15, 28. 35. 23. 1. 19. 4ti. 68. 46s 116. 666.36-10, R-�L -1 15 9- O.S. 8.1i 78L-- 82t..- -69v 47, -450 52,,---3)t , 46.t____54jL_ 10 is- _04 _J a - -63# 86 a--- 6.4 it 1 ? A t-Al 78,c..37 PASTO 112. 62. 106o 103. 107. 79. 61. 590 7T. , 58. 45. 37. 23. 44. 63. 1. 25. 46, 135. 1245v33 TUMAC 135. 86 9 131- 127* 131. 102# 84. 82. lolq el. 69. 6it 46, 68, 66, 25, 1 . 69, 159. 1644t40 S/VTA 94. 44. 90. 85. 89. 61. 439 40. 59. 4n. 27. 19. 24. 46. 6P, 46. 69. 1. 117. 1056.42 FM -RR 24. 74. 52- ??O 79. 92o 9�0' 94. 105. 102. 99. 99, 113, t16, 134. 135. 159, ityl 1. 1766280 woRLD If)O* tSO, 148- 173s lFt. 169. 168. 166. 185. 165. 152. 144. 150. 171. 190. is?. 126. 127. 97. 2905o

100 SUM� _038. i479- 2590. 2665. 2133. 1799 . I 7 6 2 - 2264. t854. 015- tA?9- 22 7 4 . 2731, 294ii. �06?, 39�1- 24 7 2. 3266.46061sOTAL DECISION COST a 71322.37024 0OTAL oEctsioN cosT . 71030.48532 tOTAL DECISIO-4 COST a 11038.4RS32 2

Figure 12

FLOM IN rONls PERt OAV FOR PA^^e4

*---"e-v"O ...... ...................... - ....... ------ORISINS ....... oe ....... e6............. ... '- ....-'-o*olsofteoss-4

CAQTO r SAMtAR tR R/R"J 141 LAnOq 20 VILLA 23 AWMNt 30 PnPY4 IS rLORNt Ir *UYAC tlO FW RR 104

3 GlEnLu It CUCVA 14 qERIO to mo0"04 22 GIRAO 24 RUSA 34 REIVA 36 PAST" ;a R/VTA *2 SUN&t S/MAR 0, , O 0. n. o. o, o. 0. n, 0 0, 0, o, o. o, 0, 0t 0. 43. 4392 PARRN 0 0 ° 0. Oa °0 °0 ° ° Of O ° 0 Os Os °, a 000 O 184. 84.3 CARTC 125S 00 O4 O O 0 0 O 6 0 0 0 I 0 0 ° 00 00 0 0 0, 0 0 0* 12594 iZICL 2t1 0, no o ns 0 n s f, 0,0 0, n, o. o, o o, o. to 0, 0. 0 4 4 066S F{ONTR as, 09 0 * 0 n , o. o, a o, 0, 0 0 0, 0, n o. o, o, o, 0,a 0,a o. 65O CAUCS .28 0 no Os nX 0,i 0,a 0, e. 0 ,0 0,a 0, 0, a 0,. 0,a 0, 0, Os 0. a Z8r F@EOLM 204. 43, O. 0 a 0 0* O 0 00 0 0 0 0 , 0. 0, 0, O 0. 0, 385* 632,6 FU:NON 0, 0, o. 00 . 0, o. oa Os oa o, o, o, o, et 0, 0, 0, as o9 VALDP 00 0 0 ° . O 0 0 0 . 0@ ° ° ° °t Ol el O 09 0, OD 0 29, 29t

tO C?{IRA 0 0 , 00 0 a 01 n 0 00 de 0@ Oe a e °0 O f a Ol Oa O Oa as 35, i5It GA4R 0. °, 27* 00 °@ 00 ° 00 00 °0 . 0 no °. no °. 0° 0. 23s12 CUCTk Ot Oa 26, -t4 e1 04. Oa o0 O 0Q O O0 0 aX O. O O JO, O,.. Q 130,13 SUCR" 0. Oa 1450 Oa n, o, o, o, n. 0, 0, 0,O 0, 0. o. 0, O, 0. 0,O 14SE14 8/94i 0a 04 O O O, 26@ O O 0 . 0 0 0 a S O a 06 0. 0 Os Of 0 26 15 BERIO C, 00 O O, lo 10 .O 0 0 0 Oa 0 00 O0 0 0, Oa Of 00 199t6 WOOte u 0, o. 0a 0 e. r, o, o. 0 . o. o. o . o. o. o. C. o. 09 o. To1r SGAtlb o, Oa 3rO o, 0 32. no O, O, Of 0, no O, O, Oa 1, Oa O, 0. 69#18 YUNtJA s, 9, 0 a 0 0 04 00 06 0 0 a 0 a 0. 0 . 0. 0. 0, 0. O* Q0 tJQ, 80419 LADOR 0. a. Oa 0 a 0 01, 30 00 0 00 1l. 0 0 . 0 0 0 0 0 0 3 8 20 HOnNDA 09 0, 00 0. n 00 541 a 0 a Of O 0 0. 0 4 0. 0 C. 0. . Os o 0. 54.21I 9OGTA 0 O 0 n. 0 94. 'I 0 337, 900 160 1. 'O. O O 0 O Of O, OE O 19. ri?o22 VILLA 09 0a 00 0 0 '090 0@ 00 76. 0 0 . 0 0 0 0 0 0 0 0O 0 0 0 76,213 GIF1D O. 0 0 . O a 0 v n, O, O. Oa n , 64 . °0 . ° * °0 ° 0 O 00 09 6 4 92& 19vUE Oa 0 0 O O Q ) O ° a ° O 0 0 0 56 a 6441 a X D 04 Oa 0. 0. a a ISC-525 MANIZ Us t3te O. O. n) . 0. O. 0 O . O0 O . o. 0 . o. o. oa 13ro26 PERIA 0. 0, 0 , e, o, 0a . 0, n, 0, 114, a0. 0, o, n), 0, 0, 0 0 0, 11tA27 CRTGO 0. 0. 0 Oa n, o 0 , O 0. n, f), 62Z 0. 0 04 n. 00 0 0 0 O 62#28 ARMEN 0. O, O Oa no of el o, o, o, 98, O, n, o, o, , o, 0, 0, 9a,29 URl8E 0. O, O. O, n, o, O, Oa 0. O0, 1, Os O, O, n, O, Oa O, O, Is30 9UCA 0, 0, Oa Oa V.) O, O, O, O, C. aO . r3s. o. o, o. o,a o. o. 0. r3,3I1 PAL14R 0, 0, 0. 0. Oa o, o, o, o, o 0, 65. o, 0, n, o, 0, O , 0 .O 65o32 CtILI 0. 00 0. 0. 0 ° 0 0 0. 0 54. 2. 1tTt 0, 0. 0 Oo 1350 0. 362o33 SANTO O, 0, 0 . o., De no. 0. 0, co 0, 0. 20, O, go O, O, 00 Oa 20.34 POPYN 0, O, O, O, Ot , DO, O, O, n, o. as o. 'O , o, o, o, o, o, o, 0?l35 NEIVA 0, 0, n-O. 0. An, 0. 0 0, o. c. 0. 04, o 90. t 0, 00 06 0. 9136 FLURN .,o. o, oa,0 n, 0o, o, o, n, 0, 0, . 06 0, 0 , S, 0,. o0 o0 , So3? PASTO 0. 0 0 . O O a 'D 0 0. no 'O o . o, lot oa 6r, 3. II. 0@ a O. 9003A TUMAC 00 00 O. 00 0. 0 0 0. D C. 'O. O. O. 0 O) O 1, t O* 0. Ito40 B/VtA 0. O. O- aO, . n, 0 'O. n1, 0. o. . n. 0. 0. 0. 0 26, ° 26,42 FN RR . o, 0, o, o 0. Oa ,0 0. o, 0, 0, o, 'a. 0, n, 0 0. 0 . 6. 6soo WO'RLn v. A. o. o, n, o, o, o, , o, o, o, n,. o, o, o, 0, o, r4?4 4?4.

100 SU4S 661. 'I? 23t. 104. 127. 603 471 90. 245. 15ft 400. 139. 272. 90 74 3. 22 160. 1300. 453T

Fi gure 1-3

ION*,4ILES PER OAY COO)"S FOR qA'NA'E

CARTS GAN4AR 12 4/9wa t5 LADOO 20 VILLA 23 ARMEN 30 POPY'4 35 F~LORm 37 YU'4AC 40 TN RR 100

3 IEOLN it CUCTA 14 RERIO 19 In4oDA 22 GIRAf) 2R RUGA 34 'JEIVA 36 PASTO 38 R/VYA 42 SURSI S/,A 0. 0. 0. 0. 0. 0. 0. 0. n. 0. 0. 0. 0. 0. 0. 0. 0. 0. 25. 25.2 q4RR' 0. 0. 0. 6. fl. 0. 0. 0 0. a. 0, 0, 0.a a 0. 0. O 0. 0. 0. ITT. ITT.

0 3 CARTG 1. 0. 0. 0. A,. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.E 4$SPuCL 2?. 0. 0. O. 0. 0. 0. 0. O. (I. 0. 0. 0. 0. 0. 0. "). 0. 109. 136.S 5 MONoTR t?5. 0. 0. 0. 0l. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0). 0. 0. 175.T 6 CAUCS Fla A.~ 0t 0. 0 0. 0. 0. 0. O. 0. 0. 0. 0. 0. . 0. a. 0. 0. 71.I 7 MEDIN 8r?? 0. 0. 0. a. o. 0. 0. 0. 0. 0. 0). 0. 0. 0. 0. 0. 0. 2113. 2991.N 8 FUNdDN 0. 0. 0. 0. 0, 0. 0. 0. 0. 0. 0. 0a 0. 0. 0. 0. 0. 0. 0. 0.

A 9 VALOP 0. 0. 0. 0. 0. O. 0. 0. 0. 0. 0. 0. 0. 0. a. 0. 0. 0. 3.s1T 10 CHJRA 0. 0. 0 0. 0. 0. 0. ot 0. 0. 0. 0 0 0. 0. 0. 0 . 0. 0. Oa 1T. 71.I 11 GAMAR 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 12 CYCTA 0. 9, -53, ta. O. Os -Qs O. O. 0D Qs 0. 0. 0. 0. 0. 0. 0. 0. 55,N 13 RUCAN 0.: 0. 16S. 0. 0,. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 165.S 14 B/84J 0. 0. 0. 0. 0. 0. 0. 0. 0 0. 0. 0. 0. 0. 0 Os 0-. 0, 0. 0. 0.

15 BERIO 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0,16 BARSO 0. 0. 0. 0. 0, 8. 0. 0. 0. 0. 0, 0. 0. 0. 0. 0. a. 0. 0. 8.17 SOGAM 0. 0. 121. 0. 0, 62. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 183.18. In!JA Qs 0. Or. 0. 0.. 0. 0a -A 0. 0.e. 0.. 0. 04 0. 0. 0. 0. 0, 515. 515.19 LA9OR 0. 0. 0. 0. 0. 0. 0. 0. P. 0. 0. 0. 0. 0. . 0. 0. 0. 0. 0. 20 HONDA 0. on 0. 0. n0 a. 12. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 12. 621 BDGTA 0. 0. 0. 0. 350. 25. 303. 84. 147. 0. 0. 0. 0. 0. 0. 0. 0. 0. 139. 1124. -22 VILLA 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. la23 GIRAD 0. 0. 0. 0. 0. 0. 0. 0. 0. to 0. 0. 0. 0. 0. 0. 0. 0. 0. to24 I Q u.r 0.. 0.a 0.. 0. De Oa. 0a 0. 0 . 39-a 1t.. 0. a. 0. 0). 0. 0. 0.. 0.. 70.25 M4A.'IZ 0. 208. 0. 0. 0a 0. 0. 0. 0. 0. 4. 0. 0. 0. 0. 0. 0. 0. 0. 212.26 PERIA 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 35s 0. 0. 0. 0. 0. 0. 0. 0. 35.27 CRTG0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 30. 0. 0. 0. O. 0. 0. 0. 0. 30.28 ARMEN 0. 0. 0. 0. 0, 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. it29 URIRE 0, 0. 0. 0. 0, 0. 0. 0. 0. 0. I. 0. 0. 0. 0. 0. 0. 0.~ 0. le30.flJGA 0. 0. 0. 0 . 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 1.31- PALMR 0. 0 . 0. 0 . 0, 0. 0o 0 . 0 . 0. 0. 19. 0. 0. 0. 0. 0. C. 0. 19.32 CALI! 0 . 0.a 0. 0. 0. 0. 0. 0.O 0. 0. T0. to 165. 0. 0. 0. 0. 11I ~. 0. 355.33 SA'JTD 0. 0. 0f 0. 0. 0. 0. 0. 0. 0. 0. 0. 12. 0. a. 0. 0. 0. 0. 12.3* POPYN 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. to 0. 0. 0. 0. 0. 0. to35 NEIVA 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 2. 0. 0. 0. 0. 3.)A IL1-DRN .0. 0. 0. 0. .0. 0.a 0.a 0. 0. 0.a 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.37 PASTn 0. 0. a. o. n0 . 0. 0. 0. Oo 0. 0. 0. IT. 0. 381. 0. 21. 0. 0. 381.30 TUMAC 0. 0, 0. 0. 0). 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.40 B/VTA 0. 0. . 0. 0. 0, o 0. 0. 0. 0. 0. 0. 0. o 0. 0, 0. 0 0. 0. 0.42 FN RR 0. 0. 0. 0. 0. 0. 0. 0. a. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.80 WORLD 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0, 0 0. 1905. 1905.

100 SU'4S 1151. 209. 340. 1. ISO. 94. 395. 84. 143. @0f. j79. 21. 195. 1. 345. (I 21. 119. 5086. 877 5.a

Wi ure 14t

rLOW PEN SEASOV (SIIOOI rftR RAVAND

............ i,am ------------------------------ T-ORIC14S ---------------- .............................

CARTG F GAMAR 12- MID".# 13 LADOR 20 yttLA 23 ARMEN 30 popyof 35 FLORN 3? TU4AC 40 rN RR 100

3 6100 It CUCTA 14 RERIO t9 "040A 22 itRAI) 26 BUG& 34 NEIVA 36 PASTO 38 RIVTA -42 SURSI 3/MAR 00 00 0. n, A, ON 00 tio 00 00 0. 40 00 00 0. 0, 00 0, 424t. 4741,2 bARRM 00 06 1). (Y; n, 00 0, 0 0 0. 0, 0, 0 o ON 09 0 0 00 Oo 0,181720181F290 3 CARTG12783* 00 .0. 00 0. 06 00 00 00 0, 00 00 00 0. 00 Of Ot 0.122830E 4 SINCL 2054o 0, 0. 0. 0, Oo 00 00 Oo 00 0, 0. no 00 0. 0. ON 0, 4384. 646F,S 5 MONTR 8403. 00 O* 06 0, 0. no Oo 09 09 0. 00 , 0. 0. ot do 0. Os 0. $403,1 6 CAVCS 279to oll 00 ot 00 Oo 6, O'o 04 0. 0, 00 00 00 ON 00 Of 00 Os 279101 T NEDLN20066. 4;'27* 0. 00 4j 0. no 00 n. 0. 00 00 04 0, 00 oe ot 093?960.6 '2253oN a FU40N 0. 0, Of Of no 0. ot Oo 00 00 0, 00 0. 0, n, 0. 00 Ot 741a ?41�A 9 VALDP oo ON 0. 06 0. 00 00 09 (1, 0. 0, 00 00 00 M, 00 00 00 2361o 286107 to CHIRA 00 0, 0. 0, n. Oo 0, 00 Oo d. 0, 00 0, 00 0, om- 0. Os 3426s 3426p1 11 GAMAR 0 0 0. 22650 0 0 M, 6 o O. 0 0 ti 0 0, 0. Oo 0 O 0. Om 0. Oo 0 a 00 228500 12 CUCTA 0. o, Wi.10223. 0, Of 00 Oo ON 0, 0, on Of 0, Of 04 Oa. OL 0,17.?q4tA 13 DUCRM ON 0.1429A. 00 4, Oo 00 do Oa 00 60 O. 0. 0. 0. 04 Oio 0. 004298o

S 14 B/NMJ ON 0. Oo Ot 2583o Oo 00 00 fl.. 00 ON ot no 0. ot 0, Os 00 0. 2583#15 SERto 00 -0. 0. Of f) 0 1 91'4 0 0. 0. no 0 O 0. O* 0 O 0. n . 0. 00 Of 0. 1914.16 BARPO 0. 00 09 ot (it '00, no 00 O, 0. 0, Of 0. 04 no 00 00 06 00 6rot17 SOGA4 00 00 3649. 00 4, 31 .2S* f. 0. no 00 0. 04 00 0. 0. do 04 ON 0. 6774.18 JUN4A Of n, 00 00 0, ot 00 00 no go 0, 00 00 0. Os 00 Oi, Oa M4& 7904#19 LADOR 0. O. Oo O, A. 00 3?01, do Of 00 0. 0. 00 0. at 00 as 06 Oo 370to20 mON3A 0. 0, 0. 0. 4 , 0, 5273, 0 0 M. 0. 0 , 0 . 0. 00 0. 0. 0 O 06 00 5273021 BOGTA 0. 0. 0. 0, 9441. 101802?20. 8639otWc. 52. 0. Oo 1). 0. 0. 0. Oo 0. 1908.70660t22 VILLA 0. 00 0 O 60 n , Of (10 0, 7447. 0 0 0 , 0 a 0 . 0 0 0, 0 a 0 0 0 a Os Y44?s23 GIRAD 0. 1). .)O ON no 00 0. 0. n. 630to 0. O, 00 0. 0. 0. 00 0. 0. 6301*?4 18�UE Q1 01- f) t.. 0 4 ') 4 0 . 0 2 of 0 o 8450a 6301o 0 a 0 . 0. 0 a 0 a 0 e 0 a cl 1 s�5 MANIZ 0.12864. 0. Of 0. ON 00 0. 00 Os 624. 04 04 ow O* 00 Of 09 0.13435026 PERIA 0 a 0 0 0 0 0. 0 0 0 9 0 0 00 f). 0.11230, 0 0 00 6. 0, 0 , 0 . ON 001230i2? CRYGO 0. 00 0. O, n, Oo 0. 00 Os O. 6!2r. 00 ON 00 0. 00 ON 00 0. 6127028 AROEN Oo 0. 0. 0. O. 00 6. O. Oa Oo 9619. 0. 00 00 ti, 0. 09 0. ot 9619029 LORIAE 0. 00 0. 0. 0), 0. 0i 00 A. 0 9 124. 0 0 0. 0 . 0 0 0, 0 a 0 0 do 124o30. BLIGA 0. 0, 00 0. O, f), 00 no 0, 04 7154, 00 00 Os 06 do O& do 7154631 PAL6!R 0. 00 0. (a 0. 0. 0. M. 0. 0. 6423.' no 0. no 0. 0. 0. 0. 6423.32 CALI 0. 00 e). 0. 4. Do 0. 0. Oo Oi 5353. IFO#16654o O, Oo 00 0032900 005668q,33 SANTO 00 00 0. 00 n, Oo c , 0. n, 0 0 0 , 'O 0 19730 0 . 0 0 0 a 0 0 0, 0 a 19?3034 POPYN 00 0, 00 00 A, 00- Os 00 ot Do 0, Os ?036, 0. 00 0, 00 0. 0. T036,35 P.EtVA do do 0. 00 n. Of 6. O. 0. 0. 0. O-,' ' Os 8839. 137. 0, 06 00 0. 897F*36 FLUR4 0 1 0, 0. -0# M, O.t (1, Os Om 0 a 0. O, no 0, 494. 0. Os 00 0 a ;94&3? PASTn 0. 0. 0. 0. n. 0. 0. 00 no 0. 0. 0. 969. 0. 6636o 268. 1039. 00 O. 89!3o36 TUMAC 0 . 0 . f . 61 no 0 0 00 00 no 0, 00 0, 00 0. 0. 110?. Oa ON 110?,40 B/VTA 0. 0. 0. 0. n. 0. Oa 0. 0. 00 00 00 Of 0. 1). 00 0. MON do 2520t42 F4 RR 0 0 00 n. t) 0 4. 0 0 0 . 0 0 o , 00 0. 00 0, 0. 0, 0. 0 0 0, 59?. 597,60 NORLO 0. 1). n. t) , n. O* 0. 0. f). 0. 0. 00 0. 0. 0. 0. Of 0*46693.46693.

10o SuwS4562?-1709t.72803-102.-3.12tl2?. 6?29.41694. A$139.74126.t48o3.39378.t3?48.2fiA34. 8839o 7267. 248. 2147.15410.041,6,6*04,0,4,64,10

Figure 15

- 49 -

SUMMARY TABLES

This section describes a sample of the Summary Tables availablein the model. The selection of the tables is an option to theanalyst because of the mass of computer output if all the printingoptions are exercised.

The transportation summary tables discussed in this sectiongives totals by class of vehicle and system. System here denotesMODE, but the Harvard authors have used System to be more specific.For the Colombian example these systems are:

1. Highway2. Atlaritic Rails3. Pacific Rails4. Central Rails5. River6. Ocean7. Transfer by River8. Transfer by Port9. Transfer by Rail

10. Pipeline

Chart 1 presents the DOLLAR VALUE OF VEHICLE DEPRECIATION. Thisis calculated using the following equation:

VEHDEP (MODE, ICLAS) DEPRAT (M.,I) * VEHCIS (M,I) * VALVEH (M1,I)

where

VEHDEP (MODE,ICLAS) total depreciation for all vehicles in mode (M)and class (I)

DEPRAT (MODE,ICLAS) = depreciation rateVEHCLS (MODE, ICLAS)= number of vehiclesVALVEH (MODE, ICLAS)= value of each vehicle

- 50 -

Chart 2 presents the OLD VEEHICLES SCRAPPED FRaK THE FLEET.This is equivalent vehicles scrapped as calculated:

VSCRAP (MODE, ICLAS) - VEHDEP (M,I)/VALVEH (M,I)

Chart 3 presents the TOTAL VEHICLE-HOUR REQUIREMEDTS FOR THISYEAR. These figures are calculated from equation 14. page 35.

Chart 4 presents the TOTAL VEHICLE-HOUR AVAILABILITY FOR THISYEAR. These availabilities are calculated from equation 13. page 35.

Chart 5 presents the RATIO OF VEHICLE REQUIR3MENTS TO AVAILABILITIES.This is a basic ratio as to the availability of vehicles to-meet theshipping demands. Equation 16 is used. to calculate thisaratio.

Chart 6 presents the TOTAL VEHICLE DEFICIT (DESIRED-ACTUAL, ( - )SURPLUS) in vehicle hours. This deficit (surplus) is calculated from:

DEFICIT (MODE, ICLAS) (R ETOT AVATOT)

where DESRAT (MODE, ICLAS) desired ratio of vehicle actual, requirementsto availability

Chart 7 is the VEHICLE DEFICIT IN NUKBER OF VEHICLES and is obtainedby transforming the vehicle hour deficit (surplus) into vehicles by:

VEHDEF (MODE, ICLAS) DEFICIT

NSER DAYS(IS) * HRPDAY (M,I)

Chart 8 gives the NEW VEHICLES ADDED TO THE FLEET and is calculatedby:

VEHNEW (MODE, ICLAS) = TRINVS VEHDEF (M,I) * VALVEHH'(M,I)

VEHDEF (M,I.) * VLVEH (M1,I)

CONFAC (M,I)where TRINVS = amount to be invested in vehicles.

CONFAC (M,I) - an input constant factor.

- 51 -

Chart 9'gives the (VEHCLS) NUMBER OF VEHICLES BY CLASS -BLK, GEN, SPC, CC, PP. This is the net number of available vehiclesfor the next period.

Vr.iHCIS (MODE, ICLAS) = VEHCLS (M,I) - VSCRAP (M,I) + VE1 dw (M,I)t+l t

The "UNSCRUNCHED REVENUES" are the total revenues derived fromshipping the subcommodities. These revenues are calculated from thetariffs for the flow assignments as were calculated in the D4stributionModel. The revenues are calculated using the base year pri.ces and thecurrent year prices.

The Chart 10 gives the DOLLAR VALUE OF GOOD I TRANSPORTED FRDMREGION M TO REGION N. This is the dollar value of shipments as determinedin the Distribution Models and the subcommodities have been aggregatedinto commodities here. There is a chart for each of 14 Commodities10 Domestic and 4 Imports.

These Summary Tables are presented as a sample of the type of outputthat can be obtained summarizing the system utilization, transporter's costsand shipper's costs. Almost any type of performance summaries desired byan analyst can easily be obtained through the model since minute detailof the system operation is used in the model. Therefore, it is a matterof the analyst deciding what information he desires and having it printedout accordingly.

* This value is calculated in the macroeconomic model or may be an input.

N YLAR*4 nInLLAR VALUE OF VFHICLE nEPRECIATION Chart 1

CLASS t 2 3 4 ROwSUm

;,YS$,TV., m 14801000*-000 11913142*?91 2111850.000 In5ros31.?So 3056723,565 62453847,105

309819,552 61963.910 3098t.955 4642.s933 0.000 449238.350550145.972 1239278.208 406091*233 464T29.328 0.000 2660744.741

4 619639,104 774548.A80 17454.888 232364.664 0.000 1704007,5366147919.69.1 p205340.919 1537134.529 o.ono 0.000 t1886004.139

0.u00 14o45600.000 0.000 .0.000 0.000 14745600,0007 ~~~~~~0.000 0.000 0.000 0.000 0.000 0.000

d 0.000 0.000 0.000 0.000 0.000 0Q0009 0,000 0.000 0.000 0.000 0.000 0.000

to 0.000 0.000 0.000 00000 0.000 0.000

43LSUN 22428524,319 529404834708 4159,612.605 l13l4098.175 3054?23*565 93899441.872

tN YEARo6e 0.L VEWICLtS SCRAPPED FROM THE FLEET Chart 2

CLASS 1 2 3 4 S RONSUMSYSTEM

1 90.250 340c595 10.050 112.813 45,623 607,3302 5.6115 1.129 O0S65 0.565 0o000 7,904i 10,025 22.582 7,409 5.645 0.000 45S6604 11.291 14.113 l9kil 2,823 0,000 29.636t) 3,304 2.103 0.426 0.000 0.000 5.602 '6 0,000 3,686 0o000 0o000 0,000 3 686 ar 0o000 0o,000 0000 0o000 0o000 0.000

S 0.000 0.000 0.000 0.000 0.000 0.0009 0,000 0,000 0,000 0000 0,000 0,000

10 0.000 0,000 0.000 0.000 0.000 0.000COLSUM 120.k85 384,208 27.860 121.845 45,623 699.821

,N YEAR.*. TOTAL VTHICLEW"OUR REOUIREMENTS FOR THIS YEAR Chart 3

CLAbS I 2 3 4 I ROwSuw4YSTLH

1 602153,184 75230461.883 538066.317 2617s86.52s 2915628.153 37323396,0622 10987M.490 7615.411 31566.874 1915.9Q2 0.000 150976.7663 794619.398 19051.180 70407133S 5 9 Ql 3.433 0.000 1576815.9264 211862.J94 s9474,537 106337.2C7 6051.935 0o000 333r26,073

5357-88,401 369260,¶8S 68786,360 376196.571 36180.376 13!6211,693

o ?19295.333 423874,825 99644.175 46566.904 45317,232 834698.469r 0u 0o000 0o000 0.0o0 0.000 0o000t5 .0.000 0,000 0.000 0.000 0,Q00- 0,0009 0.1)02 0,003 0,004 0.000 0,000 0,010

1o 0.000 0.000 l17030789s,5o 0.000 0.000 t17030789,5003LSU4 1592'97.202 PA05Q738.624 118579261.7,3 31l7691.359 2997125.761 IS8636614,697

IN YEAR *** TOTAL VEHICLT-HOUR AVAILABILITY FOR THIS YEAR Chart 4Class 1 2 3 4 5 ROWSUMbYSTLm

I I541?2(0.000 39?qt4A4.520 210%?Q0.nO0 131?6%00.000 53747?6.,o0 70936160.S26ie S148456.boO 32Qb9t.3 6 0 164845.6RO 164P45.6Ao n.OCO 230rs39.520.1 2 l92761.5ts 6593Wa7.200 2163349.854 1 64 R4 56.80oo 0.000 1333?95.369

329'.13.600 aI21!42.00u 412114.200 824220.400 o. 00Q 8654398.2005 59639F.517 400320.125 8?88t.200 58400.000 sR400,00.0 1207399.442

r876000.000 807321.600 876000.000 8f&00.100 s16Gee'C 2r34521.600/0.u00 0.000 0.000 0.000 0.oO .o 0.000

0.000 0.000 0.0300 J1.000i 0*000 0.0000.000 0.000 0.000 0.00o 0.000 0.000

IU1 8760.000 8160.000 105120000.000 nF60.000 876.000 10514y156.000

COLSUM 19896889.432 520sTs47.406 120927430.935 1s968790.880 5475612.005 2043202Po.658

IN YAR..** RATTO or VE4ICLE REQIJIREMENTS Tn AVAILABILITTIES Chart 5

CLASS 1 2 3 4 6SYSTL4

1 0,5l 0.634 0.255 0.299 0.5472 0,067 0.023 0.191 0.012 0.0003 0.2rl 0.003 0.325 0.036 0.0004 0.064 0.002 0.258 00007 0.0005 0o,95 0.902 0.830 6.442 0.6206 0.250 0.525 0.114 0.532 0,517

7 ~~~~~~~~~0,000 0.000 0.000 0.000 0.000o0.000 0.000 0.000 0.000 0.000

9 0.000 0o000 0.000 0.000 0.000to 0.0no 0.000 t.113 0.000 0.000

IN YEAMR** TOTAL VENICLr DEFICIT (OESIRED * ACTUAL, (C) a SURPLUS) Chart 6

CLASS 1 2 3 4 5 ROWSUmSYSTEm

1 2839584.853 16286208.553 -91253?.072 -7358974.390 1150437,66r t2OO47t9.612d -1208942.842 -299229.718 -38578.163 -157181.714 -0.000 *1703932.4s53 251316. 078 651t620.081 65>935.405 -1412163.067 -0.CQO -702553t.6654 -2449464.024 -4683243.551 13234.428 -800020.661 -0,000 -7319493.9085 t15987. 1v 83026.188 8833.946 443195.478 -10159.498 640883.0826 -ss3606.223 -24)155.167 -f43141.100 -25510.795 -27177.024 -1621590.308r 0,000 0.000 0.00 0.000 0.000 0,0008 0.000 0.000 0,000 0.000 0.000 0,0.009 0.003 0.004 0.005 0.000 0.000 0.013

1o -8r60.000 -8760.000 50921052.666, -760.000 -876.000 50893896,666

COLSUM -1043885.136 521?2?5.928 49 90u100.296 -9319415.199 1112225.145 45868951.034

IN YLAR*eo VrHICLE DEFICIT iN NUMBER OF VEHICLES Chart 7

CLAbS 1 2 3 4 s ROWSUmSYSTtm

1 486.230 P7?8.r34 -156.256 -1260.09R 196.993 2055.603-138.00r -34.159 -4.404 -1.943 0. 000 -194.513

28.o89 -744.o21 r4.536 -161 .206 0.(Oo -802.001

-279.619 406. 124 1.51t -91. 327 0.000 -83s.5595 819.o61 14.217 1.513 ') .890 -1,l4 0 109.7406 -6A .62.2 .2.e,1 -84.611 -2.912 -3,I0? -18tS.13

I o,QOO O, o,noo.uo 0,000 0.000 .0.000 .000 0.000i OSUOO 0,000 0.000 0.000 0.000 0.0009 0.o0'o 0,000 0.000 0.000 0.000 0,000

10 .U 0O -1.000 5812.906 -1.o:oo -0.100 so0.o06

C0O50W 49.512 1530.005 5644.971 -1458.596 192.051 5957963

IN YLAR"** NEW VEHICLES AnOEO TO THE FLEET Chaift B

CLASS 1 2 3 4 5 RONSUIbYSTEI

1 194.492 1115,494 0.000 0.000 ,69r79 138.7e832 O.QOO 0000 0.000 0.000 0,000 0.000J 11.4r6 0.000 29.814 0.000 0,000 41.2904 0.000 0o.o0 0,604 0.000 0.000 0,604,to ?.944 5.68r 0.605 0.000 0.000 14*2366 0.000 0,000 0,000 0.000 0.000 0.000t 0,000 0,000 0,000 0.000 0,000 0.000a '.OOO 0.000 0,000 0.000 0.000 0.0009 v.000 0,000 0.000 0.000 0.000 0o000

10 ,0000 0,000 0.000 0.000 0.000 0.000

COLSUN 213,912 t121.160 31.024 0.000 78.797 144 .913

IN YEAR-.' CVEHCLS) NUMBER Of VEHICLES OY CLASS 'SLK,GENPSPC,CC.pP, Chart 9

CLASS 1 2 3 4 * ROUSUNSYSTEM

'1 1904.242 7586.797 342.950 2143.438 945,629 12926.0562 182.535 i5,50r 18.2S3 -!A:253 0.000 25S.5483 335,602 730.135 269.36Z 182.535 0.000 iSiT4j3g* 365,069 456,337 46.236 91.267 0o000 958,9115 107.336 T3,673 14.37' 10.000 10.000 215,3506 ioo.ooo 8,474 loo.ooo 10.000 o0.000 306:4.7r o0.00 0.000 0.000 0.000 0.000 0.0008 0.000 0.000 0.000 0.000 0o000 0.0009 0,000 0.000 0.000 0.000 0,000 0.00010 1.0o0 1.000 12000.000 1.000 0.100 12003.100

COLSUM 3000.184 5972,926 12791l176 2456.493 96s,r29 26187 r107UNSCRUNCHED REVENUES DERIVED FROM S'4KPPING BANANO ARE 990,599UNSCRUNCHED BASE PERIoO VALUE OF TRANSPORT rOR BANANO IS 100.983UNSCRUNCHED REVENUES DERIVED FROM SWIPPING POYUCA ARE 43,375UNSCRUNCHED BASE PERIOD VALUE Of TRANSPnRT FOR POYUCA IS 45,946UNSCRUNCHED REVENUES'DERIVEO FROM SHIPPING COTTON ARE 2.758UNSCRUNCHED BASE PERloD VALUE OF TRANSPORT FOR COTTnN i5 2,842UNSCRUNCHED REVENUES DERIVED FROM SH'IPPING ANROZ 'ARE t2,684UNSCRUNCmED BASE PERID VALuE CF TRANSPnRT FOR ARRO IS 1>,670UNSCRUNCHED REvENUES DERIVED FROM S4IPPING fiRAIN ARE 9.028UNSCRuNCHED BASE PERIOD VALUE OF TRtNSPORT FOR GRAI4 IS 9,094UNSCHUNCHED REVENUES OERIVEO FROM SHIPPING 4AIZ ARE 13,210UNSCRUNCHED 8ASE PERinD VALUE OF TRaNsPnRT FOR MAIZ IS 11.880UNSCRUNCHE' REVENUES OERIVEO FROm SwIPPT%G .lTROSA ARE s0.FT4UNSCHUNCHED BASE PERInD VALUE OF TRANSPnRT FOR OTROSA IS 5,815UNSCHuNCHEn REVENuES OERIVED FROM SHIPPING CRflOIL ARE 92.5ArUNSCRUNCHEn BASE PERino VALU'E Or TRANSPnRT CUR CRDOIL IR 97.58r

UNSCRUNCIEI OEVrNUts nflIVt: FRnO SNiPPING ttMER ARL 0.000UNSCRU'vCwEr PASE PEQRIfl WALUE OF TRANsPnRT rOR ETHER IS .000W SCU'WCHEF REVENUES DERIVEO FROM SHIPPING nT45OM ARL 46.15tUNSC,ULCkEn BAsS PE!1nD VAtLU OF TRANSPnRT rOR OTROSH IS 4A.2?TL-SCRUNCHED REVENUES 7ORIvEO FROM S41PPING rRNCoF ARE 8.409UNSCRUMC-E0 BASE PEQI:D VALUE oF TRANSPRrT FOR GRNCDF IS 8.525UNSCRUNC4E[ REVENUES 0ERIVEO rRnM SHIPPING COFFEE ARE 114.612UNSCUNCNEI) 4ASE PEQIOD VALUIE OF TRANSPnRT FOR corFEE tS 11G.A39LNSCRuNCHEr) REVENUES OERIVED FROM SHIPPING CATTLE ARL 43.342UNSC'sJNCHEn RASE PEQIOD VALUE OF TRA.lSPnRT rOR CATTLE IS 6S.664UNSCRJUCmEf REVENUES DERIvED FRON 5SHIPPING RENIDA ARL 44.1t5UNSCRJC00Eo RASL PERIOD VALUE OF TRANSPnRT FOR BEBInA TS 44.006VSCRUNCmE,) REVENUES oE4IvEn FROM SNIPPING FOPPRO ARE t35.478U9sCRUNCHEO) BASE PERIaID vALUE OF TRNSPOnRT FOU FOOPRU IS 13A.764UNSCRUNCHE0 REVENUES nERIVED FROM S4IPPtNG AIUPAN ARE 15.6R8UNSCRU%CHE.1 BASE PERIOD VALUE OF TRA4SpnRT rOR AZUPAN IS. 36.305UNSCRUeCmEO REVENUES DERIVED FROM SHIPPTNG WOOPRO ARE 15.360UNSCHJNCHE SASE PERIOD VALUE OF TRANSPnRT FOR OOPRO IS 15.400UNSCRUN:HtD REVENUES IERIVED FROM SmNIPPING LITINO ARE 22.403UNSCRUNCiED RASE PER,IDO VILUE OF TRANSPnRT FOR LITI'O IS 23.23rU1:S^RUNCPEr REVENUES DERIVED FROM S4IPPTNG 4NOCFT ARE tl.880UNSCRl.jNCHED BASE PERIOD VALUL OF TRANSPORT FOR HNDCFT IS 12.223NflSCRUNC"ED REVENUES OERIVEO FROM SHI'PtNS REFPRO ARE 35.931

UNSCRUNCHED BASE PERIOD VALUE or TRANSPORT FOR REFPRO IS 35.991UNSCRU'4CHO REVENUES DERIVEn rROm SHIPPING CHRRUJ ARE 18.4A7UNS:MUNCNEO BASE PERIOD VALUE OF TRANSPnRT FOR CHMRUB IS 1t.514

UNSCRuNCHED REVENUES DERIVED FROM SHIPPING NONMET ARE 30.735UNSCRU4CUED BASE PaRIOD VAYUII or TRANSPnRT FOR NONmET tS 30.725UNSCRUNCHED REVENUES PERIVED FROM SlIPPING BASHEr ARE 15,256U'SCRuNCHEO qRSE PEQIOD VALUE OF TRANSPnRT FUR BASmET IS 15.688UNSCRUNCHED REVENUES DERIVEn FROM S41PPTNG HVYIND ARE 10.149UNSCRUNCNED BASE PERtOD VALUE OF TRANSPORT FOR HNYINU tS 10.306UNSCRUNCHrD REVE'4LES DERIVES rioM-SHIPPTNG CONSTR ARE 19,418UHSC.J,NCHED BAS- PERIOD VALUL OF TRANSPORT FOR CONSTR IS 19.96?UNSCRUNCHED REVENUES OfR IVEO FROM SHIPPING SERVIS ARE 95,666UNSCRUNCHED BASE PERIOD VALUE OF TRANSPORT FOR SERVIS IS 97.353UNSCRuNCIDo REVENUES DERIVED FROM SH!PP:NG HI INC ARE 181.392UNSCRU.NCHED RASE PERIOD VALUE Of TRANSPnRT FOR HI INC iS 181.392UNSC-1UNCHED REVENUES DERIVEo FROM S.IPPTNG LO INC ARE * 121,000UNSCHUNC.ED RASE PE*InO VALUE OF TRANSPnRT rOR Lo INC 15 121.000UNSCRuNCHEo REVENUE% OERIVED FROM S4IPPING AGRI1P ARE 34.313UNSCRULJCHED BASE PERIOD VALUE OF TR4AspnRT FOR AGRIMP IS 34.466UNSCFU4CHED REVENUES ntRIVED FROM SHIPPING FODIMP ARE 20.512UNSCRUNCHED SASE PERIOD VALUE Of TRANSPnRT fOR FODt'P IS 20.524UNSCRUNCHEO REVENUES DERIVED FROm SHIPPING CONIMP ARE 49.4?rUNSCRUJNCHED BASE PERIOD VALUE OF TRANSPnRT FOR CONIMP IS 49.573UNSCRUNNCED REVENUES OERIVED fROM SUIPPING HVYIMP ARE 298,270

UNSCRUVCHED BASE PERIOD VALUE OF TRANSPnRT FOR NVYIMP IS 299.560

IN YEAR&.. DOLLAR VALUE F C000 I TRANSPORTED FRoN REGION H Tr REGION N Char t 10

OOU IDESTINATION I 2 3 4 5 6 7 C 9 I0 tt RONSIM

ORIGINI 144.581 29.0

98 78.554 65.32? 4.323 ta.5tr 3-350 5.06? 1.915 0.5?8 54.797 356.103

2 30.409 115.>30 111.589 r.r01 4.291 4.063 4.083 1.753 0-.3-5 1.04 3.503 304.270

3 0.057 09R3 '4.6i6 0.468 14.281 ?9.047 U.79t 1,973 0.372 O.365 0.029 220o04214 5,9Q3 4,33A 96.776 173.928 1l.8l1 117',-182 6.217 32.442 4.396 0.499 0,064 383,o9

0.006 O.U08 '1,018 0.998 8i.903 32,078 28.071 6,522 0.232 o0.1T 0.010 163,604° 1.571 1,150 t11513 6.225 11.837 156.230 5.854 20.547 4,445 0.441 0.023 219,8557 0.020 0.033 7.5r,9 0.538 18,354 6.052 12i.594 13.stg o, 3?7 4.702 0,042 200.1580 0,049 OU37 10.882 11.598 42,697 66.933 2 t1.22? 12.174 2.768 7.693 0,020 235.072,Y 0 0,001 O.,QI 0I515 0.410 o,7n3 43.751 0.395 5.227 ?1.736 2.195 0.001 76.999is) 2.378 2.476 8.573 0.386 10.4q6 3.553 128,692 4"431 0*398 85,979 0.790 248.143

11 0.0o0 0.000 o0.0no 0o000 oo0o 0.000 0.000 0.000 0 oono 0.000 0,000 0.000

0tS 185,016 152o743 41,4AS5 26r,579 222.754 476.869 334.218 164,055 39.004 104.974 59.279 2407.955

Goo00 2EsTIN4T1ON 1 2 3 4 5 6 7 8 9 1o 1I QR0SumRIGIN

1 2,133 0.144 0.I04 0.181 0.14? 0.355 0*280 0.086 0.016 0.041 1.4?? 5,603Z 221%4 2*303 2,641 0.796 (.8e07 4,618 2,499 0,473 0,091 0.279 24,855 41.5154 2;90i 1.801 72a527 1.354 2,812 5.651 5.262 0.832 0,4a9 0,607 27,419 7ta3774 12,063 7.466 14 152 30.736 5.025 26,047 14.268 3t014 0R589 1,624 128a394 243.3195 0.334 0,199 09075 0,194 1.163 O.565 0.453 0.343 0.028 0,053 0,038 3,4446 0.950 0.572 6.176 2.250 .0.967 33iS4? i.2i8 i.7TS 0.361 0.178 o,128 41.524t 0.046 0,028 0.030 0iO29 0.320 0*049 11.704 os0s58 0.004 0.230 0.032 12.531.8 0.319 09194 0.214 0.213 0.9.4 0.844 0.470 0.690 0.030 0.062 1,564 5.0749 Q.1~Of 0.06r 0.018 0o078 0,08i 0.114 0I16 0.19 0.024 0,048 0.021 0,857

10 0,810 0,499 0,046 0.104 0.157 0*095 6.507 0,068 0.013 0,813 0,695 3.80611 0,000 0,000 0,000 0.000 (,000 0.000 o.ooo 0.000 0.000 0.000 0,000 3.000

XLSU) 21.71 13,873 40,073 35.936 12.020 rt.886 36.i7o 6.859 1.306 3.934 184.572 429,050

COOU3

5TINATION I 9 3 4 5 6 7 8 9 in 11 ROWSUMTIGIN

1 28.156 1.799 0s 0000 0o000 0o000 0.000 0.000 ooo o,ooo 0.000 16.351 46,308

2 0.000 0.000 o.ono 0.000 0.000 0.000 0,000 0,000 0,000 0.000 0.000 0000

3 0.000 0.000 316,886 0.000 7.190 0.000 5.551 0.000 0.000 0.000 231.666 563.2934 3,048 O;OOO 1.045 117,771 8.112 0.0co 0.000 0.000 1.5n9 0.000 45,250 176,7355 17,6n6 18.308 3,379 0.000 S16.932 57,3'7 13.131 0.000 o0oo'o 0.000 505.156 1131.829O 0oono 0.000 Odooo 7.939 ooono 73.261 0.000 66,997 o 0ono 0.000 116.660 264.85?

0.000 0,000 0o000 0.000 0.00o0 0.000 252.811 0o000 0.000 0.000 219,644 472.455

u.653 0.000 o0o0o 15.088 29.516 59,873 o.iS8 ?6d.489 0.000 7.406 296.6A2 668,4589 0.O0O 0.000 .000 0.6000 0.000 8.882 0.000 0000 15.356 0.000 09000 24.238

o o.0ou 0000 .0o000 0.000 0.000 0.000 2.901 0.000 0.000 61.962 50.646 I1SSO911 0000 0o000 0o000 0,000 0,000 0o000 0 o0ono 0.000 o,ono 0.000 0,000 0,000

iLsum 49.465 20.10? 323,310 140,798 561?.72 199.333 275,15? 335.4s87 16s,8 69.369 1472.054 3463,71.2

0OD 4STINATInN 1 2 3 4 5 6 7 8 9 in it RowStM

1 42.974 1.U84 9,645 42.622 16.66 7 2.321 41,253 5.620 0.6%6 1.918 0.616 235.376Z1 In6.574 98,318 104.372 0.088 6,643 P.885 21.253 u.756 b0012 o0883 0,242 352.04?

3 1,454 0.391 176,1RO 6.349 11.5'0 37.161 30.2s8 2.708 0.756 1,243 0,071 218.261

o0ool o.uno 2.691 156.480 '.118 109.003 10.4A4 J.441 0.378 0.390 0.001 289.9570.0ono o.uC0 11.5l 0 0.'402 2A.fil 34.595 20.4!1 !3.o94 0.117 0.60A 0.000 107.481

6 u.o0O o0,oo 14402 0.726 23.413 8;.6C6 21.07h 3S 891 0.206 0.639 0.000 165*1107 0.00 U OU00 2.OAI 0.011 C6.3',4 0.6?9 89,21? 0.874 0,00n4 1.912 0.000 141,066

O U.010 0.000 4.572 0.464 -'i.244 47.820 27.942 1'1.268 0.132 3.029 o,ono !63.'4929 U .O- O,UOO 1.ISO 0.434 L,.1r2 133.97 13.,IQQ i,696 2,309 1.518 * 0,002' I 80.t&2

I

10 ~~~~~0. uoh 0. Ul0 U. 208 0.UO4 1. 5 9 u1 4'3 6 A ¼t'.e, 0. 12b6 U 0,0i 6 9. 9 98 ). 001I 14 1.2 24

ii o*oooV.1) 0U0 0.ooo o.000 ooo 0.0 00O.O I.oC(r 0.000 0.0'PJ" 0.000 0.000 0.000

COLSUM 151.006 99,793 2?4.4Q2 207.580 iAg.552 420.176 344.216 120.463 ;0.1'1i 82.194 0.934 1894.575

GOOD 5DEST'INATION~ 1 2 3 4 5 a,7 8 9 1 ~ 11 ROWSUMURIGIN

1 96.4S6 56,684 33.028 ?1.981 10.640 16.391 13.429 6.4 95 1.363 4.214 0.000 260.7072 46.5A7 39.d21 15.570 7.812 5.034 7.736 6.144 .3.092 0.639 1,821 0.000 136.2563 16.633 20.079 169.273 749433 318.299 53.687 45.365 21.60)5 4.101 11.742 0.000 405,256.4 17.217 8.670 14.711 123.008 24.077 67.201 26.007 20.050' 5.174 7.289 0.000 1333.4035 6.632 6.559 40.5?5 17.006 53.1061 39.306 43.748 19.213 2.951 tu,.761 0.000 239.0636 21.808 19.138 117.001 1029972 65.993 261.910 90.09i 72.15.4 24,339 23,803 0.000 819.s212I 16.572 .19.38? 104.502 43.303 1n0.973 148.277 206.280 43.141 6.432 38.754 O.723 728.3426 8.182 3.242 ?0.06A4 16.686 20.593 35.811 19.884 35.2-36 2.466 5.703 0.000 167.6679 0,794 0.690 4.064 39543 29951 8.502 3.127 2.469 1.354 n.844 0.000O 28.337

2,7 9 3 2,580 76.097 6.543 1 1 .41 8 1 3.7?1 5 21.t361 1 6 .7 16 1 I1 3 2 3 3 .131 0.000 1 33.949311 ~~~~~0.000 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000

COLSUM 235.674 176e850 564.835 367.288 3S3.138 652.S41 475.438 240.172 50.017? ¶.8.061 0.6?23. 3254.738

GCOO 6DESTINATION 1 2 3 4 5 6 7 8 9 1n It ROWSUMORIGIN

1 ~~79,564 37.399 32.292 12.122 9.898 M0M2 13.776 6.116 1.281 3.746 1.441 217.760 2 39.630 4 1.417 22.069 3.458 4.013 7.167 4.981 2.157 0.470 1.070 1.130 12T.56S 'J3 52.969 40.738 308.404 76.292 80.7f4 -161.836- 109.944 48.434 99951 -28.511 1.454 919. 30864 6.952 2.853 24.160 818.986 14.1630 57.306 14.356 11.530 3.368 2,998 o.178 226.686 r5 4 .7 A5 3. 7 4 36 .366 1 2. 751 36.,597 36 .4 05 37.ai145 1 4.-257 2-1 4 3 6. 34 4 0. 253 190.7V516 18.216 13.382 67.257 65.755 51.52r 192.177 57.203 41.440 10.976 13.782 0.659 552.3747 11.657 9.o53 61.493 25.807 47.161 61.565 112.344 24.353 3.7o7 21.169 0.744 379.1138 1.293 I.024 15.674 9.694 l4*Sql 37.275 16.196 21.932 2.094 3.598 0.1o7 i?,I8 9 0,104 0.090 2.463 1.99? 1.667 8.256 1.351 1.434 1.891 0.195 0.010 190457

10 1.351 1.121 12.686 4.331 10.989 12.266 29,734 7.169 0.772 30.154 0.42O1 110.'77511 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

COLSUM 216.461 150.819 602.883 301.193 271.409 594.379 39T.031 178.822 36.693 i~I.S67 6.177 28667454

GOOU IDESTINATION 1 2 3 4 5 6 7 8 9 It it ROWSUMURIGIN

1 39.573 19.022 20.797 13.506 6.414 19.657 11.723 4.060 0.840 2.61A 1.810 140.0172 13.988 12*157 t5.653 8,993 4.603 14.183 8.151 2.884 0.605 1.788 0.861 83.8663 8.971 8.392 86.768 15.339 15.679 27.375 21.811 5.796 1.147 5.681 0.865 197*.8634 17.902 11,699 17.962 50.500 16.310 53.162 32.707 9.431 2.590 6.958 1.325 240.5275 1.074 0.782 4.676 2.692 4.885 14.270 4.179 1.344 0.237 0.846 0.107 35.0426 1 4 .51I0 11.247 48.179 55.921 32.868 159.369 41.240 28.512 6.435 100.1 0 0 1.677 410.0507 6 .6 00 4.809 ?8 .5:76 1 7 .398 l5.162 37.740 6 3.a135 9.o06 1.59)3 8.541 0.538 193.3276 0.226 0.162 0.8$12 0.703 1.641 1.513 0.820 4.210 0.063 0.188 0,024 10.4319 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 .n 0.000ooo 0.000 0.000

tu U.~0098 0.070 o.3A7 0.250 0.194 0.515 0.451 0.132 0*022 1.662 0,013 3,79311 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.000

COLSUM 102.942 68.341 243.819 165.301 97,777 327.764 11a4o23A V).373 13,1153 38.378 7.520 1314.924

G000 8L)ESTINAT1InN I 7 3 5 a, 7 in it R04Sum

1 ~~~~69.679 0.000 (00(0 0,000 0.000 0.00.0 0.000 0.000 0o'son 0.000 0.000 69,67911.013 5I..157 o.00 000 0.000 0.000 0.000 0 .000 0.010o 0.000 0.000 lt 62.271

3, ~~~~0.000 0,000 25i,078 0.000 6.000o 0.000 0.000 0.000 0.0ti0 0.000 0.000 250.0284 7~~~~~.005 0.000 0.2711 t-2.i27 0.0100 0.000 0.000 0.000 0.0010 0.000 0.000 149.90Z

OO 0.000 0, ono000 0.000 83.4.i1 0.000 0.226. 0.000 O.OnC 0.000 0.000 83.6881708?9 35,299 090549 53,907 A7.116 348.78A 0.276& 23.331 9.370 1'.609 0.000 578.0400.000 0,000o 0.000 0.000 0.000 0.000 225.690 0.000 0.0010 10.829 0.000 2359o.00u O.coo 0000(t 0.000000 0.000 0.000 to 64,659 0.0o0 0,000 0.000 64,6590.000u 0.0000 0.0(c0 0.196 2,605 o.153 0.196 0.000 t4909o 0.000 0.000 17.2050.000 0.000 000 0 .000 0.0000 0 .000 0 .000 0 .000i ooo 0.000 30.401 0.000 30.14010.000 0.000 0.00le 0.000 0.0010 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0o s0t 105.926 86.557 270.847 196.331 153.202 348.936 226,319 87.990- 23.426 42.839 0.000 1342,393

0000 9)ESTINA TI-ON 1 2 3 4 5 6 78 9 to 11 ROWSUN

RIG IN1 399,597 77.797 0,220 0.025 0.001 0.000 0.000 0.001 0.000 0.005 0.782 478. 4352 11.648 251,268 4.698 0.037 0.005 0.001 0.002 0.004 0.0O0)1 0.011 0.936 274.6103 10.019 4.612 1193.569 28.999 20.855 2.205 5.021 .8.179 0.594 4,474 14.469 122302?

4 ~~6,785 0.001 0.266 469.768 0.008 0.030 0.001 0.021 0.006 0.006 0.114 477.0o65 1,897 0.102 2t.806 9.488 521.876 4.965 56.354 39.776 0.679 5.294 2.979 646.2946 4.222 0.068 4.455 200.669 2.1.623 1480.004 0.654 88.408 12.983 0.680 19424 1615.1887 3,788 0.350 2.4158 9,100 82.828 2.372 826. -361 19.574 0.944 114.416 18.176 1060.346

8 0.~~~~O309 0.012 o.339 2.*183 8.063 6.,529 0.671i 275.572 0.634 0.432 0.3t6 295.0679 09236 09000 0.117 II.7Z22 0 a1,19 1,.4*66 0.013 0.473 80.388 0.o37 0.173 '84.808

10 ~~~~0.027 0.00 2 0 o.oiS. 0.059 0.214' 0 .012 0,969 0s.496 060,11 129.94 31 0,1 08 131,36311 ~~~~~0,000 0~.0,00 00001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 I

&OLSUM 4-4,4. 5 0 334, 2,9 7 It,8. 9A,6 7722.050 6 3&5.6-81 1 491.584 890.053 4 32. 504 96.259 254-.786 39.476 6486.144 co

0000 1.0DtSTI'NATI,0% 1 2 ~ 3 4 5 `'6 7 8 9. 16 11I RO'4SUNORIGIN

1 20,786 00922 0.11 0,112 0006* 0.055 0,093 0.046 0.00)8 0.03? 0.000 22.23?2 ~~0,5S39 15,54,6 0.470 0.090 0.4066 0.053 0.090 0.044 0.006tl o.034 0.000 16.939

3 0,041 0.085 150.266 0.121 0.526 o.103 0.186 0.105 0.012 o.037 0.000 51,4S24 0.737 0. 092 0.2?3 3'2.873 0.191 n.342 0.196 0.190 0.040 0.067 0.000 34o9535 0.035 0.050 0.142 0.169 29.317 0.286 1.861 0.711 0.019 0.073 0.000 32.72416 v.047 O,. 044 0.1I1I' 0.926 0.295 6o.758 0.0156 0,444 0.0O2 0.038 0.000 62.908

1 OeO0.66 0.092 0.201l 0,239 19448 0.315 371.215 0.298 09026 0.631 0.000 40,5318 ~~~~~0e033 0,036 0.086 0,174 0,376 1.093 0,240 20.541' 0.021 O,Q53 0.000 22.653

9. 0.009 0.008 0.017 0.053 0.030 0..085 0.024 0.034 4.5,50 0.007 0,0000 4.81810 0.034 0.043 0.40 70 0J.098 0.15I3 0.094 014 25 0.1,00 0.014 12,.120 0.000 13,1481.1 o). o0 o.VOO O.Ofono 0.000 0.0 010 0.000 0.000( 0.000 0.000 0.00 0 0.000 0,000

OLS#JM4 22.327' 16.918 51I.*707 34,854 12,5,8a 63. 184 40.487 22.512 4*775 13.098 0.000 302.392

GOO') it)ESTINATIOn 1. 27 3 4 5 -, ,' 8 9 1n it ROWSUMJRIGIN

1 (0.000 0.000 0.000 0.000 n0. 000 0.000 O) 0.000 00 0 0.000 0,000 0.000 0.0001 0~~~~(.000 0.000O 0.000 (.000 0.010 0.00(, '00 (.0 0.0(( 000 0.0 .0

3 u.on0 0.000 0.000o 0.000 0.000 0.000 (.000 0.000 0.0"0 0.000 0,000 0.000

4~ ~~.0 0 .000 0.0)00 on 0.000 0.010 0.000 0l0(0 0.000 0.000 0.000 0.000 0.0000 .o)ov 0.000 0.0%0 00.000 .000 0.000 0.000000 0)0 0.00 -.0 0.000 0.000

I. 0.000~ooo 0. 000 0.000 0. 000 0.0no 0 .0no0 0 .00 0 0.0(00 0.0 0000 0 ,000 0. 000d ~~~~~0.000 0.uoo 0.I0 00 0. 0 00 0. 010 o.ooo0 0. 000 0.000 0 0'C 0.000 0.000 0.0009~~~~~~.( 0.000 000 0.000 0 0 000 U. 000 0.0(00 on O 0. 000 0 ,0 "I 0. 000 n.00o0 0 00 0

~~~~~~~10 .000 0. 000 0.9000 0.000 U.0On0 0. 000 0. 000 0.000 0. 001) 0. 000 0.000 0.00011 ~~~~II0115 0 8. 476 7 1 , A2 1 4,9 35 13 .3117 26.,6 45 2o). 755 9. ;A.9 I .995 6. 030 0.0000 1 3 4.444

COLSUM I4 115 0 8.44 76 '1t, 78 2 14.935 1 3. 37 26.645 20 . 55 9. 289 1.995 6.030 0.000 134.444

GCOOI 12DESTINATION 1 2 3 4 5 6 789 I0 11I ROWSUNORIGIN

I 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.0", ) 0.000 0.000 0,0002 0000 0000 0 .000 0 .000 0 .000 0 .000 0.000 0.000 0 .000oon 0.000 0.000 0.0003 0.000 0.000 0.000 0,000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.0004 0.000 0.000 0.000 0.000O 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.00.0

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 ~0.000 0.000 0.000 0.0006 ~~~~0,0000 0.000 0,0000 0.0000 0.00000 00 0.000 0.000 0.000 000 0,0 .0

7 0.000 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0006 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.0009 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.00010 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000

11 7.a;j 5.695 16.465 10.662 10.831 18.380 13.636 7.229 1.478 4m112 0.000 95.959

COLSUM 7.491 5,695 16.465 10.662 10.831 18.360 13.636 7.229 1,47'8 4.112 0.000 95,959

GOOO 13DESTINATION 1 2 3 4 5 6 7 89 10 it MM#UMORIGIN

I 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0,000 0.00-02 0,000 0.000 0.000 0.000 0.000 0.000 0.a000 0.000 0.000 0.000 0.000 0.000 \3 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 4 0.000 0.000 0.000 0.00O0 0.000 0.000 0.000 0.000 06000 0.000 0,000 0.0005 0.000 0.000 0.000 0.6000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0006 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0,0007 0.000 0.000 0.0000 0.000 0.000 0.000 0.0000 0.000 0.000' 0.000 0.00o 0,0~08 0.000 0,000 0.000 0,000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0009 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.000 0.000 0.000

to 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,000 0.000 0.000 0.000 0.00011 16.,513 11.807 80.759 21,347 20.221 41,006 29,677 13,096 2,591 8.102 0.000 205.119

COLSUm 16.513 11.807 40,759 21.347 20.221 41.006 29.677 139096 2.591 6,102 0.000 205,119

GOOD 14DESTINATION 1 2 3 4 5 6 7 to 1 11 ROWSUMORIGIN

I 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0,0002 0.00 0000 0.000 0 .000 0,000 0,000 0.000 0.000 0 .000 0 .000 O.O 0,000 0.0003 0.000 0.000 0.000 0.000 O( 0.000 0.000 0.000 0.00 0 0.000 0 .000 0000.0004 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0,0005 0.000 0,000 0.000 0,000 0.000 0.000 0,000 0.000 0,000 0.000 0.000 0.0006 0,000 0.000 0.000 0.000 0.000 0,000 o.odo o.ono 0.000 0.000 0,000 0,0007 0.OOu 0,000 0.000 0.000 0,000O 0.000 0.000 0.000 0,0000 0.000 0,000 0,0008 0.000 0,000o 0.000 0.000 0,000 0.000 0.000 0,000 0.-000 0.000 0,000 0.0009 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

10 ~~~~~0,000 0.000 0.000 0,000 0.000 0000 0.000 0 .000 0 ,000 'n 0.000 0,000 0.00011 ~~~~100,904 78,890 214,161 217,88o 73,5?2 315.520 !72.654 131.8919 l2.F-)0 36.011 0.000 1274.250

COLSUM I0G.9n4 7A. d 9 0 21'4.i6i 217.88o 73.522 315.520 172.654j 51.819 l:.'u 3-6.011l 0.000 1274.250

- 60 -

Appendix B

Data Requirements

Although there is a large data requirement, it is basically the samerequirement as needed in conventional transportation analysis. The volumeand type of commodities to be shipped with the origin and destination, thephysical characteristics of the transporta1ion links and the physicalcharacteristics of the vehicles are needed.

The data needed for the disaggregation portion of the model, if used,ist

1. Supply of Commodity by region and season;2. Demand of Commodity by region and season;3. Subcommodity production as a percentage of the commodity output;4. Subcommiodity production by node as a percentage of the regional

production.

This portion of the model may be by-passed if the macro-economicmodel is not utilized. If it is desired, the supplies and demands of thesubcommodities may be placed in the model directly eliminating thedisaggregation process altogether.

- 61 -

Appendix C

Network Data Requirements

The network data requirement is made up from the data as used in theLink Performance Models. In fact, the same data as is required in eachof the Link Performance Models is used for the Network Xodel. The datautilized is called the Link Characteristic Vector and includes the following:

Hi igb.way R_fi Transfer

Dis,ance Distance No. berths (incoming)T'ype Surface Max Speed No. berths (outgoing)Jesigr. Speed Min Speed Loading ratesRise ancd Fall Ruling Grade Unloading ratesLane Width Average Grade Crew sizeNo. of Lanes Type Signals

No. SidingsType LocomotiveNo. Loco per Train

Operating cost and vehicle characteristic data is also needed for eachof the models.

Highway Rail Transfer

Weight Weight (Loco) Crew SizeHorsepower Horsepower Crew WagesPayload Frontal Area Fixed Terminal CostsNo. tires No. Drive AxlesTire Life Payload (Cars)Vehicle Life Weight (Cars)Crew Size Fuel ConsumptionInitial Cost Loco CostInterest Rate Car CostTire Cost Fuel CostCrew Wages oil CostFuel Cost Way maintenanceMaintenance Cost Car LifeOil Consumption Yard TimeFleet Size Handling TimeDepreciation Rate Capital Recovery Factor

Locomotive LifeFleet SizeDepreciation Rate

- 62 -

The model is now limited to the three Link Performance Models andutilizes a cost per ton feature for the pipeline, air and inland waterwaymodes. If the application of the model warrants an in-depth analysisof these other transportation modes, more detailed models could be designed.

The Harvard Group used both direct and indirect costs in theirconsideration of determining the optimal allocation of traffic among modes.The data for the indirect considerations include the travel time costs,waiting time costs, shipping time variability costs and probability of losscosts; then the shipping tariffs are the direct charges. These five factorswere combined for each conmodity and called the Commodity Preference Vector(CPV). See pp. 17-21.

If the indirect costs are not available, two options are available:

1) Deal only with the direct Co0ts or2) Estimate the total indirect costs by each mode and for each commbdity.

However, this inclusion of the indirect costs into the total shipping chargesis essential if the total effect. in changes to the transportation system areto be meaningful. Therefore efforts should be made to collect data on theindirect costs incurred for the different commodities.

- 63 -

Appendix D

TRANSPORT DICTIONARY

AVATOT (MODE, ICIAS) the number of vehicle hours available

C1 waiting time in route, in hours

C2 link travel time, in hours

lCJ time variability, in hours

probability of shipment loss

c5 transportation charge in $/ton (see LPV)

CONFAC (M,I) an input constant factor

COST (M,N) the cost of transporting the subcommodity from M to N

COSTS (MODE, ICLAS) the total cost

CPV(K) commodity preference vector (see W1 - w )

CUMR the sum of the R-factore incurred in shipping from thesupply point to the demand point

DAYS (IS) the number of days in a season

DEFICIT (MODE,ICLAS) vehicle deficit (surplus) in vehicle hours

DEMAND (I,M,J) aggregate demand by industry J or sector I in region Mfor the output of industry I

DEMAND (N) the demand for the subcommodity at node N

DEPRAT (MODE, ICLAS) depreciation rate

DESRAT (MODE, ICLAS) desired ratio of vehicle actual requirements toavailability

EXP an empirically determined exponent

FLOW(M,N) the flow of the subcommodity from M to N

HRPDAY (MODE) the hours worked each day by vehicles of this mode

i links

I industry I:

ICLAS vehicle class

INODE beginning node

- 64 -

IRATE table a table containing information on the unloading and loadingrates in tons per hour, the normal working hours of thefacility per day, the maximum number of workers employed ateach loading or unloading berth, the average basic wageof the labor force per hour, the fixed operating cost for thefacility per day and the variable operating cost for thefacility per hour, the wage multiplier for computing over-timewages and the probability of loss associated with handlingcargo by means of this technology.

IS season

J a chain made of links, i, which form a single path, out ofthe set of all possible paths, J.

J industry J

JNODE end node

K subcommodity K (a component of aggregate commodity I)

K2 subsector K2 (a, component of industry J)

L iink L

LCV link characteristic vector

LPV(L) link performance vector (see C - C )

LUV link utilization vector

M region M

MODE mode

MSYS number of modes

NODE point of production. (located within a region)

NSEZNS number of seasons

RATIO (MODE, ICLAS) ratio of requirements to availability

REQTOT (MODE, ICLAS) total vehicle hours required to accomplish the goodsmovement undertaken by the system

REVNUE (MODE, ICLAS) total revenue

RFAC(L,K) R-factor is the product of the link performance factorsand the commodity preference ratings associated with eachof those factors (see CPV and LPV)

SUBCCM (K,NODE) the proportion of the regional production of industry Iwhich is due to the production of subcommodity K at locationNODE (an exogenously supplied subcommodity disaggregation factor)

SUBDEK (K,NODE) the demand for subcommodity K at location NODE

SUBSUP (K, NODE) supply of subcommodity K produced at NODE

SUPPLY (I,M) aggregated supply of subcommodity K produced at NODE

SUPPLY (M) the supply of the subcommodity produced at node M

TERIML (MODE, ICLAS) total time which vehicles in this mode and class spendloading and unloading at origin and destination nodes

TONMI (MODE, ICLAS) total number of ton miles carried

TRAVEL (MODE, ICLAS) total time which the vehicles in this mode and classspend traveling, including seasonal delays in route

TRINVS amount to be invested in vehicles

TRNSFR (MODE, ICLAS) total time which the vehicles in this mode and class spendloading and unloading at transfer links

VALVEH (MODE, ICLAS) value of each vehicle

VEHCLS (MODE, ICLAS) the number of vehicles of this mode and class in the system

VEHCIS t+l(MODE, ICLAS) net number of available vehicles for the next period

VEHDEF(MODE, ICLAS) vehicle deficit, in vehicles

VEHDEP (MODE, ICLAS) total depreciation for all vehicles in mode (M) and class (I

VEHMI (MODE, ICLAS) total system vehicle miles

VEHNEW (MODE, ICLAS) new vehicles added to the fleet

VSCRAP (MODE, ICLAS) equivalent vehicles scrapped

W cost of waiting, including loss or damage due to1 waiting, in $/hr/ton

W2 cost of time spent traveling, including losses duringtravel, in $/hr/ton

w3 cost due to uncertainty of arrival time, in $/hr/ton

Wh cost or value, in $/ton of commodity

w5 commodity rate factor (usually 1.0) (see CPV)

WAIT (MODE, ICLAS) total time which the vehicles of this mode and classspend waiting while switching, changing drivers, encounterindelays in cities, etc.