Pergamon 0305-0548(95)00047-X

Computers Ops Res. Vol. 23, No. 4, pp. 393-404, 1996 Copyright 1996 Elsevier Science Ltd

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EFF IC IENCY OF TRUCKS IN ROAD CONSTRUCTION AND

MAINTENANCE: AN EVALUATION WITH DATA

ENVELOPMENT ANALYS IS

Lennart Hjalmarsson* and James Odeck ~ Department of Economics, Goteborg University Grteborg, Sweden

Scope and PUrlmSe--This study investigates the efficiency of trucks in road construction and road maintenance. Efficiency is defined relative to a benchmark in the form of best-practice trucks. For every truck, not serving as a best-practice benchmark itself, its benchmark is derived within the framework of Data Envelopment Analysis (DEA). With the same approach distance measures i.e. efficiency scores, are calculated. A main attraction with this approach is that it is possible to handle multiple input-multiple output technologies. The efficiency scores measure different aspects of a truck's performance relative to its best-practice benchmark (potential input saving, output augmenting etc). We shall calculate efficiency at the production unit level (the truck) and then, since the choice of output variables may be controversial, compare the stability of efficiency rankings between different choice of output definitions. Further, we shall investigate the impact of other factors such as the vintage year of the truck, make and model of the truck and its area of operation. The data set consists of heavy trucks, owned and operated by the Norwegian public roads administration.

Abstract--This paper focuses on the performance of trucks involved in road construction and maintenance, and operated by the regional agencies of a national public roads administration. The performance is evaluated from the productive efficiency point of view. The framework is that of a deterministic non- parametric (DEA) approach to efficiency measurement. In this context several important issues are addressed: efficiency ranking and distribution among trucks, the importance of an appropriate output measure, impact of regional characteristics and the significance of the make and model of the trucks.

1. INTRODUCTION

In this paper we evaluate the performance of heavy trucks, owned and operated by the Norwegian public roads administration (PRA) from the point of view of productive efficiency.

PRA is responsible for approximately 40% of all road construction and 80% of road main- tenance in Norway. It is subdivided into 19 branches (or agencies) each performing road construction and maintenance within its assigned region. Each branch owns a number of machines that are used in its activities in the region and are orgainzed as an entity (office). This is done to ensure adequate machinery and material supplies for the construction and maintenance units. The fleet of machines comprises heavy trucks, tractors, excavators etc. There is a total of 50 machine groups of which "heavy trucks" is one of the 3 largest. Heavy trucks are used both in road construction (in transportation of mass from rock blasting, transport of asphalt, sand etc.) and in road maintenance, notably snow plowing.

In the recent years, the public sector in Norway, as in many other countries, has been criticized for not performing as well as it should in providing services. A recent report by a government commission shows that there is a great potential for increasing efficiency in providing infrastructural services. One way to realize the potential is to identify the causes of inefficiency within a sector. A

*Lennart Hjalmarsson is currently Professor of Economics at Goteborg University, Sweden. His main research fields are industrial economics, productivity, production theory, energy economics and deregulation. His list of publications include 12 monographs and edited books, more than 20 articles in international journals and a large number of contributions to edited books.

S James Odeck is currently economist with the Norwegian Public Road Administration in Oslo, Norway. He holds his Ph.D. from Goteborg University, Sweden.

393

394 Lennart Hjalmarsson and James Odeck

first step may then involve an evaluation of micro units of the sector, e.g decision making units of the road sector, and find out how these units perform. By relating the performance of units to one another and identifying the most efficient units, benchmarks or yardsticks are provided. If such efficiency scores are made public, the inefficient units may be encouraged to adopt the technology of the efficient ones and hence increase efficiency in the sector as a whole (so called yardstick competition).

In this study efficiency measures for the utilization of trucks in road construction and main- tenance are computed within the framework of a deterministic non-parametric model, Data Envelopment Analysis (DEA). We shall calculate efficiency at the production unit level (the truck) and then compare the stability of efficiency rankings between different output measurements. Further, we shall investigate the impact of other factors such as the vintage year of the truck, make and model of the truck and its area of operation. Efficiency calculations and the subsequent comparisons are done for all the 72 units, spread all over the country and performing the same set of tasks.

Applications of DEA in the measurement of efficiency are now abundant. For a more extensive bibliography of DEA studies, see [1]. Applications on the road sector are, however, rare. To our knowledge the closest one gets to the road sector in this extensive literature is [2] on ferry services, and [3] on maintenance patrols.

The rest of this paper is organized as follows: Section 2 presents the methodology and Section 3 the data along with discussions on the different output measures. The empirical results are presented in Section 4, while concluding remarks are in Section 5.

2. METHODOLOGY

The DEA method is closely related to Farrell's original approach [4] and should be regarded as an extension of this approach initiated by Charnes et aL [5] and related work by F~re et al. [6]. In this approach the efficiency of a micro unit is measured relative to the efficiency of all the other micro units, subject to the restriction that all micro units are on or below the frontier.

The Farrell measures are illustrated in Fig. 1 where a one input (x) and one output (y) production activity for which statistical data are available (e.g in cross-sectional form) is assumed. The frontier technology with variable returns to scale is XAABCD and the frontier with non- increasing returns to scale is OBCD. The constant returns to scale (CRS) frontier is the ray from the origin through point B.

In measuring efficiency we adopt the system of efficiency measurement introduced in [7]. This system is a generalization of Farrell's measures to a variable returns to scale (VRS) technology. The efficiency measures for any unit in K in Fig. 1 are given as:

(i) E1 = Xj/XK, input saving technical efficiency (VRS) (ii) E2 = Yk/YL, output increasing technical efficiency (VRS)

(iii) E3 = XI/XK, gross scale efficiency (input saving when (CRS)) (iv) E4 = E3/E1 = XI/X~, pure scale efficiency (input corrected) (v) E5 = E3/E1 = YL/YM, pure scale efficiency (output corrected).

The input saving measure shows how large a proportion of the observed input would have been necessary for the output quantity observed if the unit in question had been moved to the efficient frontier. The output increasing efficiency measure compares the actual output produced to that of a unit at a point on the production frontier that uses the same amount of input. These measures are such that the efficient units will have a value of 1 and the inefficient ones will be less than 1. As an example, a point such as J in Fig. 1 will, under VRS be input saving efficient since the efficiency measure is Xj/XI = 1. Point K will be both input saving and output increasing inefficient since Xs/X K < 1 and YK/YL < 1. When technology is CRS, the input saving efficiency measure coincides with the gross scale efficiency. This can be seen in Fig. 1 for point K where both measures are calculated as XI/XK.

Once input saving, output increasing and gross efficiencies are obtained, pure scale efficiencies are calculated as in (iv) and (v) above (E4 = E3/Ea and E5 = E3/E2).

Efficiency of trucks 395

Scale properties, for a unit i, are expressed as follows, see [7]:

Eli > g2i indicates that the unit is performing with increasing returns to scale Eli < E2i indicates that the unit is performing with decreasing returns to scale Eli = g2i Indicates that the unit is performing with constant returns to scale.

2.1. Computation of the efficiency scores

Compared to Farrell's approach, DEA offers a more operational framework for the estimation of efficiency; efficiency is calculated separately and directly for each production unit in turn, while at the same time the location of the corresponding linear facets is determined.

Calculating efficiency measures as defined above is trivial as long as the production activity consists of only 1 input and 1 output. In order to handle more than 1 input/output, it has been shown, notably in [5], that a linear programming problem (LP) can be solved for each unit at time.

The input saving measure is found by solving the following LP-problem for each unit, k, with output Yk and input Xk, to obtain the input saving measure under VRS (where Ak is a vector containing the non-negative weights, Akj, which determine the reference point):

rain Eak (1)

Ak

subject to the following restrictions

y.k

396 Lennart Hjalmarsson and James Odeck

When efficiency is measured along a ray from the origin a micro unit may turn out as fully efficient, although it is not fully efficient in the sense that it is dominated by other units (regardless of assumption about scale property). In empirical applications this can be controlled for by inspection of the slack variables.

The output increasing efficiency measure is achieved by restricting the reference point on the unknown frontier to employing the same amount of input(s) as observed for unit k. The efficiency scores are obtained by the following LP-problem:

1 max ~72k w.r.t (2)

1 N (2a) EzkYrk~ zN,~kjXij, i = 1 , . . . ,n (2b)

zN,~kj = 1 (2c)

),ej 1> 0, j = 1, . . . , N (2d)

where E2k is the output increasing efficiency measure for unit k. The rest of the variables are defined as in (1-ld). Restriction (2a) states that the efficiency corrected volume of output [(1/E2k)Yrk] must be less than or equal to the amount of output produced by the reference unit. Restriction (2b) states that the amount of inputs used by unit k must at least equal the amount of input used by the reference unit. Restrictions (2c) and (2d) are interpreted as in (lc) and (ld). Observed outputs, r = 1 , . . . , m, of unit k will now be efficiency adjusted proportionally upwards to be less or equal to output at the frontiers reference point, where at least one output equals the reference point.

Since scale inefficiency is due to either decreasing or increasing returns to scale, one can easily determine the case by inspecting the sum of weights, S:

s = (3)

for the E1 calculations with CRS technology. If this sum is less than one we have increasing returns to scale (both at K and at the adjusted point J at the VRS frontier), and if it is larger than one we have decreasing returns to scale.

Banker et al. [8] defines a specific scale measure termed Most Productive Scale Size (MPSS). MPSS is obtained as:

Mess = E3 (4) ~_dN_-i Akj

The relation between the actual scale and Mess is that for units exhibiting increasing returns to scale, input saving efficiency improvement will move the unit further away from MPSS. The implication is that the units are encouraged to increase their activities rather than reduce them.

Some caution is in order concerning DEA as a technique for efficiency measurement. Since DEA yields relative efficiency measures and defines a unit (in this case a truck) as ineffective by comparing combinations of input and output with other units, units operating with input-output quantities sufficiently far from the other units at both ends of the size distribution will be identified as efficient due to the lack of comparable units. Problems of this kind are, however, minimal if the sample size is large in comparison to the number of inputs and outputs. This is because larger samples decrease the average level of efficiency, due to the positive probability of including more efficient outliers in the sample.

3. THE DATA

For the analysis we have used 2 sets of data available in the PRA's data base involving trucks of

Efficiency of trucks 397

vintage 1983-1985. The data are collected and monitored by the regional branches according to a standard set up by the PRA.

The first data set is the yearly accounts of costs associated with the running of each truck. The following comprises this data set:

- - model year (vintage) of the truck - - make and model of the truck - - capacity of the truck in tons - - region of operation - - wage costs of the driver per year - - fuel costs of the truck per year - - cost of rubber accessories (tires, belts etc.) for the truck per year - - maintenance costs for the truck per year (excluding rubber maintenance equipment).

All costs are expressed in Norwegian currency (NOK). The capacity of trucks is, however, fixed (all at 16.5 ton) for the whole fleet of trucks. These data are available for 72 units.

The second data set contains tasks performed by each of the 72 trucks. This data set consists of:

- - transportation work in kilometers per year - - volume transported in cubic meters per year - - effective hours in production per year (i.e excluding stoppage time).

3.1. Inputs The accounting data given above cover all the costs related to running a truck with the exception

of fixed costs. Fixed costs are not registered and it is difficult to obtain them. The insurance premium, being one of the major components of fixed costs could have been used as a proxy. However the insurance companies informed us that a difference of 3 yr (note that our data comprise of trucks of model (1983-85) is insignificant when considering insurance premiums. Therefore the fixed costs are excluded.

The driver's wage is measured as the annual driver's wage given in the accounts. Each machine employs only one type of labour (the drivers) and hence the problem of heterogeneity does not arise. Since the machines are publically owned, the drivers are on the same wage scale. The price of labour is therefore not expected to vary by units due to variations in local labour markets.

Concerning fuel, although we have no liter prices, the information gathered indicates no variation in price per liter across units or regions.

The cost of rubber accessories (tires etc.) is registered separately from the maintenance costs. For an ordinary vehicle, these 2 cost components should be aggregated together. Itere, they are kept as separate inputs because rubber accessories for trucks tend to vary according to kilometers covered and most importantly, volume of the mass transported.

There is no reason to expect variation in maintenance and rubber costs across units and regions since prices for most of the services are standardized throughout. The analysis is therefore carried out with 4 inputs, wage (W), fuel (F), rubber (R) and maintenance (M). As is evident from Table 1, wages are by far the largest single input followed by maintenance.

3.2. Output The traditional output measure of transportation work is the transported volume of mass times

kilometer, i.e. tonkm. The trucks belonging to PRA perform several tasks both in maintenance and construction of roads. These trucks generally transport massess during construction but they also plow snow during the winter season. The volume of mass transported (snow plowed) is, however, not registered in maintenance operations. Thus, tonkm cannot be applied as an output measure.

Therefore, we have chosen to use 2 alternative output measures: Total transport distance (KM) and effective hours in production (EH). While the latter measure reveals the degree of capacity utilization of the trucks the first measure is a more direct output measure.

An overview of the input and output variables used is given in Table 1.

C~OR 23:4-G

398 Lennart Hjalmarsson and James Odeck

Table 1. Summary statistics of inputs and outputs

In NOK1000 W F R M EH KM

Sum 20718603 3112910 4616280 6742941 130888 2555128 Avg 287758 432354 64115 93652 18t8 35488 Min 4293 7051 11441 12789 252 8158 Max 553084 114699 146389 247478 3263 76537 S.D. 100606 20715 29056 53386 582 15982

4. EMPIRICAL RESULTS

For each truck in the sample, the LP-problems (1) and (2), outlined in Section 2, were solved with and without constraint (lc) and for the 2 alternative output measures.

4.1. Efficiency results We use the Farrell measures to compare observed performance with potential frontier perfor-

mance, keeping the factor inputs or outputs as observed. The 3 types of efficiency we calculate in this paper are those illustrated in Fig. 1.

The distribution of E 1 (VRS) for both the alternative measures of output are presented in Figs 2 and 3. Each histogram in Figs 2 and 3 represents a unit (truck). The size of the truck, as measured by output is represented by the width of the histogram normalized by the output shares.

The input saving efficiency distribution E1 (VRS) when output is measured by kilometer transportation work, presented in Fig. 2, shows that the most efficient trucks represent about 25% of total output. The efficiency values then decrease evenly down to about 0.6 then continue falling rapidly to the least efficient unit with an efficiency value of 0.36.

For effective hours in production (EH) as an output measure, the values of E1 (VRS) in Fig. 3 indicate that the most efficient trucks represent about 30 of total output. Compared to KM-output, the efficiency values fall at a slower pace and ending at the least efficient truck, measuring 0.63 and, representing about 2% of the total output. In total, there are 13 efficient trucks under KM-output as compared to 24 under EH as output measure.

A summary of results for all the computations using the two alternative output measures are given in Tables 2 and 3.

Consider first the input saving efficiency measure when variable returns to scale technology is imposed, i.e El in Tables 2 and 3. This measure indicates the input saving potential for the individual truck had frontier technology been employed. The results in Table 2 show that if frontier technology

l0' 0.9

0.8

0.7

0.6

0.5.

0.4.

0.3.

0.2.

0.1

E 1

10 20 30 40 50 60 70 80 90 Output shares

100 -~ %

Fig. 2. The distribution of E~ - VRS with KM as output measure.

Efficiency of trucks

1.0t El

0.9 0.8

0.7

0.6

0.5

0.4 0.3

0.2 0. : : .'-

0 I 10 20 30 40 50 60 '70 80 90 100 Output shares

Fig. 3. The distribution of E I - VRS with EH as output measurc.

%

399

had been imposed, the average truck and the least efficient truck could have covered the observed annual distance with only 76 and 36% of the inputs, respectively.

The values in Table 3 indicate that there is potential for input saving of 12% for the average truck, i.e. the average truck could have managed the observed annual effective hours in production with only 88 % of the inputs (i.e wage, fuel, rubber and maintenance) if the frontier technology had been employed. The least efficient truck could have managed its observed output with only 64% of the observed inputs had it adopted the frontier technology, i.e. the potential for input saving achieved by adopting frontier technology is 36% for the least efficient truck.

Consider now E2 which is the ratio of observed output to potential frontier output, keeping the level of input unchanged. Table 3 shows that the outputs for the average and the least efficient trucks could have been increased by 11 and 47/0 respectively had frontier technology been employed. When the output specification is changed to annual kilometers travelled, these measures are at 23.5 and 170% for the average and the least efficient truck, respectively.

Turning to the gross scale efficiency measure (E3), which can also be interpreted as an input saving efficiency measure for the constant returns technology (see Section 2), we find the values to be lower than those of Ea and E2. The potential saving assuming CRS technology are always greater than potential savings assuming a VRS technology, simply because the envelope, under a VRS assumption, will wrap data more closely (i.e. more units are efficient/define the envelope) than under a CRS assumption.

Table 2. Summary statistics for efficiency measures and scale indicator (effective hours in production as output measure)

E1 E2 E3 E4 E5 Scale MPSS

Mean 0.88 0.90 0.82 0.93 0.91 1.51 0.70 Min 0.64 0.68 0.55 0.58 0.58 0.23 0.20 Max 1.00 1.00 1.00 1.00 1.00 3.46 2.40 S.D. 0.10 0.09 0.12 0.08 0.08 0.71 0.47 Weighted mean 0.89 0.90 0.82 0.92 0.90 1.64 0.83

Table 3. Summary statistics for efficiency measures and scale indicator (distance in km as output measure)

El E2 E3 E4 E5 Scale MPSS

Mean 0.76 0.81 0.64 0.85 0.79 1.36 0.65 Min 0.36 0.37 0.29 0.56 0.50 0.26 0.18 Max 1.00 1.00 1.00 1.00 1.00 3.45 3.17 S.D. 0.18 0.16 0.17 0.13 0.13 0.66 0.55 Weighted mean 0.80 0.84 0.67 0.84 0.80 1.59 0.88

400 Lennart Hjalmarsson and James Odeck

Input and output adjusted pure scale efficiencies, E4 and Es, are obtained by dividing E3 by E 1 and E2 respectively. The tales depict that these scale efficiency measures follow the same pattern as the other 3 measures of efficiency under the 2 alternative measures of output. There is obviously no severe scale efficiency problem in this industry. Technical inefficiency accounts for the largest potential of efficiency improvement.

When less than one, the scale indicator "scale", in both Tables 2 and 3 indicates an output smaller than the optimal scale, but larger than the optimal scale when it is larger than one. The results in the tables indicate that an average truck is larger than the optimal size. This implies that an average truck will be more productive had the unit been smaller, i.e. the utilized capacity of an average truck is too large relative to the tasks that it performs irrespective of output specification. On the other hand, the magnitude of this efficiency loss is fairly small as indicated by the small difference between the gross scale efficiency, E3, and the pure scale efficiencies, E 4 and Es.

The results of the MPSS measures in Tables 2 and 3 show that the optimal level of inputs for an average truck should be smaller than observed, i.e. 65 and 70% of the observed input for KM and EH as output measures respectively.

These unweighted figures are averages that exert equal importance to small and large units. In order to obtain a proper picture of the stock of trucks as a whole weighting the different results with some measure of size is required. In Tables 2 and 3 the output related measures i.e. E2 and Es, have been weighted with total output. The input related measures, i.e. E 1 and E4, have been weighted with total input while E3 and S are weighted with total output. The tables reveal that the weighting improves the average efficiencies and scale but only slightly and not consistently.

The following conclusions can be drawn. First, there is a notable potential for efficiency gains among trucks due to technical inefficiency, much less so due to scale inefficiency.

Second, since we are comparing observed performance with potential frontier performance keeping the inputs or outputs as observed, the difference in potential efficiency gains is present between technologies. On average E2 > El, implying decreasing returns to scale for the average unit in the sample; see [7]. This observation is consistent with the mean of scale measures which are found to be greater than 1.

Third, the values of efficiencies depend upon the choice of output measure. On average measuring output by effective hours gives a higher level of efficiency measure in comparison to distance in kilometers. The explanation for this is that the effective hours in production are highly correlated to wages (which is also the largest input) as opposed to distance driven in kilometers. We note that the use of fuel and rubber varies in the opposite direction i.e. more with distance driven than with effective hours in production.

4.2. Potential efficiency gains To measure the input saving and output increasing potential for this fleet of trucks as a whole,

sector efficiency measures t may be used. These measures are defined as follows:

I1- ZsyJ (5) Yl

Zs e2j(t) where

I1 is the output increasing potential for the fleet of trucks yj is output for truck j E2j is output increasing efficiency measure for truck j t is technology (either CRS or VRS)

I2 ~-'dxijElj(t) (6) -- ~ xo"

tin [9] the input and output saving potentials for the whole sector are calculated as individual measures by entering the average as a unit. These measures are termed structural efficiency and are denoted by Si. To avoid confusion in calculation, we denote the measure applied in this paper by Ii.

Efficiency of trucks 401

where

12 is the input saving potential for the fleet of trucks x/j is input i for truck j Elj is the input saving efficiency (VRS) for truck j.

Equation (5), thus, measures observed output in relation to potential output, while (6) measures potential input in relation to observed input. The percentage by which total output can be increased is then calculated as (100/I1- 1)100. The percentage measure for input saving potential is calculated as (1 - 12)100. The values obtained for 11 and 12 are given in Table 4.

On average, we find that when measured by effective hours in production (EH), output could be increased by 25 and 12.4%o for CRS and VRS technologies respectively. When output is measured by transportation kilometers (KM) the potential for increasing output is 59 and 23% for CRS and VRS technologies respectively. The difference between technologies is quite large, 12.6% for EH and 36,/o for KM. Comparing the 2 alternative output measures, the values for EH are higher than the values for KM. This implies that kilometers as an output measure yields lower total gains.

When CRS is imposed, smaller gains are obtained in comparison to VRS independent of output measure. This latter observation conforms with our previous observation that the average unit does not operate at constant returns to scale (in fact at decreasing returns to scale).

The potential input savings, 12, when technology is VRS are about 22 and 12% for KM and EH respectively. As the results illustrate, the effect of different factor proportions on input savings is rather small. Once again KM yields lower gains. In terms of levels, the input potential (VRS) for savings is greater than the potential increase in output.

4.3. Sensitivity analysis How robust are the efficiency scores with regard to output measures and technology assumption.

One measure of robustness is the extent of similarity in ranking i.e. the correlation between the efficiency scores for different model specifications. Therefore, Spearman's ranking correlation coefficient for pairwise comparisons of different model specifications was calculated.

In general, the rank correlation coefficient is fairly high, about 0.75, for comparisons between CRS and VRS technology for the same output measure and efficiency measure. On the other hand, there is only a weak correlation in ranking between the 2 output measures, with the same technology. To take one example, in the CRS case the rank correlation coefficient for a comparison of the E1 measure for the 2 output measures, EH and KM, is 0.24. Thus, it matters a lot for the efficiency ranking which output measure is chosen.

4.4. The importance of background factors 4.4.1. The significance of the brand type and vintage of the trucks. The brand type of the trucks is

also of interest. Our data set provides this piece of information. Out of the 72 trucks analyzed there were 54 Volvos, 9 Saab Scanias, 3 Mercedes Benzes and 3 M.A.Ns. Thus, trucks of the Volvo type dominate the sample.

In testing the significance of brand type, Volvo trucks were compared to a set of all the other vehicles in the group. A Mann-Whitney test was then carried out to compare the efficiency rating of

Output = KM

Output = EH

Tab le 4. Sector eff ic iency measures

11 /2

t = CRS 0.63 t = VRS 0.81

t = CRS 0 .80 t = VRS 0,89

0.78 i = W 0.78 i = F 0.76 i = R 0.76 i = M

0.88 i = W 0.87 i = F 0.87 i = R 0.88 i = M

402 Lennart Hjalmarsson and James Odeck

the 2 populations. The results indicate no influence of make on efficiency level irrespective of the choice of output variable.

A common assumption is that old trucks require more inputs (repair, lubrication, consumes more fuel etc.) in producing the same output than newer vehicles. Our data comprise of trucks of 3 different age groups: those produced and set into operation in 1983, 1984 and 1985. A Mann- Whitney test on the influence of age on performance was also carried out.

The result shows that the model of truck does not significantly influence vehicle performance. No test could be rejected at the 10% significance level. An obvious reason here is that a 3yr age difference is not long enough period for trucks to perform differently on the basis of age.

4.4.2. Regional comparison of efficiency measurement. When investigating the performance of trucks in the road sector and when these trucks are both used in maintenance and construction, some regional aspects need to be considered. For a start, in maintenance services such as snow plowing there will always exist differences across regions for instance in terms of cubic meters of snow plowed annually. This is mainly due to differences in climatic conditions. As regards construction, the distance driven by trucks depends on the amount of mass being transported and their place of disposal. As an example, regions along the Norwegian coast are mountainous and hence rock blasting is more common. Tunnel construction is common in these areas. This implies that a much larger amount of mass transported here than in other regions. One might then expect regional differences in efficiency.

The data set allows for regional comparisons. For this purpose we have aggregated the data to only 2 regions as follows: regions along the coast which also have relatively low annual snow fall and the non-costal regions with relatively high amounts of snow fall. Again, a Mann-Whitney test is performed. The results presented in Table 5 indicate that the observed differences in efficiency between regions are all significant at the 1% level for measures apart from E1 (VRS) and E2 (VRS) when output is KM, and E1 (VRS) when output is EH. These results indicate that the region factor is important when measuring efficiency across regions.

The figures in Table 5 show that when output is measured by KM, the mean efficiency in the coastal regions are higher than in the inland regions. When output is measured by effective hours worked the result is the reverse. An explanation here is that trucks are disposed differently in the different regions, i.e. in costal regions they do more of mass transportation while they perform more of snow plowing in the inland regions.

4.5. The frontier units A main purpose of calculating efficiency scores is to get ideas for improving the performance of

the ineffective units relative to the best practice units. It is, therefore, quite important that the best practice units and their properties are revealed. In Table 6 the frequency of occurrence on the frontier by efficiency and output measure is presented.

Let us first look at the dominating units relative to the output measure. When output is measured by KM, 3 units dominate (unit 28, 54 and 71) under all technology restrictions. However, when VRS technology is imposed units 41, 45 and 50 also become dominant. Changing output measure to EH increases the number of dominant units (and also the number of efficient ones) under all specifications of technology. The most dominant units are 8, 24, 54 and 63. It is only 1 unit that is dominant under both output measures (unit 54). Again there are more frontier units when VRS

Table 5. Test of the impact of regional differences on efficiency scores

EH KM Coastal Inland Coastal Inland

~'1 (CRS) Mean efficiency 0.84 0.79 0.61 0.69 Sign. level 0.0763 0.0000

E~ (VRS) Mean efficiency 0.90 0.85 0.74 0.82 Sign. level 0.1556 0.3715

E~ (VRS) Mean efficiency 0.91 0.87 0.78 0.85 Sign. level 0.1407 0.0304

Efficiency of trucks

Table 6. Frequency of units on the frontier

403

Output KM EH Size

E l E l E2 Unit CRS VRS VRS Sca le E l E l Ez Sca le EH Kid

2 - - - - - - 1 .53 3 2 2 1 .00 1810 21106

5 - - 10 5 0 .35 14 5 5 1 .00 525 9117 8 - - - - 1 .09 34 28 27 - - 1 .00 1810

14 - - - - - - 0 .26 6 2 2 1 .00 1339 14100

19 - - - - - - 0 .98 - - 1 1 0 .50 1151 20694

20 - - 8 11 1 .85 - - - - - - 1 .06 1855 38909

24 3 16 - - 1 .00 25 12 13 - - 1 .00 1679

25 - - 1 1 1 .85 - - 1 1 2 .46 3133 76537 26 - - - - - - 0 .66 - - 3 4 1 .99 2382 36893

28 24 4 6 2 .16 - - - - - - 2 .21 2155 51204 30 - - - - - - 1 .40 8 7 6 1 .00 1941 29488

40 - - - - - - 1 .53 - - - - - - 0 .99 1725 34276

42 - - - - - - 1 .14 - - 1 1 1 .78 2149 41527

45 - - 18 22 3 .50 - - - - 1 .50 2308 73520 46 - - 16 1 0 .39 - - 3 1 0 .30 252 8158

47 - - - - - - 0 .87 6 7 9 1 .00 1911 43799

48 - - 13 7 1 .00 - - 3 4 1 .63 2942 72412

50 - - 17 23 2 .87 - - 1 1 1 .83 3263 63372

51 - - - - - - 2 .30 37 48 - - 1 .92 3245

52 - - - - 1 .00 2 7 2 1 .00 1962 29335

54 67 60 61 1 .00 48 25 22 - - 1 .00 360

62 - - - - - - 0 .72 2 6 1 1 .00 1462 23123 63 - - - - 0 .82 42 36 28 - - 1 .00 1430

71 28 39 47 1 .00 - - 8 2 2 .60 2982 75644

72 - - 1 2 3 .48 - - - - - - 1A9 1793 73321

AVG 1817.8

technology is imposed. A clear observation from Table 6, which is also mentioned in the previous section, is that the composition of units on the frontier varies with the output specification.

Consider now the units on the frontier, given in Table 6, relative to their size measured by outputs. The units that dominate in all specifications and output measures differ when size is considered. As an example, units 54 and 71 dominate when KM is specified as output measure. Their sizes by the KM-measure reveal that while unit 54 is smaller than the average unit, unit 71 is twice the size of the average unit. It is also noted that unit 40 although efficient, does not appear as best practice for all other units than itself. This is one of the largest units in the sample.

In terms of optimality with respect to scale, most dominant units are scale optimal, i.e. have scale values of 1. This observation being irrespective of the choice of output. It is also observed that there exist a few dominant units that operate under Strong increasing returns to scale. These are 5, 14 and 46 when the KM-output measure is used and 19 and 46 when the output measure is EH. Unit 45 is the only one among the dominant ones that operates with strong decreasing returns to scale, and only when the KM-output measure is used.

5. C O N C L U D I N G R E M A R K S

The results received indicate substantial variations in efficiency across trucks. An average truck is found to have an effciency score of 0.76 and 0.88 when the output measure used in kilometers (KM) and effective hours (EH) respectively.

The potential for increasing output/ saving input is measured by /1 and 12 underlines the importance of technology when dealing with trucks. An imposition of the VRS technology when output is measured by EH would increase output by 25% as opposed to 12.4% when CRS is imposed. An average unit is, however, found to exhibit decreasing returns to scale technology.

Appropriate measures of output are important when dealing with trucks involved in more than one type of operation. The results reached here indicate that when all units are considered as one group the number of kilometers as an output measure generates lower efficiency measures in comparison to effective hours in production. When trucks are classified according to their regions this difference has, however, a second dimension. KM are found to generate high scores in inland regions while EH generate higher scores in the coastal regions. The difference is due to the

404 Lennart Hjalmarsson and James Odeck

composition of operations i.e. trucks in the inland regions undertake more snow plowing than those in the coastal regions where there is less snow and more mass transportation.

Neither the make of the truck nor the model were found to influence performance. Regarding size of trucks measured in terms of annual output, the influence on efficiency measures were slight when output is measured by DM and insignificant when measured by EH.

In summary, it can be concluded that there is substantial variation in the performance of trucks and that there is scope for eradicating some of the causes of the inefficiency. For the latter, the most useful information relates to the region in which the truck operates, the output measure to be used and, the units that define the frontier and their relative weights.

The results arrived at here have a number of policy implications. The efficiency results obtained by DEA methodology yield values of inputs, outputs and scale which, in principle, an agency should be able to achieve. For example in Section 4.1, we showed that if the frontier technology had been employed the average truck could have sustained the annual effective hours in production with only 88% of the input (i.e. wage, fuel, rubber and maintenance). Although the adoption of frontier technology would bring the truck to the frontier, complete adjustment may not be possible because some factors that influence performance may not be under the control of the agency concerned. Nevertheless, while DEA does not provide a precise mechanism for achieving efficiency, it does help in quantifying the magnitude of change required to make the inefficient units (trucks) efficient.

The tasks, thus, involve finding explanations for variation in performance. One way to go about this is to inspect the key characteristics of each frontier truck and then compare it to the inefficient trucks that it defines the frontier for. The agency with inefficient trucks can then learn from the frontier trucks and/or explain the causes of own inefficiency. The central authority (PRA) could also isolate the agencies that use public funds inefficiently from those that perform satisfactorily. More administrative attention may then be paid to those that perform poorly.

The Public Roads Administration of Norway lacks market prices for its services. A common way of measuring productivity in public sectors, when market prices are lacking, is by dividing physical output by physical input. However, when there are many outputs and inputs, managers of public sector agencies prefer multiple output/input ratios, each of which tells a different story. In this case no robust conclusions can be drawn on the performance on any particular agency, in comparison to others of the same nature. It is in this respect that the DEA approach used in this study could assist in aggregating several measures so that a single indicator for an agency's performance is obtained.

Acknowledgement--Financial support from HSFR and Jan Wallander Research Foundation is gratefully acknowledged.

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