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Slide 1ILLINOIS ‐ RAILROAD ENGINEERING
A Quantitative Decision Support Framework for Optimal
Railway Capacity Planning
Yung-Cheng (Rex) LaiUniversity of Illinois at Urbana-Champaign
25 April, 2008
Presentation at The William W. Hay Railroad Engineering Seminar Series
Urbana, IL
Slide 2ILLINOIS ‐ RAILROAD ENGINEERING
The North American railroad industry is facing capacity problems
• Capacity and network efficiency have become more important as traffic volumes increase
• The demand for freight rail services is projected to increase by 88% in 2035 compared to 2007
• Capacity constraints are affecting network efficiency
• Problems range across many aspects of the railroad operation including:– Infrastructure– Equipment– Train dispatching, traffic mix– Human resources
Network Capacity must be increased
Slide 3ILLINOIS ‐ RAILROAD ENGINEERING
The demand for freight rail services is projected to increase by 88% in 2035 compared to 2007
20052035w/o upgrade
A,B,C: Below CapacityD: Near CapacityE: At CapacityF: Above Capacity
E & F = 45%
Slide 4ILLINOIS ‐ RAILROAD ENGINEERING
A “Decision Support Framework” to determine how to allocate capital in the best possible way
• Railroads rely on experienced personnel and simulation software to identify bottlenecks and propose methods to reduce the congestion
• Experienced railroaders often identify good solutions but this does not guarantee that all possible alternatives have been evaluated
• Simulation usually deals with a section of the network, which may result in moving bottleneck around instead of solving it
• I propose a decision support framework to generate & evaluate possible alternatives and tackle the capacity planning problems in network level
Slide 5ILLINOIS ‐ RAILROAD ENGINEERING
A “Decision Support Framework” to enhance the strategic capacity planning process
• Today’s network analysis: – Bottleneck identification– Manual routing
• Today’s simulation analysis: – Great corridor-based tool– Slow alternatives evaluation– Stuck in local solution
There is a need for a better network analysis process combining network routing, automatic alternatives generation and selection
Slide 6ILLINOIS ‐ RAILROAD ENGINEERING
This decision support framework contains three individual strategic planning tools
• Alternatives Generator: – Enumerate possible expansion options with their cost and additional capacity
• Investment Selection Model (ISM): – Determine which subdivisions need to be upgraded with what kind of
improvements (alternatives)
• Impact Analysis Module: – Evaluate the tradeoff between capital investment and delay cost
Link (sub) properties
Alternatives generator
Capacity expansion alternatives (cost & additional capacity)
Estimated future traffic
(trains/day/OD)
Budget
Investment Selection Model
Feasible solution?
Done
Yes
Impact Analysis
No
Slide 7ILLINOIS ‐ RAILROAD ENGINEERING
Identifying appropriate capacity evaluation tools to develop the alternatives generator
Theoretical models are the simplest among the three, and can often be computed manually:
– Quick evaluation of relative effectsSimulation models mimic train dispatcher logic, and is the most sophisticated and computationally intensive method:
– Closest representation of the actual operationsParametric models are developed from simulation and focus on the key elements of line capacity:
– Fill the gap between simple theoretical model and detailed simulation
Computation Efficiency AccuracyTheoretical
Parametric
Simulation
Good Compromise
Slide 8ILLINOIS ‐ RAILROAD ENGINEERING
CN Parametric Capacity Model was selected to be the basis of the alternatives generator
• Practical capacity is computed based on the following key parameters: – Plant parameters:
• Length of Subdivision• Meet & Pass Locations (Spacing, Uniformity)• Intermediate Signal Spacing
– Traffic parameters:• Traffic Peaking• Priority & Speed Ratio• Minimum Run Time
– Operating parameters• Track Maintenance (Slow Orders, Outages)• Stop on Line Time
Slide 9ILLINOIS ‐ RAILROAD ENGINEERING
Adding enumeration and cost evaluation modules into CN model to create the alternatives generator
• Enumeration Module: automatically enumerating alternatives based on possible engineering options – adding (1) passing sidings, (2) intermediate signals, (3) 2nd main track
• Cost Evaluation Module: incorporating cost data into the parametric model to compute the construction cost of each alternative
• For example, a 100-mile sub with 9 sidings and no intermediate signalAlternatives Sidings Signals/Spacing Capacity (trains/day) Cost
1 + 0 + 0 + 0 $02 + 0 + 1 + 3 $1,000,0003 + 0 + 2 + 4 $2,000,0004 + 1 + 0 + 3 $5,470,0005 + 1 + 1 + 6 $6,570,0006 + 1 + 2 + 7 $7,670,0007 + 2 + 0 + 6 $10,940,0008 + 2 + 1 + 9 $12,140,0009 + 2 + 2 + 10 $13,340,000
10 Adding 2nd Main Track + 50 $204,750,000
Slide 10ILLINOIS ‐ RAILROAD ENGINEERING
This decision support framework contains three individual strategic planning tools
• Alternatives Generator: – Enumerate possible expansion options with their cost and additional capacity
• Investment Selection Model (ISM): – Determine which subdivisions need to be upgraded with what kind of
improvements (alternatives)
• Impact Analysis Module: – Evaluate the tradeoff between capital investment and delay cost
Link (sub) properties
Alternatives generator
Capacity expansion alternatives (cost & additional capacity)
Estimated future traffic
(trains/day/OD)
Budget
Investment Selection Model
Feasible solution?
Done
Yes
Impact Analysis
No
Slide 11ILLINOIS ‐ RAILROAD ENGINEERING
7 7
4 4
1
1 1
23
3
3
trains/day
i j Alternatives Capacity (trains/day) Cost1 2 1 + 3 $1,000,0001 2 2 + 4 $2,000,0001 2 3 + 6 $6,570,000. . . .. . . .
Trains with different ODs are similar to multiple commodities, and they share the line capacity
7 7
4 4
Task: • Which link(s) to upgrade ?• With what kind of capacity
improvement alternative?
6 \
4
Slide 12ILLINOIS ‐ RAILROAD ENGINEERING
The investment selection model is formulated as a multicommodity network flow problem
Minimize Cost = Capital Investment + Flow Flow Costs.t.
Budget ConstraintCapacity Constraint (capacity can be increased by upgrade infrastructure)
Alternatives ConstraintFlow Conservation Constraint (fulfill future demand)
:( , )
1, ( , )0,
k thij
thq
ij
Decision Variablesx Number of trains running on arc i j from k OD pair
if the q alternative is used for arc i jyotherwise
=
⎧= ⎨⎩
Slide 13ILLINOIS ‐ RAILROAD ENGINEERING
General Investment Selection Model (ISM)
. .
1
α γ+
≤
≤ + ∀ ≠
≤ ∀ ≠
−
∑∑∑ ∑∑∑
∑∑∑
∑ ∑
∑
∑ ∑
q q kij ij ij ij
i j q i j k
q qij ij
i j q
k q qij ij ij ij
k q
qij
q
k kij ji
j j
min h y c x
s t h y B
x U u y i , j (i j)
y i , j (i j)
x x =
{ }0,1
∈⎧⎪− ∈ ∀⎨⎪⎩
∈ ∈
k k
k k
k qij ij
d if i sd if i t k
0 otherwiseand x positive integer, y
capital invest + flow cost
budget constraint
capacity constraint
alternative constraint
flow conservation
Slide 14ILLINOIS ‐ RAILROAD ENGINEERING
Lead Time (t)
The investment selection model is formulated as a multicommodity network flow problem
Minimize CI + FC – RV = NC + FCCI = initial capital investment FC = flow cost within horizon = transportation + MOW costRV = residual value at the end of decision horizonNC = net cost = CI – RV
m0 mt mt+N
CI RV
N-Year Operations
If N = 5, RV = (Remaining Service Life) / (Total Service Life) x CI= 15/20 x CI = 0.75 CI
NC = CI – RV = 0.25 CI
FC Life Cycle Cost Analysis
Slide 15ILLINOIS ‐ RAILROAD ENGINEERING
0.25 52
. .
1
× + ×
≤
≤ + ∀ ≠
≤ ∀ ≠
∑∑∑ ∑∑∑∑∑
∑∑∑
∑ ∑
∑
q q kij ij mij wij
i j q m w i j k
q qij ij
i j q
k q qwij ij ij ij
k q
qij
q
min h y c x
s t h y B
x U u y i , j , w(i j)
y i , j (i j)
{ }0,1
∈⎧⎪− − ∈ ∀⎨⎪⎩
∈ ∈
∑ ∑wk k
k kwij wji wk k
j j
k qwij ij
d if i s x x = d if i t w, k
0 otherwiseand x positive integer, y
ISM for Class 1 Railroad Multi-Year Planning
Net Cost Flow Cost
Slide 16ILLINOIS ‐ RAILROAD ENGINEERING
This decision support framework contains three individual strategic planning tools
• Alternatives Generator: – Enumerate possible expansion options with their cost and additional capacity
• Investment Selection Model (ISM): – Determine which subdivisions need to be upgraded with what kind of
improvements (alternatives)
• Impact Analysis Module: – Evaluate the tradeoff between capital investment and delay cost
Link (sub) properties
Alternatives generator
Capacity expansion alternatives (cost & additional capacity)
Estimated future traffic
(trains/day/OD)
Budget
Investment Selection Model
Feasible solution?
Done
Yes
Impact Analysis
No
Slide 17ILLINOIS ‐ RAILROAD ENGINEERING
There is a trade-off between “Capital Investment” and “Train Delay Cost”
• ISM determines the best set of capacity improvement alternatives with the premise that “Level of Service remains the same”
• However, it is possible to gain modest capacity by increasing delay (lowering Level of Service)
Capacity (trains/day)
Del
ay (h
ours
)
• Impact analysis module determines if the capital investment is cost-effective by comparing the capital investment & delay cost
• The output will be a set of options that eventually the capacity planner will make the final decision
Current LOS
Volume
Slide 18ILLINOIS ‐ RAILROAD ENGINEERING
There is a trade-off between “Capital Investment” and “Train Delay Cost”
Net Cost from Upgrading Infrastructure
Capacity (trains/day)
Del
ay (h
ours
)
Current LOS
Capacity (trains/day)
Del
ay (h
ours
)
Current LOS
Delay Cost = Unit Delay Cost x Hours x TrainsVSVS
Benefit = Delay Cost / Net Cost(return on investment)
Volume Volume
Slide 19ILLINOIS ‐ RAILROAD ENGINEERING
Two case studies were conducted to show the feasibility and potential use of this tool
• Case Study I – a network with secondary lines requiring major work to upgrade: – 15 nodes, 22 links, 14 OD pairs– Scenario 1: capacity improvement with existing network– Scenario 2: capacity improvement including secondary line– Trade-off between capital investment and flow cost
• Case Study II – a multiyear plan for a class 1 railroad: – 39 nodes, 42 links, ~1,000 OD pairs in a week– 50% traffic demand increase– Trade-off between capital investment and delay cost
• In both cases: – Operational horizon – N=5
Slide 20ILLINOIS ‐ RAILROAD ENGINEERING
Empirical Case Study IMainlineSecondary Line
[15,100] [line capacity (trains/day), distance (miles)]eg. [20,100] = [20 trains/day, 100 miles]
[20,100]
[15,100]
[30,100]
[25,150]
[25,100]
[20,100]
[15,100] [0,200]
[15,150]
[15,50][15,50]
[15,50]
[20,100]
[0,300]
[25,200]
[15,50]
[0,100] [20,100]
[25,100]
[30,100]
[70,50]
Slide 21ILLINOIS ‐ RAILROAD ENGINEERING
Future Traffic Demand and Capacity Improvement Alternatives
Demand for each OD pairTo Increase Capacity of Arcs:• Adding sidings: one, two, three, etc.
until the spacing is less than 8-mile• Adding intermediate signals: none,
one per spacing, two per spacing, etc.
Capacity improvement optionsOD Pair Future Demand
(trains/day)(1)~(9) 8(3)~(6) 6(3)~(11) 9(3)~(15) 8(4)~(6) 8(4)~(13) 7(6)~(3) 6(5)~(15) 9(9)~(13) 5(10)~(3) 2(13)~(3) 8(15)~(3) 5(15)~(6) 8(13)~(9) 5
Slide 22ILLINOIS ‐ RAILROAD ENGINEERING
Scenario One – Not Considering Secondary Lines
(3)
(4)
(1)
(2)
(5)
(6)
(7)
(9)
(8) (10)
(11)(12)
(13)
(14)(15)
MainlineSecondary Line
+3
+7
+12+9
+19+13
+10
+14
• Net Cost = 45 million• Flow Cost = 2,707 million• Total = 2,751 million
Slide 23ILLINOIS ‐ RAILROAD ENGINEERING
Scenario Two – Considering Secondary Lines
(3)
(4)
(1)
(2)
(5)
(6)
(7)
(9)
(8) (10)
(11)(12)
(13)
(14)(15)
MainlineSecondary Line
+15
+15
+3
+2 +2+6
+5
+4+7
+3
• Net Cost = 161 million higher• Flow Cost = 2,505 million lower• Total = 2,666 million BETTER solution
+15
Slide 24ILLINOIS ‐ RAILROAD ENGINEERING
Capacity improvement plans according to ISM for Scenario One and Scenario Two
Scenario One
Scenario Two
i j Alternatives Cost ($millions)3 7 Add signals (3) 1.603 5 Add 2 sidings & signals (2) 13.748 9 Add 3 sidings 16.419 11 Add 3 sidings & signals (1) 17.41
11 12 Add 3 sidings & signals (1) 17.015 6 Add 5 sidings & signals (2) 29.357 13 Add 5 sidings & signals (2) 32.355 8 Add 8 sidings & signals (1) 45.26
i j Alternatives Cost ($millions)3 11 Upgrade secondary line 300.006 9 Upgrade secondary line 200.00
11 13 Upgrade secondary line 100.008 9 Add signals (1) 0.30
11 12 Add signals (1) 0.307 13 Add signals (2) 4.003 5 Add 1 sidings & signals (2) 8.075 8 Add 1 sidings & signals (3) 7.075 6 Add 2 sidings & signals (1) 11.649 11 Add 2 sidings & signals (2) 11.84
Slide 25ILLINOIS ‐ RAILROAD ENGINEERING
[15,0]
[17,17]
Identify the “important” & “unimportant” links
(3)
(4)
(1)
(2)
(5)
(6)
(7)
(9)
(8) (10)
(11)(12)
(13)
(14)(15)
MainlineSecondary Line
[15,0]
[line capacity, used capacity]
[20,8]
[30,8]
[30,30]
[25,21]
[20,7]
[21,20] [15,8]
[19,19]
[17,17][15,0]
[15,2]
[27,27]
[15,9]
[28,28]
[15,10] [20,0]
[25,17]
[30,13]
[70,30]
Slide 26ILLINOIS ‐ RAILROAD ENGINEERING
Empirical Case Study II39 nodes, 42 links, ~ 1,000 of OD pairs
Slide 27ILLINOIS ‐ RAILROAD ENGINEERING
Capacity improvement for 50% demand increase
+12 +6+6
+2+4
+1
+1
+1+2+2
+1
+1
+16+16 +11 +5
+5+8
+5
+5+3 +3
No. of Variables: 89,712No. of Equations: 41,015 Solution Time: 3.5 sec
Slide 28ILLINOIS ‐ RAILROAD ENGINEERING
Impact analysis module compares capital investment cost with train delay cost
• ISM determines required upgrade with the premise “LOS is unchanged”
• It is possible to gain modest capacity by increasing delay (reduce LOS)
• Unit Train Delay Cost = $ 261 per train-hour
i j Sun Mon Tue Wed Thu Fri Sat1 2 16 15 16 16 16 16 162 3 14 15 15 16 15 16 133 4 9 10 10 11 10 11 84 5 4 4 5 4 5 4 55 6 1 0 0 0 0 0 16 7 1 2 2 1 2 0 27 8 1 0 1 1 1 0 07 9 1 2 0 1 0 1 19 10 1 2 0 1 0 1 1
10 11 0 1 0 1 0 1 111 12 2 0 4 0 4 0 34 15 3 5 5 5 5 5 4
15 16 7 7 6 7 6 7 85 18 4 5 5 5 5 5 5
18 19 4 5 5 5 5 5 519 20 1 3 3 3 3 3 320 21 1 3 3 3 3 3 333 34 6 4 5 5 6 5 634 35 5 4 2 6 5 6 635 36 0 0 1 0 1 0 035 38 2 7 9 11 12 12 1038 39 0 0 0 1 0 1 0
Capacity (trains/day)
Del
ay (h
ours
)
Current LOS
Required addition in capacity
Volume
Slide 29ILLINOIS ‐ RAILROAD ENGINEERING
There is a trade-off between “Capital Investment” and “Train Delay Cost”
Net Cost from Upgrading Infrastructure
Capacity (trains/day)
Del
ay (h
ours
)
Current LOS
Capacity (trains/day)
Del
ay (h
ours
)
Current LOS
Delay Cost = Unit Delay Cost x Hours x TrainsVSVS
Benefit = Delay Cost / Net Cost(return on investment)
Volume Volume
Slide 30ILLINOIS ‐ RAILROAD ENGINEERING
Difference ($,k) Benefit Cumulativei j Current Max Train Delay Net Cost Delay - Net Cost Benefit
35 38 24 36 31,107 2,289 28,818 13.59 145 18 34 39 18,200 1,643 16,558 11.08 253 4 40 51 135,720 13,169 122,551 10.31 35
18 19 34 39 12,663 2,735 9,928 4.63 4020 21 36 39 5,015 1,393 3,622 3.60 4315 16 14 22 7,953 2,435 5,518 3.27 462 3 35 51 132,612 42,188 90,425 3.14 50
19 20 36 39 5,015 1,693 3,322 2.96 534 5 27 32 8,116 4,278 3,839 1.90 541 2 35 51 131,173 84,813 46,361 1.55 56
33 34 20 26 6,372 4,870 1,502 1.31 5734 35 20 26 5,822 4,870 952 1.20 594 15 16 21 4,004 4,870 (866) 0.82 596 7 15 17 852 1,218 (366) 0.70 60
38 39 23 24 326 1,218 (892) 0.27 6011 12 6 10 584 2,435 (1,851) 0.24 6135 36 32 33 224 1,218 (994) 0.18 615 6 15 16 217 1,218 (1,000) 0.18 617 8 15 16 217 1,218 (1,000) 0.18 619 10 5 7 258 2,435 (2,177) 0.11 61
10 11 6 7 95 1,218 (1,122) 0.08 617 9 5 7 153 2,435 (2,282) 0.06 61
Sum 506,697 185,852 320,845
Link Capacity Cost ($,k)Net Cost vs. Train Delay Cost
min ( )
. .
−
≤
∑
∑
l ll
l ll
Delay no upgrade x d
s t x c Budget
Slide 31ILLINOIS ‐ RAILROAD ENGINEERING
• AG can enumerate possible expansion options with their cost and additional capacity
• ISM successfully and efficiently solved the problem regarding where to upgrade and what kind of engineering options should be conducted
• IAM can further explore the trade-off between capital investment and train delay cost
• This process will help RRs maximize their benefit from expansion projects and thus be better able to provide reliable service to their customers, and return on shareholder investment
• Future work: – Enable demand rejection scenario for insufficient budget– Develop a multi-period decision making model with stochastic
future demand
A decision support framework is developed to assist railway capacity planning projects
Slide 32ILLINOIS ‐ RAILROAD ENGINEERING
Thank you!