A Quantitative Decision Support Framework for Optimal Railway … · 2019. 2. 13. · Slide 1 ILLINOIS ‐RAILROAD ENGINEERING A Quantitative Decision Support Framework for Optimal

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


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


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%


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


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


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


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


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


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











(trains/day/OD)

Budget


Feasible solution?

Done

Yes

Impact Analysis

No


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


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

=

⎧= ⎨⎩


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


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


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











(trains/day/OD)

Budget


Feasible solution?

Done

Yes

Impact Analysis

No


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



Net Cost from Upgrading Infrastructure


Del

ay (h

ours

)

Current LOS


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


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


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]


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


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


Scenario Two – Considering Secondary Lines

(3)

(4)

(1)

(2)

(5)

(6)

(7)

(9)

(8) (10)

(11)(12)

(13)

(14)(15)


+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


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


[15,0]

[17,17]

Identify the “important” & “unimportant” links

(3)

(4)

(1)

(2)

(5)

(6)

(7)

(9)

(8) (10)

(11)(12)

(13)

(14)(15)


[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]


Empirical Case Study II39 nodes, 42 links, ~ 1,000 of OD pairs


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


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


Del

ay (h

ours

)

Current LOS

Required addition in capacity

Volume



Net Cost from Upgrading Infrastructure


Del

ay (h

ours

)

Current LOS


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


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


• 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


Thank you!

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A Quantitative Decision Support Framework for Optimal Railway … · 2019. 2. 13. · Slide 1 ILLINOIS ‐RAILROAD ENGINEERING A Quantitative Decision Support Framework for Optimal