Do we have Locomotive

Shops at right Location,

with right Capacity and

Capability?

Weijun Xie, Yanfeng Ouyang, University of

Illinois at Urbana-Champaign

Kamalesh Somani, CSX Transportation

October 15, 2012

Operational Definitions

Repair/Maintenance

— Breakdown (random)

— Preventive maintenance (quarterly)

— Damage (in case of accidents)

— Heavy repair or Overhaul (revive old locomotives)

Servicing

— Sanitary Maintenance, Sand, Water, Lube Oil,

Supplies (service interval)

2

Operational Definitions (contd…)

Shop: facility for breakdown repair or preventive

maintenance

Heavy Shop: facility for accident repair, heavy repair or

overhaul

Service Center: facility for servicing, minor

repair/maintenance and fueling

Service Trucks: a truck which can travel and go to the

locomotive and is equipped to service and/or fuel the

locomotive

3

Operational Definitions (contd…)

Capacity: # of locomotives that can be worked on at

any given point of time based on space, manpower

and productivity level

Capability: kind of work that can be performed, for ex:

GE vs. EMD, Drop Tables, Cranes, Wheel True

Failure rate: # of times a locomotive needs to be

shopped per year for each of the capability types

Repair time: amount of time locomotive occupies the

capacity

4

Locomotive Shop Footprint

What-if (sensitivity) analysis, what is the Impact of

Shutting down a particular shop

Change shop capability

Traffic change

Change in repair time (productivity)

Change in failure rate

A strategic optimization model could be used to

perform such analysis

5

Locomotive Shop Footprint – Model (contd…)

6

Objective Function: • Minimize expense

Constraints: Business rules • Geographical network • Train pickup/drop off rules • Capacity expansion rules • Demand should be satisfied

Locomotive Shop

Footprint Model

Inputs •Current/Candidate shops, their capabilities and capacities •Failure rate •Avg. Repair time •Train time, route and loco assignment •Cost parameters •Fleet Size and attributes

Outputs

•Optimal shops, their Capabilities and capacities

Locomotive Shop Footprint – Cost parameters

7

* Train delay because of locomotive

out of service events and labor

expense in downsizing of shop are

not considered in the model

Locomotive cost

• Transportation cost

• Ownership cost

• Delay cost of pick-up/drop off

along the route

• Extra locomotive/crew for light

train

• Wait in Shop Queue cost

• Ownership cost

Facility cost

• Construction cost

• Maintenance cost

• Expansion cost

• Adding capability

Benefits

• Capacity reduction savings

• Shop shutdown savings

Solution Techniques

8

Compute Repair demand

Reduce candidate shops

Solve MIP

Output

Calculate transportation cost

Compute Repair demand

9

A failed locomotive is assumed to be available at the

destination of the train on which it failed

Repair demand is aggregated for each destination yard

The demand is divided by different manufacturer type

(GE vs. EMD), locomotive type (yard vs. road) and

breakdown type (small vs. big)

Calculate transportation cost

Three shipping methods: by train versus light

move versus mixed

10

Transfer cost

Mixed Ship by train Ship by light move

Transfer cost

Reduce candidate shops

11

Shop

Demand

Local Search Interchange

MIP Formulation

Objective function

— M/M/n queue is considered

— The higher utilization rate of a shop will be, the more

time a locomotive will stay in the shop

Number of variables

— Original: continuous variables ~3,600,000; integer

variables ~3,000

— Reduced: continuous variables ~400,000; integer

variables ~350

C# with Gurobi 5.0

Total running time is ~ 5 min

12

Base case (current shops fixed)

Case 1 (current shop location fixed, remove one small shop)

Model Results

13

Statistics

Delta (Case 1 -

Base Case)

Dwell Time from failure to shop (hrs per locomotive) 0.08

Transit time from failure to shop (hrs per locomotive) 0.22

Miles from failure to shop (miles per locomotive) 8.00

Avg. utilization rate 0.00

Capacity Small Shops -3.00

Capacity Big Shops 2.00

Locations -1.00

Yearly cost

Transportation Cost $515,120

Wait in Queue Cost ($180,615)

Construction Cost $0

Capacity Expansion Cost $450,000

Add Manufacturing Cost $0

Shutdown Benefit ($100,000)

Capacity Reduction Benefit ($600,000)

Total Cost $84,505

Model Results

Assignment solution

14

Maintenance type 2

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

x 105

-3.3

-3.2

-3.1

-3

-2.9

-2.8

-2.7

-2.6

-2.5x 10

5

Latitude

Longitude

Small shop

Big shop

15

Thank You