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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
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