0. Truck Maintenance Project for MOPTA Competition
Ron Dearing
Jason Kratz
Angelika Leskovskaya

1. Outline Introduction and Project Statement Methodology Model Results
Software

2. Introduction Competition to showcase AIMMS software package
Large truck maintenance problem to be solved with AIMMS software

3. AIMMS Modeling language with GUI
Contains functionality to work with Excel
Contains functionality to create a dashboard for input/output
Provides for multiple solvers including CPLEX

4. Problem Statement
425 Trucks in three different size classes (Small, Medium, Large)
3 Different types of maintenance need to be kept up (Routine, Transmission, Engine)
Limited Maintenance Capacity
Overall
For each truck size

5. Requirements If possible, keep 400 trucks on the road at all times.
Each type of truck has a required number of trucks to be kept on the road.

6. Maintenance Parameters associated with maintenance types: Cost
Duration of maintenance
Interval between maintenance
Which maintenance types are included in each maintenance

7. Data Table Truck Size Available Trucks Required Trucks Small 85 75
Medium
295
280
Large 45 40
Total
425
400
Maintenance Type
Cost ($)
Duration (wks)
Interval (wks)
Routine
250
0.5 15
Transmission
2000 1 50
Engine
7500 3 90

8. Maintenance Capacity Truck Type Total Maintenance Type Small Medium
Large
Routine 3 8 2 11
Transmission 1 4
Engine 15

9. Project
Given an Excel Spreadsheet with initial time since last maintenance of each type
Determine a minimum cost maintenance schedule for 2 years
Determine the maximum number of trucks that can be kept on the road for 2 years

10. Methodology Problem is extremely large Program run over all variables:
105 weeks
425 trucks
3 types of maintenance
Program run over all variables:
1,654,592 constraints
939,228 variables (669,375 Integer)
5,558,988 non-zero values in matrix

11. Methodology Break up problem into smaller time periods
Run problem over 6-10 weeks, move on to next time period, taking previous result as given
Decreases time required for solution
Less accurate optimal solution

12. Model Sets
t in Trucks s in Size m in MaintenanceType w in Week

13. Binary Variables 1 if t is on the road in week w; 0 otherwise
1 if t is in maintenance in week w;
0 otherwise
1 if t starts maintenance m in week w;
0 otherwise
1 if t ends maintenance m in week w;
0 otherwise
1 if t is over the interval for maintenance m in week w;
0 otherwise

14. Other Variables
Number of weeks since last maintenance of type m for truck t during week w
Only used when decreasing Last due to maintenance
Total trucks available during week w
Number of trucks of type s available during week w
Number of trucks of type s in maintenance type m during week w

15. Binary Variable Constraints
Availability Constraints
The following constraints force a truck to be unavailable if the truck is in maintenance or past a maintenance due date. Conversely, a truck is forced to be available if it is neither in maintenance or past a due date.

16. Binary Variable Constraints
Failure Constraints
The following constraints force a truck to be “failed” when past a maintenance due date, or not failed if at or before the maintenance due date

17. Binary Variable Constraints
Maintenance Constraints
The following constraints force a truck to be in maintenance after the start of maintenance and before the end of maintenance. The end of maintenance takes place Duration(m) weeks after the start of maintenance

18. Last Maintenance Constraints
The following constraints track the last maintenance of the truck.

19. Objective
We minimize the following objective, which is the sum of all maintenance costs, plus a penalty for not meeting demand:

20. Results Runs Base Case (no optimization) 6 Week Planning Interval
10 Week Planning Interval with expanded transmission capacity

21. Minimize Cost (expanded)
Results
Model Run
Total Cost ($M)
Min Available Trucks
Running
Total
Small
Medium
Large
Time
Under Demand
base
4.0
164 50
106 3
<1m
>10,000
6- week
5.04
341 64
238.5
30.5
34m
4,615
Minimize Cost
(no expansion)
5.15
362 70
255
34.5
4h34m
2,241.5
Minimize Cost (expanded)
4.92
370
72.5
258 35
4h37m
1,324.5

22. Summary of Results
Unable to meet goal of keeping a minimum of 400 trucks in service with the current capacity of the maintenance facility.
Vast improvement in meeting demand with optimization
Increase in meeting demand with decrease in total cost when increasing size of transmission maintenance facility.

23. Software Demonstration

24. Questions?