Truck Maintenance Project for MOPTA Competition

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

2. Outline • Introduction and Project Statement • Methodology • Model • Results • Software

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

4. 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

5. 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

6. 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.

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

8. Data Table

9. Maintenance Capacity

10. 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

11. Methodology • Problem is extremely large • 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

12. 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

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

14. 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

15. 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

16. 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.

17. 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

18. 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

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

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

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

22. Results

23. 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.

24. Software Demonstration

25. Questions?