Truck Maintenance Project for MOPTA Competition

Ron DearingJason KratzAngelika Leskovskaya

Outline

• Introduction and Project Statement

• Methodology

• Model

• Results

• Software

slide 2

Introduction

• Competition to showcase AIMMS software package

• Large truck maintenance problem to be solved with AIMMS software

slide 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

slide 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

slide 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.

slide 6

Maintenance

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

maintenance

slide 7

Data Table

Truck Size Available Trucks Required Trucks

Small 85 75

Medium 295 280

Large 45 40

Total 425 400

slide 8

Maintenance Type Cost ($) Duration (wks) Interval (wks)

Routine 250 0.5 15

Transmission 2000 1 50

Engine 7500 3 90

Maintenance Capacity

Truck Type Total

Maintenance Type

Small Medium Large

Routine 3 8 2 11

Transmission 1 3 1 4

Engine 3 11 2 15

slide 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

slide 10

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

slide 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

slide 12

Model Sets

t in Trucks

s in Size

m in MaintenanceType

w in Week

slide 13

Binary Variables

slide 14

wmt

wmt

wmt

wt

wt

Fail

End

Start

In

Avail

,,

,,

,,

,

,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

Other Variables

slide 15

wsm

ws

w

wmt

wmt

TotIn

TypeAv

TotAv

Dec

Last

,,

,

,,

,,

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

Binary Variable Constraints

slide 16

mwmtwtwt

wmtwt

wtwt

FailInAvail

FailAvail

InAvail

,,,,

,,,

,,

1

1

1

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.

Binary Variable Constraints

slide 17

1/

)1/(

,,,,

,,,,

mwmtwmt

mwmtwmt

IntervalLastFail

IntervalLastFail

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

Binary Variable Constraints

slide 18

))((,,,,

,,,,1,,

mDurationCeilwmtwmt

mwmtwmtwtwt

StartEnd

EndStartInIn

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

Last Maintenance

slide 19

1,1,1,,,

1,1,1,,,

,,1,,,,

,1,,

**2/

**

1

1

mmmwmtmwmt

mmmwmtwmt

wmtwmtwmt

mtmt

IncEndIntervalDec

IncEndBigMDec

DecLastLast

StartMLast

Last Maintenance Constraints

The following constraints track the last maintenance of the truck.

Objective

slide 20

wmt w

wmwmt UndertEnd,,

,, *000,10cos*

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

Results

• Runs– Base Case (no optimization)– 6 Week Planning Interval– 10 Week Planning Interval– 10 Week Planning Interval with expanded

transmission capacity

slide 21

ResultsModel Run Total Cost

($M)Min Available Trucks Running Total

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

slide 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.

slide 23

Software Demonstration

slide 24

Questions?

slide 25