Solving Stochastic Project Scheduling Problems Using Simulation/Optimization

Approach

By: Omar Al-ShehriSupervised by: Prof. A. M. Al-Ahmari

Winter 1429/2008

oalshehri@ksu.edu.sa

King Saud UniversityCollege of Engineering

Industrial Engineering Department

بسم الله الرحمن الرحيم

Contents

1 -Introduction.

2 -Stochsticity (Problem definition).

3 -Project Objectives.

4 -Solution Methodology.

5 -Converting the AON Network into Simulation

Model.

6 -Future Work (In IE 499) .

1 -Introduction

-10 Trillion dollar are invested in projects world wide.

-60 Million professional person

involved.

-More profitable projects, means more GDP and more growth.

The Project Life Cycle

Initiation Planning Scheduling

ExecutingMonitoring and control

Closing

Problems with Projects

1 -Unexpected necessary activities.

2 -Tracking the plan.

3 -Actual vs. Planned makespan .Time

Num

ber o

f ac

tiviti

es

The actual path of the project.

The planned path of the project.

The project manager.

!This is the

Stochasticity Zone!

2 -Stochasticity

- For scheduling real world problems, there are:

1 -Many uncertainties.

2 -Complex relations

between factors .

3 -Many constraints.

4 -Many non-linearities .

?????????

Is it possible to build the

model?

NoWhat to do?

Will we get the optimal

solution?

No

UsingSimulation

UsingOptimization

Very long time.

How long it takes?

Yes

Simulation + Optimization

Simulation Optimization overcome that, where:

1 -The simulation model this

stochasticity.

2 -The optimization manage it.

Trad

ition

alop

timiz

atio

nSimulation optimization

Many realistic problems

Size

Time

Arena & OptQuest

-We used Arena software for simulation

modeling.

-And we will use OptQuest for optimization.

Arena software

OptQuest

Performance estimates

Candidate results

3 -The Project Objectives

1 -To suggest a proper scheme for converting jjffproject network into Arena model.

2 -To determine the optimum number or the llllresources required by the project, as well as llllthe makespan.

4 -The Solution Methodology1 -Identifying a set of rules for converting the

network into Arena model.

2 -Modeling the stochastic resource constrained project when the resources are subjected to

break downs, using Arena.

3 -Linking the developed model into OptQuest.

The Methodology (Continued)

4 -Verifying and validating the simulation using

optimization model using simulation

experiment.

5 -Interpreting and analyzing the results.

5 -Converting of the Network

-We are basically dealing with the activity on node networks (AON).

-Based on the Arena modules, we can divide the AON network into four basic elements:

1 -Starting node (source).

2 -Activities nodes.

3 -Arrows.

4 -Finishing node .Start Finish84

3

2

5 6

7

1

5.1 converting of Starting Node

Start

5.2 converting of Activities

1

5.2 converting of Activities

32

5.2 converting of Activities

4

5

6

5.2 converting of Activities

5

6

7

5.3 converting of Finishing Node

7 Finish

5.4 Complete Network & Model

8

4

3

2

5 6

7

Start Finish1

The selected project has the following network:

First Case study

The stochastic project data are as follows:

Activity Act. TimeResources Needed

Worker Machine

1 Norm(10,2) 1 1

2 Norm(12,3) 2 -

3 Unif(5,8) 2 2

4 5 1 -

5 Tria(4,5,6) 2 1

6 Expo(12) 1 -

7 Norm(10,1) 1 2

8 Tria(4,6,8) 2 -

Simulation Stage

Using the scheme which we had developed, the corresponding Arena model is as depicted:

Simulation Stage (Cont.)

-We defined some priorities which will represent the sequence of the activities which will take

place.- -This priorities was defined using

- Assign module in Arena Basic- Process Panel.

Simulation Stage (Cont.)

-This priorities will be the controls which will be defined in OptQuest.

-The objective is to minimize the project completion time or makespan.

Simulation Stage (Cont.)

Optimization Stage

Optimization Stage (Cont.)

- -Now, getting into OptQuest, the following data are defined:

OBJECTIVE: Minimize the Project Completion Time.

CONTROLS: Predetermined Priorities.

Optimization Stage (Cont.)

RESPONCES:

1 -PCT.

2 -The Project’s Single Entity.

Optimization Stage (Cont.)

THE PROJECT PARAMETERS:

1 -Number of Replications.

2 -Tolerance when two solutions are equal.

3 -Others.

Optimization Stage (Cont.)

Optimization Stage (Cont.)

Now, we can run the program and get the results.

-The projects activities sequence is as follows:

-The various solutions for the various number of replications for both approaches are :

Activity 1 2 3 4 5 6 7 8Sequence 1 2 4 3 6 5 7 8

Results and Discussion

Number of Runs

Average MakespanUsing Simulation

OnlyUsing Simulation

Optimization

100 67.43 57.8500 66.91 57.03

1000 66.26 56.42

e.g. for the 1000 replication)66.26-56.42/(66.26=14.85% had been reduced

from the makespan.

Results and Discussion (Cont.)

Second Case Study

For this example, we used the same network of the previous case but we added a failure to the machines.

Also, we have chosen another objective for this case.

Simulation Stage

The machine failure rate is 5 hours for every expo(10) hours up time.

Optimization Stage

Optimization Stage (Cont.)

- -Now, getting into OptQuest, the following data are defined:

OBJECTIVE: Minimize the Project Cost.

The equation used for calculating total cost is:PCT*100+PCT*10*[Machine1]+PCT*20*[Worker]

Project holding cost

M/C costPerhour

Worker costPerhour

No. of M/Cs No. of workers

Project completion time

CONTROLS:

1-Predetermined Priorities.

2 -Recourses (Machine and Workers)

Optimization Stage (Cont.)

RESPONCES:

1 -PCT.

2 -The Project’s Single Entity.

Optimization Stage (Cont.)

THE PROJECT PARAMETERS:

1 -Number of Replications.

2 -Tolerance when two solutions are equal.

3 -Others.

Optimization Stage (Cont.)

Optimization Stage (Cont.)

Now, we can run the program and get the results.

-The projects activities sequence is as follows:

-And the optimal no. of resources is three workers and four machines.

-The various solutions for the various number of replications for both approaches are :

Activity 1 2 3 4 5 6 7 8Sequence 2 3 1 5 4 6 7 8

Results and Discussion

e.g. for the 1000 replication) 10697.60-8901.903/(10697.60 =16.78% had

been reduced from the total cost.

Number of Runs

Average Cost

Using Simulation Only

Using Simulation Optimization

100 10865.92 9073.379

500 10699.20 8915.489

1000 10697.60 8901.903

Results and Discussion (Cont.)

Conclusion

-Simulation optimization is a helpful approach in the project scheduling where

the activity times are stochastic .

-It has been found in this project that there is good improvement when optimization tool

is used with simulation model .

-It would be good for further research to develop automatic transformation tool for model primary data to simulation model.

Conclusion (Cont.)

• -In addition, linking the simulation model with other optimization tool such as Genetic Algorithm will simplify comparisons

between these optimization tools .

O.D.Alshehri@gmail.com

Thank You

Q & A