Solving Stochastic Project Scheduling Problems Using Simulation/Optimization Approach By: Omar...
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Transcript of Solving Stochastic Project Scheduling Problems Using Simulation/Optimization Approach By: Omar...
Solving Stochastic Project Scheduling Problems Using Simulation/Optimization
Approach
By: Omar Al-ShehriSupervised by: Prof. A. M. Al-Ahmari
Winter 1429/2008
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 .