1. Solving Stochastic Project Scheduling Problems Using Simulation/Optimization Approach By: Omar Al-Shehri Supervised by: Prof. A. M. Al-Ahmari Winter 1429/2008 oalshehri@ksu.edu.sa King Saud University College of Engineering Industrial Engineering Department بسم الله الرحمن الرحيم

2. 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).

3. 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.

4. The Project Life Cycle Initiation Planning Scheduling Executing Monitoring and control Closing

5. Problems with Projects 1- Unexpected necessary activities. 2- Tracking the plan. 3- Actual vs. Planned makespan. Time Number of activities The actual path of the project. The planned path of the project.

6. The project manager. ! This is the Stochasticity Zone !

7. 2- Stochasticity - For scheduling real world problems, there are: 1- Many uncertainties. 2- Complex relations between factors. 3- Many constraints. 4- Many non-linearities.

8. Is it possible to build the model? No What to do? Will we get the optimal solution? No Very long time. How long it takes? Yes

9. Simulation + Optimization Simulation Optimization overcome that, where: 1- The simulation model this stochasticity. 2- The optimization manage it.

10. Traditional optimization Simulation optimization Many realistic problems Size Time

11. Arena & OptQuest - We used Arena software for simulation modeling. - And we will use OptQuest for optimization. Arena software OptQuest Performance estimates Candidate results

12. 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.

13. 4- The Solution Methodology 1- 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.

14. The Methodology (Continued) 4- Verifying and validating the simulation using optimization model using simulation experiment. 5- Interpreting and analyzing the results.

15. 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 Finish 84 3 2 56 7 1

16. 5.1 converting of Starting Node Start

17. 5.2 converting of Activities 1

18. 32

19. 4 5 6

20. 5 6 7

21. 5.3 converting of Finishing Node 7 Finish

22. 5.4 Complete Network & Model 8 4 3 2 56 7 Start Finish 1

23. The selected project has the following network: First Case study

24. The stochastic project data are as follows: ActivityAct. Time Resources Needed WorkerMachine 1Norm(10,2)11 2Norm(12,3)2- 3Unif(5,8)22 451- 5Tria(4,5,6)21 6Expo(12)1- 7Norm(10,1)12 8Tria(4,6,8)2- Simulation Stage

25. Using the scheme which we had developed, the corresponding Arena model is as depicted: Simulation Stage (Cont.)

26. - 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.)

27. - 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.)

28. Optimization Stage

29. Optimization Stage (Cont.) -- Now, getting into OptQuest, the following data are defined: OBJECTIVE: Minimize the Project Completion Time.

31. CONTROLS: Predetermined Priorities. Optimization Stage (Cont.)

33. RESPONCES: 1- PCT. 2- The Project’s Single Entity. Optimization Stage (Cont.)

36. THE PROJECT PARAMETERS: 1- Number of Replications. 2- Tolerance when two solutions are equal. 3- Others. Optimization Stage (Cont.)

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

40. - The projects activities sequence is as follows: - The various solutions for the various number of replications for both approaches are: Activity12345678 Sequence12436578 Results and Discussion

41. Number of Runs Average Makespan Using Simulation Only Using Simulation Optimization 100 67.43 57.8 500 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.)

42. 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.

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

45. Optimization Stage

46. 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 cost Per hour Worker cost Per hour No. of M/CsNo. of workers Project completion time

48. CONTROLS: 1-Predetermined Priorities. 2- Recourses (Machine and Workers) Optimization Stage (Cont.)

50. RESPONCES: 1- PCT. 2- The Project’s Single Entity. Optimization Stage (Cont.)

53. THE PROJECT PARAMETERS: 1- Number of Replications. 2- Tolerance when two solutions are equal. 3- Others. Optimization Stage (Cont.)

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

57. - 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: Activity12345678 Sequence23154678 Results and Discussion

58. 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.)

59. 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.

60. Conclusion (Cont.) - In addition, linking the simulation model with other optimization tool such as Genetic Algorithm will simplify comparisons between these optimization tools.

61. O.D.Alshehri@gmail.com