1. Dept. of MMME, University of Newcastle upon Tyne
Genetic Algorithms for multiple resource constraints Production Scheduling with multiple levels of product structure
By : Pupong Pongcharoen (Ph.D. Research Student)
Supervisors : Prof. Paul Braiden
Dr. Chris Hicks
26 April 1999
Dept. of MMME, University of Newcastle upon Tyne

2. Overview of this presentation
Background and literature review
Characteristics of production scheduling problem
Optimisation algorithms
Genetic Algorithms(GAs) applied to production scheduling
Experimental Program
Results
Discussions and conclusions

3. What is scheduling ?
“ The allocation of resources over time to perform a collection of tasks ”
Baker(1974)
“ Scheduling problems in their simple static and deterministic forms are extremely simple to describe and formulate but difficult to solve ”
King and Spackis(1980)

4. Scheduling problems n jobs & m machines = (n!)m possible solutions
e.g. 20 x 10 problem => x10183 solutions

5. Type of scheduling problems in literature
Job shop problem (JSP)
different routing of jobs Þ machines
Flow shop problem (FSP)
same routing of jobs Þ machines
Permutation scheduling problem (PSP)
same job sequence Þ machines
King and Spackis (1980)

6. Literature review

7. Optimisation algorithms
Conventional optimisation algorithms
Example Branch & Bound, Integer Linear Programming and Dynamic Programming.
works well with small problems
slow
can’t solve “big” problems
Approximation optimisation algorithms
Example Dispatching rules, Simulated Annealing, Taboo Search and Genetic Algorithms.
fast
can be applied with big or small problems
approximate “optimal” solutions.
Jain et.al. (1999)

8. Product structure from company

9. Type of scheduling environment
Machine environment
Þ Single or Multiple machines
Product environment
Þ Single or Multiple products
Capacity planning
Þ Infinite or Finite resources constraints
Research methodology
Þ Analytical or Simulation methodology

10. The objectives of this research
Apply Genetic Algorithms to complex capital goods production scheduling problems
Minimising penalty cost due to earliness and tardiness
Assume finite capacity
Using simulation methodology for testing plans

11. Production Scheduling
with multiple levels of product structure

12. Example of Gantt Chart

13. Fitness function Minimise : å Pe(Ec+Ep) + å Pt(Tp)
Where Ec = max (0, Dc - Fc)
Ep = man (0, Dp - Fp)
Tp = max (0, Fp - Dp)

14. Genetic Algorithms

15. Crossover Operation

16. Mutation Operation

17. Demonstration of Genetic Algorithm Program
Genetic Algorithms for scheduling problems was written by using Tcl/Tk programming language.
The program was runs on Unix system V release 4.0 on a Sun workstation.

18. Case study (data from Parsons)

19. Experimental program Full factorial experimental design was performed.
Total number of runs = 3 x 2 x 2 x 4 x 5 = 240 (per replication)

20. Results from 240 runs on each problem sizes

21. Analysis of Variance

22. The best performance of GAs on the problems

23. Mean and standard deviation for each population

24. Discussions
When the problem size increases the execution times increase exponentially.
Next step is to break “large” problems down into smaller independent problems that can be solved in a “reasonable” amount of time.
The solutions to the small problems will be integrated to give an overall solution.

25. Conclusions
Genetic algorithms represents a powerful technique for solving scheduling problems.
Practical software produced for solving scheduling problems.
Solutions far better than original schedules obtained from Company
Appropriate levels for Genetic Algorithm parameters identified.

26. Further Research Bicriteria scheduling problems.
Multiple criteria scheduling problems.

27. Any questions please ?