Dr Christian Hicks University of Newcastle upon Tyne

1. Determining optimum Genetic Algorithm parameters for designing manufacturing facilities in the capital goods industry Dr Christian Hicks University of Newcastle upon Tyne http://www.staff.ncl.ac.uk/chris.hicks/presindex.htm

2. Two main themes: Facilities layout problem (FLP) Group Technology / Cellular Manufacturing Layout literature

3. “The determination of the relative locations for, and the allocation of available space among a number of workstations” (Azadivar and Wang, 2000). Block layouts represent resources as rectangles FLP formulated as: quadratic set covering problem, mixed integer programming problem and a graph theoretic problem. The FLP involves the solution of inefficient NP-complete algorithms. The longest time for solution increases exponentially with problem size. A lot of research based upon small or theoretical situations. Facilities Layout Problem

4. Clusters of dissimilar machines are placed close together Manufacturing cells design steps: Job assignment; cell formation; layout of cells within plant; Layout of machines within cells Transportation system design 3 approaches to cell formation: part family grouping, machine grouping and machine-part grouping. Cell formation and the layout problems are both NP-complete problems. Cellular Manufacturing

5. CM can reduce set-up and flow times, transfer batch sizes and WIP. However: 8/9 simulation studies found that functional layouts performed better than CM in terms of a range of evaluation criteria 14/15 empirical studies revealed CM produced significant operational benefits. Possible explanation: CM facilitates teamworking and provides a starting point for JIT. This may explain the difference in results obtained by research based upon simulation and empirical studies. Cellular Manufacturing

6. Use GAs to create sequences of machines. Apply a placement algorithm to generate layout. Measure total direct or rectilinear distance to evaluate the layout. Two approaches: Algorithm can treat layouts as a single facilities layout problem, or it can treat them as a hierarchical set of cell problems. The approach supports both FLP and CM. GA Procedure

7. Genetic Algorithm

8. Genetic representation Chromosome for single area

9. Genetic representation Chromosome with hierarchical constraints

10. Placement Algorithm

11. Case Study • 52 Machine tools • 3408 complex components • 734 part types • Complex product structures • Total distance travelled • Directdistance 232Km • Rectilinear distance 642Km

12. Random generation

13. Factor Levels Layout type Single cell, multiple cells Population size 50, 250, 500 Probability of crossover 0.3, 0.6, 0.9 Probability of mutation 0.02, 0.1, 0.18 Experimental Design

14. Hierarchy of areas The number of generations was the only significant factor. Best configuration

15. Significant factors: Population size Probability of crossover Number of generations Single area Best configuration

16. Developed a GA tool that can treat layouts as a single area or a hierarchy of cell layout problems. GA tool significantly better than random search GA worked better with unconstrained single area problems. In this case, population size, probability of crossover and number of generations were significant factors. With the hierarchy of cells approach only the number of generations was significant. Quality of layout influenced by initial allocation of machines to cells. Conclusions