© C.Hicks, University of Newcastle IGLS04/1 Determining optimum Genetic Algorithm parameters for designing manufacturing facilities in the capital goods industry Dr Christian Hicks University of Newcastle upon Tyne

© C.Hicks, University of Newcastle IGLS04/2 Layout literature Two main themes: Facilities layout problem (FLP) Group Technology / Cellular Manufacturing

© C.Hicks, University of Newcastle IGLS04/3 Facilities Layout Problem “ 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.

© C.Hicks, University of Newcastle IGLS04/4 Cellular Manufacturing 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.

© C.Hicks, University of Newcastle IGLS04/5 Cellular Manufacturing 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.

© C.Hicks, University of Newcastle IGLS04/6 GA Procedure 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.

© C.Hicks, University of Newcastle IGLS04/7 Genetic Algorithm

© C.Hicks, University of Newcastle IGLS04/8 Genetic representation Chromosome for single area

© C.Hicks, University of Newcastle IGLS04/9 Genetic representation Chromosome with hierarchical constraints

© C.Hicks, University of Newcastle IGLS04/10 Placement Algorithm

© C.Hicks, University of Newcastle IGLS04/11 Case Study 52 Machine tools 3408 complex components 734 part types Complex product structures Total distance travelled –Direct distance 232Km –Rectilinear distance 642Km

© C.Hicks, University of Newcastle IGLS04/12 Random generation

© C.Hicks, University of Newcastle IGLS04/13 Experimental Design FactorLevels Layout typeSingle cell, multiple cells Population size50, 250, 500 Probability of crossover 0.3, 0.6, 0.9 Probability of mutation 0.02, 0.1, 0.18

© C.Hicks, University of Newcastle IGLS04/14 Hierarchy of areas The number of generations was the only significant factor. Best configuration

© C.Hicks, University of Newcastle IGLS04/15 Single area Significant factors: Population size Probability of crossover Number of generations Best configuration

© C.Hicks, University of Newcastle IGLS04/16 Conclusions 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.