Three perspectives for solving the job grouping problem

The production efficiency of printed circuit board (PCB) assembly depends strongly on the organization of the component placement jobs. This is characteristic, especially in a high-mix low-volume production environment. The present study discusses the problem of arranging the jobs of one machine into groups in such a way that the job change costs will be minimized when the costs depend on the number of the job groups. This problem is motivated by the practical case where the group utilizes a common machine set-up and the number of set-up occasions is the dominating factor in the production line optimization. The problem is well known and its large instances are hard to solve to optimality. We show how real-life problem instances can be solved by three different methods: efficient heuristics, 0/1-programming, and constraint programming. The first two of these are standard approaches in the field, whereas the application of constraint programming is new for the job grouping problem. The heuristic approach turns out to be efficient: algorithms are fast and produce optimal or nearly optimal groupings. 0/1-programming is capable of finding optimal solutions to small problem instances and it therefore serves as a benchmark to approximative methods. The constraint approach solves moderately large problem instances to optimality and it has the great advantage that changing the problem formulation is relatively easy one can add new constraints or modify the details of the existing ones flexibly.

[1]  Alan K. Mackworth Consistency in Networks of Relations , 1977, Artif. Intell..

[2]  Anil K. Jain,et al.  Algorithms for Clustering Data , 1988 .

[3]  Oded Maimon,et al.  Group set-up for printed circuit board assembly , 1989 .

[4]  Avraham Shtub,et al.  Grouping methods for printed circuit board assembly , 1991 .

[5]  Avraham Shtub,et al.  Role of similarity measures in PCB grouping procedures , 1992 .

[6]  Satoru Hashiba,et al.  Heuristic and Simulated Annealing Approaches to PCB Assembly Setup Reduction , 1992, PROLAMAT.

[7]  F. Glover,et al.  In Modern Heuristic Techniques for Combinatorial Problems , 1993 .

[8]  Gert Smolka,et al.  Object-Oriented Concurrent Constraint Programming in Oz , 1993, KI.

[9]  C. Reeves Modern heuristic techniques for combinatorial problems , 1993 .

[10]  Frits C. R. Spieksma,et al.  Production planning in automated manufacturing , 1994 .

[11]  Michael J. Maher,et al.  Constraint Logic Programming: A Survey , 1994, J. Log. Program..

[12]  T. T. Narendran,et al.  Grouping PCBs for set-up reduction: a maximum spanning tree approach , 1996 .

[13]  Yves Crama,et al.  The approximability of tool management problems , 1996 .

[14]  Barbara M. Smith,et al.  The Phase Transition Behaviour of Maintaining Arc Consistency , 1996, ECAI.

[15]  Gang Yu,et al.  Approximation Algorithms for the k-Clique Covering Problem , 1996, SIAM J. Discret. Math..

[16]  Joachim Schimpf,et al.  ECLiPSe: A Platform for Constraint Logic Programming , 1997 .

[17]  Avraham Shtub,et al.  Grouping components in printed circuit board assembly with limited component staging capacity and single card setup: Problem characteristics and solution procedures , 1997 .

[18]  M. R. Rao,et al.  Combinatorial Optimization , 1992, NATO ASI Series.

[19]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[20]  Mika Johnsson,et al.  Fuzzy Approach for Modeling Multiple Criteria in the Job Grouping Problem , 1998 .

[21]  Brett A. Peters,et al.  A comparison of setup strategies for printed circuit board assembly , 1998 .

[22]  Mika Johnsson,et al.  Job Grouping in Surface Mounted Component Printing , 1999 .

[23]  Chris N. Potts,et al.  Constraint satisfaction problems: Algorithms and applications , 1999, Eur. J. Oper. Res..

[24]  Hana Rudová Over-Constrained Systems , 1999, AAAI/IAAI.

[25]  Mika Johnsson,et al.  An Interactive System for Scheduling Jobs in Electronic Assembly , 1999 .

[26]  Mika Johnsson,et al.  A Comparison of Group and Minimum Setup Strategies in PCB Assembly , 2000 .