Three perspectives for solving the job grouping problem

The production efficiency of printed circuit board (PCB) assembly depends s trongly on the organization of the component placement jobs. This is charac teristic, especially in a high-mix low-volume production environment. The p resent study discusses the problem of arranging the jobs of one machine int o 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 th e number of set-up occasions is the dominating factor in the production lin e 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 solv ed by three different methods: efficient heuristics, 0/1-programming, and c onstraint programming. The first two of these are standard approaches in th e field, whereas the application of constraint programming is new for the j ob grouping problem. The heuristic approach turns out to be efficient: algo rithms are fast and produce optimal or nearly optimal groupings. 0/1-progra mming is capable of finding optimal solutions to small problem instances an d it therefore serves as a benchmark to approximative methods. The constrai nt 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 o nes flexibly.