A mathematical model and heuristic procedure to schedule printed circuit packs on sequencers

Abstract

This paper considers the NP-hard problem of scheduling printed circuit packs (PCPs) on sequencers to minimize the total number of changeovers of input tapes required to produce PCPs. A mathematical model for this problem is given. However, when the size of the problem increases, the model will not be computationally feasible. An effective and fast heuristic to solve this problem is presented. The heuristic has shown its effectiveness over two previous heuristics found in the literature. It has been tested on a problem with 45 PCPs, two sequencers, each with seven dispensing heads, and a total of 20 input tape types. Comparison results showed that the heuristic reduced the total number of changeovers by 34% and 23% over previous heuristics. In addition, the proposed heuristic provided balanced workload across available sequencers. To investigate the efficiency of our heuristic further, we tested it against data sets from the literature. The proposed heuristic performs reasonably well compared with the reported results. In printed circuit packs' environment, set-up reduction is a main concern. Set-up is composed of the time required to changeover input tapes on sequencers when switching from PCP type to another. The proposed heuristic is more effective in reducing the number of changeovers of input tapes than heuristics found in the literature. The same heuristic can be used to schedule jobs on CNC machines so that total amount of tool switching is minimized.