Genetic algorithm for rotary machine scheduling with dependent processing times

Abstract

This paper focuses on scheduling a rotary injection molding machine with dependent processing times. The injection machine has n pairs of positions to process n pairs of shoes. It is rotated after every cycle time. Cycle time is the maximum injection time of the jobs currently loaded in the machine. Thus, for all practical purposes, the processing time of a job depends on the combination of the jobs currently assigned to the machine. The uncertainty of processing time makes this problem more complicated than traditional parallel machine scheduling problems. Additionally, since switching jobs leads to mold changes, set-up time is also included in the analysis. We develop a Sequential Genetic Algorithm (SGA) to identify the best schedule with regard to makespan. In this approach, multiple GA evolvers are connected by using a feeding strategy, where each GA evolver identifies the best schedule with minimum makespan for the corresponding product family. A multi-segment (product lines) chromosome representation is applied to represent the product line sequence as well as the job sequence within a product family. Furthermore, an adaptive feeding strategy is also proposed to improve results and reduce computation times. Besides SGA, we also improve the performance of a traditional heuristic procedure by proposing a minimum ΔIT heuristic approach. The experimentation is performed by using four experimental data sets with different demand patterns and nine data sets from a shoe manufacturing plant. The results indicate that our SGA provides better schedule with respect to makespan value, while heuristic procedures take insignificant time to obtain results. Another observation is that adaptive feeding strategy helps to find good results in a shorter time.