Novel Heuristic Algorithm for Flexible Job Shop Scheduling based on the Longest Processing Time Rules to Minimize Makespan

Abstract

This research examined the scheduling of jobs with multiple stages unto identical parallel machines to minimize the makespan. The work is motivated by a Flexible Manufacturing System case that produces various parts and has multiple machining centers. Early research towards this system proposed a stage-by-stage independent scheduling, resulting in a non-optimal solution. This study aimed to create a better solution for the system by developing a novel heuristic algorithm based on the classical longest processing time algorithm and simultaneously considering processing time for all stages when deciding the job sequencing and job-machine allocation. The algorithm is defined as Modified LPT for Multiple Identical Machine with Multi-process Capability (M-LPT MIMMPC). We performed a numerical experiment to assess the algorithm's performance by incorporating various cases. We concluded that the resulting makespans are always better than LPT's theoretical bound for parallel machine scheduling. In some cases, it successfully gave an optimal value. Although the experiment scope was still limited, the algorithm showed promising performance results.

Keywords

• scheduling
• heuristic algorithms
• flexible machines
• job shop
• makespan