Solving Distributed and Flexible Job-Shop Scheduling Problems for a Real-World Fastener Manufacturer

Over the last few decades, there has been considerable concern over the multifactory manufacturing environments owing to globalization. Numerous studies have indicated that flexible job-shop scheduling problems (FJSPs) and the distributed and FJSPs (DFJSPs) belong to NP-hard puzzle. The allocation of jobs to appropriate factories or flexible manufacturing units is an essential task in multifactory optimization scheduling, which involves the consideration of equipment performance, technology, capacity, and utilization level for each factory or manufacturing unit. Several variables and constraints should be considered in the encoding problem of DFJSPs when using genetic algorithms (GAs). In particular, it has been reported in the literature that the traditional GA encoding method may generate infeasible solutions or illegal solutions; thus, a specially designed evolution process is required. However, in such a process, the diversity of chromosomes is lost. To overcome this drawback, this paper proposes a refined encoding operator that integrates probability concepts into a real-parameter encoding method. In addition, the length of chromosomes can be substantially reduced using the proposed algorithm, thereby, saving computation space. The proposed refined GA algorithm was evaluated with satisfactory results through two-stage validation; in the first stage, a classical DFJSP was adopted to show the effectiveness of the algorithm, and in the second stage, the algorithm was used to solve a real-world case. The real-world case involved the use of historical data with 100 and 200 sets of work orders of a fastener manufacturer in Taiwan. The results were satisfactory and indicated that the proposed refined GA algorithm could effectively overcome the conflicts caused by GA encoding algorithms.