A Two-Phase Iterative Mathematical Programming-Based Heuristic for a Flexible Job Shop Scheduling Problem with Transportation

Abstract

In a flexible job shop problem with transportation (FJSPT), a typical flexible manufacturing system comprises transporters that pick up and deliver jobs for processing at flexible job shops. This problem has grown in importance through the wide use of automated transporters in Industry 4.0. In this article, a two-phase iterative mathematical programming-based heuristic is proposed to minimize makespan using a machine-operation assignment centric decomposition scheme. The first phase approximates the FJSPT through an augmented flexible job shop scheduling problem (FJSP + T) that reduces the solution space while serving as a heuristic in locating good machine-operation assignments. In the second phase, a job shop scheduling problem with transportation (JSPT) network is constructed from these assignments and solved for the makespan. Compared to prior JSPT implementations, the proposed JSPT model considers job pre-emption, which is instrumental in enabling this FJSPT implementation to outperform certain established benchmarks, confirming the importance of considering job pre-emption. Results indicate that the proposed approach is effective, robust, and competitive.

Keywords

• flexible job shop
• heuristic
• job shop scheduling problem with transportation
• mixed integer linear programming
• simultaneous scheduling