Earliness/tardiness minimization in a no-wait flow shop with sequence-dependent setup times

Abstract

The no-wait flow shop scheduling problem (NWFSP) plays a crucial role in the allocation of resources in multitudinous industries, including the steel, pharmaceutical, chemical, plastic, electronic, and food processing industries. The NWFSP consists of n jobs that must be processed in m machines in series, and no job is allowed to wait between consecutive operations. This project deals with NWFSP with sequence-dependent setup times for minimizing earliness and tardiness. From the literature review of the last five years in NWFSP, it is noticeable that only around 1.92% of the researchers have studied that multi-objective function, which could help to improve the productivity of industries where methods such as just in time are considered. Be-sides, there is no information about previous researchers that have solved this problem with sequence-dependent setup times. Firstly, a MILP model is proposed to solve small instances, and secondly, a genetic algorithm (GA) is developed as a solution method for medium and large instances. Compared with the mathematical model for small instances, the GA obtained the optimal solution in 100% of the cases. For medium and large instances, the GA improves in an average of 31.54%, 38.09%, 44.58%, 47.72%, and 37.33% the MDD, EDDP, ATC, SPT, and LPT dispatching rules, respectively.