Minimizing energy consumption and tardiness penalty for fuzzy flow shop scheduling with state-dependent setup time

This paper addresses a flow shop scheduling problem in a production system where the machine setup times depend on their prior states. State-dependent setup times exist widely in thermal facilities such as boilers and furnaces. The fuzzy set theory is introduced to describe the uncertainty of processing times and due dates in this study. The goal of the proposed fuzzy flow shop scheduling problem is to dispatch jobs to the machines and to determine the job sequence and state transition of each machine to minimize energy consumption and tardiness. To most efficiently determine the impact of uncertainty, the problem is formulated based on accurate operations of fuzzy numbers, which differ from approximate calculations in the existing literature on scheduling. To solve the problem, two common pattern matching schemes and heuristics are proposed to be combined with the classical genetic algorithm. Computational experiments show that the proposed GA performs better than the random key GA method, especially for large problems. The numerical results also provide practical implications for the proposed problem. The state-dependent setup time constraint significantly influences the scheduling results. In addition, the objective can be improved by reducing the uncertainty of processing times and due dates.