An extended flexible job shop scheduling problem with parallel operations

Traditional planning and scheduling techniques still hold important roles in modern smart scheduling systems. Realistic features present in modern manufacturing systems need to be incorporated into these techniques. Flexible job-shop scheduling problem (FJSP) is one of the most challenging combinatorial optimization problems. FJSP is an extension of the classical job shop scheduling problem where an operation can be processed by several different machines. In this paper, we consider the FJSP with parallel operations (EFJSP) and we propose and compare a discrete firefly algorithm (FA) and a genetic algorithm (GA) for the problem. Several FJSP and EFJSP instances were used to evaluate the performance of the proposed algorithms. Comparisons among our methods and state-of-the-art algorithms are also provided. The experimental results demonstrate that the FA and GA achieved improvements in terms of efficiency and efficacy. Solutions obtained by both algorithms are comparable to those obtained by algorithms with local search. In addition, based on our initial experiments, results show that the proposed discrete firefly algorithm is feasible, more effective and efficient than our proposed genetic algorithm for the considered problem.