A discrete firefly algorithm for solving the flexible job-shop scheduling problem in a make-to-order manufacturing system

This work presents a multi-objective discrete firefly algorithm (MO-DFFA) for solving the flexible job-shop scheduling problem (FJSP) in a make-to-order production. Three different objectives are minimised simultaneously, being these objectives the weighted sum of the completion times of the orders, the workload of the critical machine and the total workload of all machines. Customer orders are ranked by priority according to the variables that the company considers the most relevant for its classification. Then, this priority is included in the FJSP model giving more preference in the scheduling phase to client requests with higher priority while, at the same, the volume of work of the resources is balanced to avoid machines saturation or under-utilization. With this approach both customer and company requirements can be satisfied and balanced. Furthermore, in the proposed framework customers can customize their orders choosing between some eligible product characteristics, which are considered as the different manufacturing operations which constitute each job. For solving the two sub-problems (i.e. operations assignment and sequencing) required for the scheduling of a flexible manufacturing system, we implemented a discrete version of the firefly algorithm metaheuristic. The computational results of several problem instances show that the presented MO-DFFA is a promising and efficient alternative to solve the FJSP in a customer-centric production system.