Studies in the literature on flexible job-shop scheduling problems (FJSP) generally assume that one worker is assigned to each machine and that processing times are constant. However, in some industries, multiple workers with cooperation can process complex operations faster than one worker. If the possibility of completing jobs in a shorter time with worker cooperation is not taken into account, the opportunity to create more effective schedules may not be taken advantage of. Therefore, it is essential to consider the flexibility of collaboration between employees. However, to increase labor efficiency in businesses, jobs are also expected to be done with the minimum number of workers possible. This study considers the FJSP with both machine and number of workers dependent processing times. The objectives are minimizing the total tardiness and the total number of workers. A bi-objective mathematical model and an NSGA-II algorithm for large-sized problems have been proposed. The performance of the proposed solution approaches is demonstrated by using randomly generated test problems. For each problem, the most successful Pareto solution among the obtained solutions by the mathematical model and the NSGA-II algorithm was determined using the TOPSIS method. Furthermore, the effect of the total number of workers on the total tardiness is examined. The performance of proposed solution approaches, and when the worker number increases, the total tardiness of jobs can be reduced by an average of 75.88%, have been shown through comprehensive experimental studies.

We present here a hybrid algorithm for the Flexible Job-Shop Scheduling Problem (FJSSP). This problem involves the optimal use of resources in a flexible production environment in which each operation can be carried out by more than a single machine. Our algorithm allocates, in a first step, the machines to operations and in a second stage it sequences them by integrating a Multi-Objective Evolutionary Algorithm (MOEA) and a path-dependent search algorithm (Multi-Objective Simulated Annealing), which is enacted at the genetic phase of the procedure. The joint interaction of those two components yields a very efficient procedure for solving the FJSSP. An important step in the development of the algorithm was the selection of the right MOEA. Candidates were tested on problems of low, medium and high complexity. Further analyses showed the relevance of the search algorithm in the hybrid structure. Finally, comparisons with other algorithms in the literature indicate that the performance of our alternative is good.