An integrated greedy heuristic for a flexible job shop scheduling problem

The job shop scheduling problem (JSP) deals with the sequencing operations of a set of jobs on a set of machines with minimum cost. The flexible job shop scheduling problem (FJSP) is a generalization of the JSP, which is concerned with both the assignment of machines to operations and the sequencing of the operations on the assigned machines. The paper first presents an extension of the geometric approach for solving a two-job shop problem, when there is one flexible job and the second job is a job shop job. Based on this extension and the notion of the combined job, an integrated greedy heuristic that simultaneously deals with the assignment and the sequencing subproblems is developed to solve the general case with more than two jobs. The results obtained by the greedy heuristic on existing benchmarks from the literature are promising