Genetic Algorithms for Job-Shop Scheduling Problems

The n×m minimum-makespan general job-shop scheduling problem, hereafter referred to as the JSSP, can be described by a set of n jobs {Ji}1≤j≤n which is to be processed on a set of m machines {Mr}1≤r≤m. Each job has a technological sequence of machines to be processed. The processing of job Jj on machine Mr is called the operation Ojr. Operation Ojr requires the exclusive use of Mr for an uninterrupted duration pjr, its processing time. A schedule is a set of completion times for each operation {cjr}1≤j≤n,1≤r≤m that satisfies those constraints. The time required to complete all the jobs is called the makespan L. The objective when solving or optimizing this general problem is to determine the schedule which minimizes L. An example of a 3× 3 JSSP is given in Table 1. The data includes the routing of each job through each machine and the processing time for each operation (in parentheses). Figure 1 shows a solution for the problem represented by “Gantt-Chart”.