A Decomposition Method for Makespan Minimization in Job-Shop Scheduling Problem Using Ising Machine

To cope with daily changes in manufacturing production orders and plans, more efficient scheduling of production is highly required. The job-shop scheduling problem (JSP) provides a way to solve the production planning problem automatically, and the makespan criterion is an important metric for evaluating production efficiency. Several studies on the JSP using an Ising machine have been reported, but it is difficult to minimize the makespan by using an Ising machine. In this paper, we present a new method for minimizing the makespan in the JSP using an Ising machine. The makespan minimization problem is decomposed into two problems, the minimum makespan estimation problem and the constraint satisfaction problem. These problems are repeatedly solved until the solution converges to a sub-optimal result or until the termination conditions are satisfied. Experimental comparison with a commercial-based solver demonstrated that the proposed method is up to 5.2 times faster.