Modeling of Job-shop Scheduling Problem with In-process Buffer Capacity

Abstract

In recent years, as the diversification of demand and the progress of production technology have brought about a wider variety of products, the necessity of scheduling and inventory control is increasing. This paper deals with a job-shop scheduling problem with consideration of the capacities of in-process buffers, and proposes three kinds of methods of modeling the problem. First, the problem is formulated mathematically into a mixed integer programming (MIP) problem, and referring to the MIP, a way of modeling the problem into a disjunctive graph, is presented. Once the problem with in-process buffers is represented by the disjunctive graph, it can be solved effectively by using a conventional algorithm. e. g., a branch-and-bound method, for the ordinary job-shop scheduling problem. Second, the problem is described by another type of the MIP and is modeled using an extended timed Petri net which is useful as a tool for various kinds of simulation. Third, the problem is modeled by using a Gantt chart which is often used to represent a schedule graphically. This model is suitable for developing heuristic methods of scheduling.