Novel Formulation and Resolution of Job-Shop Scheduling Problems

Abstract

Job-shop scheduling is an important problem in planning and operation of manufacturing systems. For such difficult problems to be solved daily within short amounts of time, the only practical goal is to obtain near-optimal solutions with quantifiable quality fast. Recent developments of powerful Mixed-Integer Linear Programming (MILP) methods such as branch-and-cut provide an opportunity for a fresh perspective at new effective MILP formulation and resolution of the problem. Moreover, formulation tightening is critically important since if constraints directly delineate the convex hull of an MILP problem, it can be solved by linear programming without combinatorial difficulties. To achieve the above goal, three major contributions of this letter are: 1) to efficiently formulate the problem in an MILP form; 2) to develop a novel systematic formulation tightening approach for the first time; and 3) to establish a decomposition and coordination method with exponential reduction of complexity and accelerated convergence to efficiently solve the problem. Testing results show that our formulation tightening is effective in terms of computational efficiency and solution quality. With decomposition, time-consuming branching is no longer needed when solving subproblems, and coordination is effective. For dynamic job-shop scheduling problems, schedule can be regenerated fast based on previous scheduling results. This work opens up new directions for more exploration to efficiently solve MILP problems.