A GOAL PROGRAMMING NETWORK FOR MIXED INTEGER LINEAR PROGRAMMING: A CASE STUDY FOR THE JOB-SHOP SCHEDULING PROBLEM

Abstract

Job-shop scheduling is an np-complete optimization problem subject to precedence and resource constraints. Recently, Foo and Takefuji have introduced a network-based solution procedure for solving job-shop problems formulated as mixed integer linear programming problems. To obtain the solution, the Tank and Hopfield linear programming network was repeatedly used. However, since such a network frequently produces constraint-violating solutions, the reliability of Foo and Takefuji’s approach is doubtful. In this article, it is shown that reliability of the network approach can be greatly improved, by guaranteeing constraint-satisfying solutions, if the original job-shop problem is reformulated as a goal programming problem, before it is mapped onto a goal programming network.