Abstract
We treat a scheduling problem as follows: We have n jobs which are to be processed by any of m parallel facilities in a shop. It takes time Ti for any facility to process job i (i=1, 2, …, n), and a cost of cij is incurred during the changeover from job i to job j. Furthermore, each job i has a due-date Di, and all jobs on each facility must be completed within a horizon of length H. The purpose is to find an optimal schedule, which is to partition the set J of n jobs into m subsets and to sequence the elements of each subset so that the due-date and horizon constraints are met and the total changeover cost is minimized. In this paper, we formulate this problem as a 0-1 integer problem, and present an efficient algorithm which makes use of the branch-and-bound method. It is shown that the algorithm can work efficiently, and, in particular, it can be apllied to some problems having upto 25 jobs. Furthermore, we propose a method of treating an extended problem that has no feasible solution satisfying the due-date constraint.
