Scheduling Algorithm for Multi-Stage Process : Scheduling under the Constraints of the Processing Time and Capacity at the Succeeding Stations (Part III)

Abstract

In the previous papers, it is shown that the scheduling problem for the Multi-Stage Process can be reduced to the single machine scheduling problem of allotting jobs between the earliest and latest end times for each job, and a practical scale problem can be efficiently reduced to a smaller scale problem by using our reducing method of model size. This paper presents an optimization algorithm for the scheduling problem based on the Branch-and-Bound method so as to minimize the total flow time in the post-process. The branching operation using reducing method and the strong lower bound which is derived by determining the minimum total overlap time for unassigned jobs will enhance the computational efficiency. The efficiency of proposed algorithm is also shown through the numerical illustrations.