A Column Generation Approach to Solve Proportionate Flexible Flow Shop for Common Due Date Scheduling

Abstract

Abstract-This paper addresses a proportionate flexible flow shop for common due date scheduling problem. A proportionate flexible flow shop problem is generalization of the proportionate flow shop problem with multiple identical machines at any stage. The problem of minimizing total weighted deviations of job completion time from a common due date on a single machine is typical scheduling model in Just-In- Time production environment. In this paper, we propose a column generation approach which is based on some properties from V-shaped schedule on a single machine. This problem is actually a portioning problem, and a dynamic programming algorithm is proposed to find an early schedule and a tardy schedule with minimum reduced cost. The combination of column generation and linear programming demonstrate the capability of solving large scale problems. Computational result shows the effectiveness and the capability of solving problems with up to 40 jobs.