Production sequencing problem with re-entrant work flows and sequence dependent setup times

Abstract

This paper addresses a shop scheduling problem where a set of n jobs needs to be scheduled on two machines for the side frame press shop in a truck manufacturing company. A most unusual aspect of the problem is that the setup limes required for a job in the first machine depend not on the immediately preceding job but on the job which is two steps prior to it. Redefining the job elements, the problem is formulated into a general two machine flow shop problem which can be solved by dynamic programming with the objective of the minimum makespan. An optimal schedule is found utilizing the sequence dominance conditions and the decision-delay scheme. Since the computational requirements of dynamic programming are impracticably demanding for large-sized problems, a genetic algorithm is developed and its performance is examined through a comparative study.