Worst-case analysis for flow shop scheduling problems with an exponential learning effect

Abstract

A real industrial production phenomenon, referred to as learning effects, has drawn increasing attention. However, most research on this issue considers only single machine problems. Motivated by this limitation, this paper considers flow shop scheduling problems with an exponential learning effect. By the exponential learning effect, we mean that the processing time of a job is defined by an exponent function of its position in a processing permutation. The objective is to minimize one of the four regular performance criteria, namely, the total completion time, the total weighted completion time, the discounted total weighted completion time, and the sum of the quadratic job completion times. We present heuristic algorithms by using the optimal permutations for the corresponding single-machine scheduling problems. We also analyse the worst-case bound of our heuristic algorithms.

Keywords:

• scheduling
• flow shop
• learning effect
• worst-case analysis

Acknowledgements

We are grateful to two anonymous referees for their helpful comments on earlier version of this paper. This research was supported by the National Natural Science Foundation of China (Grant No. 11001181 and 71031002) and the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 70725004).