Flow-shop scheduling with a learning effect

Abstract

The paper is devoted to some flow-shop scheduling problems with a learning effect. The objective is to minimize one of the two regular performance criteria, namely, makespan and total flowtime. A heuristic algorithm with worst-case bound m for each criteria is given, where m is the number of machines. Furthermore, a polynomial algorithm is proposed for both of the special cases: identical processing time on each machine and an increasing series of dominating machines. An example is also constructed to show that the classical Johnson's rule is not the optimal solution for the two-machine flow-shop scheduling to minimize makespan with a learning effect. Some extensions of the problem are also shown.

Keywords:

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

Acknowledgements

We thank two anonymous referees for their helpful comments on earlier version of the article. This work is supported by the foundation of Ph.D. Units of Chinese Education Ministry, under Grant number: 20020141013.