Games,Critical Paths and Assignment Problems in Permutation Flow Shops and Cyclic Scheduling Flow Line Environments

In this paper we address the non-pre-emptive flow shop scheduling problem for makespan minimization in a new modelling framework. A lower bound generation scheme is developed by using appropriately defined linear assignment problems and, based on this new approach, a special class of permutation flow shop problems is identified. We present a game theoretic interpretation of our modelling approach which leads to an integer programming formulation of the scheduling problem. A new branch and bound scheme is developed based on these results. The major advantage of our modelling framework and branch-and- bound approach is that it can be easily extended to address a general class of cyclic scheduling problems for production flow lines with blocking. After a discussion of this extension, we report on computational experience that indicates the very satisfactory performance of the new optimal solution procedure for cyclic scheduling problems with finite capacity buffers.