Proportionate Flow Shop Games
Journal of Scheduling , Volume 11 p. 433- 447
In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines. By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face two problems: the first one is how to obtain an optimal order that minimizes the total processing cost, the second one is how to allocate the cost savings obtained by ordering the jobs optimally. In this paper we focus on the allocation problem. PFS games are defined as cooperative games associated to proportionate flow shop problems. It is seen that PFS games have a nonempty core. Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency. For this case an explicit game independent expression for the Shapley value is provide
|Proportionate flow shop problems, core, convexity|
|Journal of Scheduling|
|Distributed Implementations of Adaptive Collective Decision Making|
|Organisation||Networks and Optimization|
Estévez-Fernandéz, A, Mosquera, M.A, Borm, P, & Hamers, H. (2008). Proportionate Flow Shop Games. Journal of Scheduling, 11, 433–447.