Strongly balanced cooperative games
International Journal of Game Theory
On games corresponding to sequencing situations with ready times
Mathematical Programming: Series A and B
Two-machine proportionate flowshop scheduling with breakdowns to minimize maximum lateness
Computers and Operations Research
Stochastic proportionate flowshop scheduling with setups
Computers and Industrial Engineering
Fair Queuing and Other Probabilistic Allocation Methods
Mathematics of Operations Research
Job scheduling, cooperation, and control
Operations Research Letters
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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 is how to obtain an optimal order that minimizes the total processing cost, the second 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 provided.