Decentralized subcontractor scheduling with divisible jobs

Abstract

Subcontracting allows manufacturer agents to reduce completion times of their jobs and thus obtain savings. This paper addresses the coordination of decentralized scheduling systems with a single subcontractor and several agents having divisible jobs. Assuming complete information, we design parametric pricing schemes that strongly coordinate this decentralized system, i.e., the agents' choices of subcontracting intervals always result in efficient schedules. The subcontractor's revenue under the pricing schemes depends on a single parameter which can be chosen to make the revenue as close to the total savings as required. Also, we give a lower bound on the subcontractor's revenue for any coordinating pricing scheme. Allowing private information about processing times, we prove that the pivotal mechanism is coordinating, i.e., agents are better off by reporting their true processing times, and by participating in the subcontracting. We show that the subcontractor's maximum revenue with any coordinating mechanism under private information equals the lower bound of that with coordinating pricing schemes under complete information. Finally, we address the asymmetric case where agents obtain savings at different rates per unit reduction in completion times. We show that coordinating pricing schemes do not always exist in this case.

Shared processor scheduling

“…Observe that by construction, S is synchronized and all jobs from J appear on the shared processor, see [10] and [7]. We now prove that any processing time ordered schedule is an optimal solution for an antithetical instance.…”

“…The shared processor scheduling problem has recently been studied by Vairaktarakis and Aydinliyim [10], Hezarkhani and Kubiak [7], and Dereniowski and Kubiak [6]. Vairaktarakis and Aydinliyim [10] consider the (unweighted) problem with a single shared processor and with each job allowed to use at most one time interval on the shared processor.…”

Shared multi-processor scheduling

“…Recently, Vairaktarakis and Aydinliyim [11] consider scheduling divisible jobs on subcontractor's processor in supply chains to reduce the job's completion times. Hezarkhani and Kubiak [7] refer to the problem as the subcontractor scheduling problem. Vairaktarakis [10] points out that the lack of due attention to the subcontractors' operations can cause significant complications in supply chains.…”

Shared processor scheduling of multiprocessor jobs

“…The shared processor scheduling problem with a single shared processor has been studied by Vairaktarakis and Aydinliyim [12], Hezarkhani and Kubiak [8], and Dereniowski and Kubiak [6]. Vairaktarakis and Aydinliyim [12] consider the unweighted problem with each job allowed to use at most one time interval on the shared processor.…”

“…The tension calls for coordinating mechanisms to ensure the efficiency. Hezarkhani and Kubiak [8] show such coordination mechanism for the unweighted problem, and give examples to prove that such mechanisms do not exist for the problem with weighted jobs. Dereniowski and Kubiak [5] consider shared multi-processor problem.…”