Just-in-time scheduling with two competing agents on unrelated parallel machines

Yunqiang Yin, Shuenn-Ren Cheng, T.C.E. Cheng, Du-Juan Wang and Chin-Chia Wu

Omega, 2016, vol. 63, issue C, 41-47

Abstract: This paper considers two-agent just-in-time scheduling where agents A and B have to share m unrelated parallel machines for processing their jobs. The objective of agent A is to maximize the weighted number of its just-in-time jobs that are completed exactly on their due dates, while the objective of agent B is either to maximize its maximum gain (income) from its just-in-time jobs or to maximize the weighted number of its just-in-time jobs. We provide a bicriterion analysis of the problem, which seek to find the Pareto-optimal solutions for each combination of the two agents׳ criteria. When the number of machines is part of the problem instance, both the addressed problems are NP-hard in the strong sense. When the number of machines is fixed, we show that the problem of maximizing agent A׳s weighted number of just-in-time jobs while maximizing agent B׳s maximum gain can be solved in polynomial time, whereas the problem of maximizing both agents׳ weighted numbers of just-in-time jobs is NP-hard. For the latter problem, we also provide a pseudo-polynomial-time solution algorithm, establishing that it is NP-hard in the ordinary sense, and show that it admits a fully polynomial-time approximation scheme (FPTAS) for finding an approximate Pareto solution.

Keywords: Scheduling; Two agents; Unrelated parallel machines; Just-in-time scheduling; FPTAS (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (20)

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DOI: 10.1016/j.omega.2015.09.010

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