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Journal Articles Computers and Operations Research Year : 2007

An exact method for Pm / sds,ri /∑ni=1 Ci problem

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Abstract

This paper addresses an identical parallel machine scheduling problem, with sequence-dependent setup times and release dates to minimize total completion time. This problem is known to be strongly NP-hard. We prove a sufficient and necessary condition for local optimality which can also be considered as a priority rule. We then define a dominant subset based on this condition. We present efficient heuristic algorithms using this condition to build a schedule belonging to this subset. We also prove dominance theorem, and develop a lower bound that can be computed in polynomial time. We construct a branch-and-bound algorithm in which the heuristic, the lower bound and the dominance properties are incorporated. Computational experiments suggest that the algorithm can handle test problems with 40 jobs and 2 machines.

Dates and versions

hal-02490590 , version 1 (25-02-2020)

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Rabia Nessah, Chengbin Chu, Farouk Yalaoui. An exact method for Pm / sds,ri /∑ni=1 Ci problem. Computers and Operations Research, 2007, 34 (9), pp.2840-2848. ⟨10.1016/j.cor.2005.10.017⟩. ⟨hal-02490590⟩

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