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Scheduling jobs with release dates and tails on two unrelated parallel machines to minimize the makespan. (English) Zbl 0953.90029

Summary: This paper deals with the problem of assigning a set of \(n\) jobs, with release dates and tails, to either one of two unrelated parallel machines and scheduling each machine so that the makespan is minimized. This problem will be denoted by \(R2|r_i,q_i|C_{\max}\). The model generalizes the problem on one machine \(1|r_i,q_i|C_{\max}\), for which a very efficient algorithm exists. In this paper we describe a branch and bound procedure for solving the two machine problem which is partly based on Carlier’s algorithm for the \(1|r_i,q_i|C_{\max}\). An \(O(n\log n)\) heuristic procedure for generating feasible solutions is given. Computational results are reported.

MSC:

90B35 Deterministic scheduling theory in operations research
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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