## 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

### Keywords:

scheduling theory; branch and bound; parallel machines; makespan
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### References:

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