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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 $O\left(nlogn\right)$ heuristic procedure for generating feasible solutions is given. Computational results are reported.
##### MSC:
 90B35 Scheduling theory, deterministic 90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut 68M20 Performance evaluation of computer systems; queueing; scheduling