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The Simple and Multiple Job Assignment Problems

Abstract : This paper addresses two real-life assignment problems. In both cases, the number of employees to whom tasks should be assigned is significantly greater than the number of tasks. In the simple job assignment problem, at most one task (job) should be assigned to each employee; this constraint is relaxed in the multiple job assignment problem. In both cases, the goal is to minimize the time the last task is completed; these problems are known as Bottleneck Assignment Problems (BAPs for short). We show that the simple job assignment problem can be solved optimally using an iterative approach based on dichotomy. At each iteration, a linear programming problem is solved: in this case the solution is integer. We propose a fast heuristic to solve the multiple job assignment problem, as well as a Branch-and-Bound approach which leads to an optimal solution. Numerical examples are presented. They show that the heuristic is satisfactory for the application at hand.
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https://hal.inria.fr/inria-00072918
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 11:16:43 AM
Last modification on : Thursday, February 11, 2021 - 2:48:12 PM
Long-term archiving on: : Thursday, March 24, 2011 - 12:20:42 PM

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  • HAL Id : inria-00072918, version 1

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Fabrice Chauvet, Jean-Marie Proth, A. Soumare. The Simple and Multiple Job Assignment Problems. [Research Report] RR-3744, INRIA. 1999, pp.15. ⟨inria-00072918⟩

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