The simple and multiple job assignment problems

The simple and multiple job assignment problems

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Article ID: iaor20012102
Country: United Kingdom
Volume: 38
Issue: 14
Start Page Number: 3165
End Page Number: 3179
Publication Date: Jan 2000
Journal: International Journal of Production Research
Authors: , ,
Keywords: programming: linear
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. 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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