Algorithms and Model Formulations in Mathematical Programming pp 170–171 Cite as

## Procedures for Solving Bottleneck Generalized Assignment Problems

- Alan W. Neebe 2 &
- Joseph B. Mazzola 3
- Conference paper

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Part of the NATO ASI Series book series (NATO ASI F,volume 51)

We discuss bottleneck (or minimax) versions of the generalized assignment problem. The basic problem involves the assignment of a number of jobs to a number of agents such that each job is performed by a unique agent, and capacity limitations on the agents are not exceeded. Two versions of the bottleneck generalized problem (BGAP) are defined. The first of these is called the Task BGAP and has as its objective the minimization of the maximum of the costs of the assignments that are made. The second version is referred to as the Agent BGAP and has as its objective the minimization of the maximum of the total costs assigned to each agent.

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## Author information

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School of Business Administration, University of North Carolina, USA

Alan W. Neebe

Fuqua School of Business, Duke University, USA

Joseph B. Mazzola

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## Editor information

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Chr. Michelsen Institute, Fantoftvegen 38, N-5036, Fantoft, Norway

Stein W. Wallace

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© 1989 Springer-Verlag Berlin Heidelberg

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Neebe, A.W., Mazzola, J.B. (1989). Procedures for Solving Bottleneck Generalized Assignment Problems. In: Wallace, S.W. (eds) Algorithms and Model Formulations in Mathematical Programming. NATO ASI Series, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83724-1_24

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## IMAGES

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## COMMENTS

We consider two versions of bottleneck (or min–max)

generalized assignment problem(BGAP) under capacityuncertainty:Task–BGAP and Agent– A robust optimization solution tobottleneck generalized assignment problem under uncertainty| SpringerLinkBottleneck Generalized Assignment Problem.

Bottleneck generalized assignment problem(BGAP), is the min-max version of the well-known(min-sum) generalized assignment problem.In the BGAP, the maximum penalty incurred by assigning each task to an agent is minimized.We discuss

bottleneck(or minimax) versions of thegeneralized assignment problem.The basicprobleminvolves the assignment of a number of jobs to a number ofagentssuch that each job is performed by a uniqueagent,and capacity limitations on theagentsare not...In this study, we consider the multi resource

agent bottleneckgeneralisedassignment problem. Our aim is to minimise the maximum load over allagents. We take our motivation from anassignmentproblemfaced in heating, ventilating and air conditioning sector. We study the linear programming (LP) relaxation of theproblem.The min-max version of the generalized assignment problem is considered. We introduce relaxations and show that they produce, as sub-problems, min-max versions of the multiple-choice

knapsack problemand of the 0–1knapsack problem.An

assignmentproblemarises when there exists a set of tasks that must be allocated to a set ofagents. Thebottleneckassignmentproblem(BAP) has the objective of minimising the most costly allocation of a task to anagent.We discuss

bottleneck(or minimax) versions of the generalized assignment problem. The basic problem involves the assignment of a number of jobs to a number ofagentssuch that each job is performed by a uniqueagent,and capacity limitations on theagentsare not exceeded.We discuss a

bottleneck(or minimax) version of thegeneralized assignment problem,known as the taskbottleneck generalized assignment problem(TBGAP). TBGAP involves the assignment of a number of jobs to a number ofagentssuch that each job is performed by a uniqueagent,and capacity limitations on theagentsare not exceeded.