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Open AccessJournal ArticleDOI

Notes—On a Selection Problem

M. L. Balinski
- 01 Nov 1970 - 
- Vol. 17, Iss: 3, pp 230-231
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TLDR
In this article, the authors proposed a combinatorial station selection problem that can be solved by identifying minimum cuts with optimal selection, and showed how to solve this problem with minimum cuts and optimal selection.
Abstract
John Rhys [Rhys, J. 1970. Shared fixed cost and network flows. Management Sci. 17(3, November).], and then J. D. Murchland [Murchland, J. D. 1968. Rhys's combinatorial station selection problem. Report LBS-TNT-68, London Graduate School of Business Studies, Transport Network Theory Unit, June 10.], have discussed a model aimed at making an optimal selection in a particular situation having several applications. This note shows how this problem can be solved by identifying minimum cuts with optimal selection.

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Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints

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The boolean quadric polytope: Some characteristics, facets and relatives

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Quadratic knapsack problems

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Minimum cuts and related problems

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Journal ArticleDOI

A Selection Problem of Shared Fixed Costs and Network Flows

J. M. W. Rhys
- 01 Nov 1970 - 
TL;DR: In this article, an apparently combinatorial problem is defined, and a method given for solution by reduction to a network flow problem, where the benefits to be obtained cannot be related to individual cost-incurring items (facilities) but only to combinations.