Neighborhood Systems for Production Sets with Indivisibilities

Herbert E. Scarf
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Herbert E. Scarf: Yale University

Chapter 5 in Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, 2008, pp 105-130 from Palgrave Macmillan

Abstract: Abstract A production set with indivisibilities is described by an activity analysis matrix with activity levels which can assume arbitrary integral values. A neighborhood system is an association with each integral vector of activity levels of a finite set of neighboring vectors. The neighborhood relation is assumed to be symmetric and translation invariant. Each such neighborhood system can be used to define a local maximum for the associated integer programs obtained by selecting a single commodity whose level is to be maximized subject to specified factor endowments of the remaining commodities. It is shown that each technology matrix (subject to mild regularity assumptions) has a unique, minimal neighborhood system for which a local maximum is global. The complexity of such minimal neighborhood systems is examined for several examples.

Keywords: Lattice Point; Integer Program; Large Firm; Knapsack Problem; Transportation Problem (search for similar items in EconPapers)
Date: 2008
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Journal Article: Neighborhood Systems for Production Sets with Indivisibilities (1986)
Working Paper: Neighborhood Systems for Production Sets with Indivisibilities (1984)
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Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-1-137-02441-1_5

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DOI: 10.1057/9781137024411_5

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