Production Sets with Indivisibilities Part I: Generalities

Herbert Scarf

Chapter 2 in Herbert Scarf’s Contributions to Economics, Game Theory and Operations Research, 2008, pp 7-38 from Palgrave Macmillan

Abstract: Abstract This paper and its sequel present a new approach to the study of production sets with indivisibilities and to the programming problems which arise when a factor endowment is specified. The absence of convexity precludes the use of prices to support efficient production plans and to guide the search for optimal solutions. Instead, we describe the unique minimal system of neighborhoods for which a local maximum is global, and discuss a related algorithm. The definition of this neighborhood system is based on techniques used in the computation of fixed points of a continuous mapping. In Part II of the paper this neighborhood system is investigated in the special case of two activities and it is shown that the algorithm may be accelerated so as to terminate in polynomial time.

Keywords: Programming Problem; Lattice Point; Large Firm; Integer Programming Problem; Neighborhood System (search for similar items in EconPapers)
Date: 2008
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Journal Article: Production Sets with Indivisibilities-Part I: Generalities (1981)
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Persistent link: https://EconPapers.repec.org/RePEc:pal:palchp:978-1-137-02441-1_2

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DOI: 10.1057/9781137024411_2

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