Econometrica: Jan 1981, Volume 49, Issue 1

Production Sets with Indivisibilities, Part I: Generalities<1:PSWIPI>2.0.CO;2-V
p. 1-32

Herbert E. Scarf

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 polynominal time.

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