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A deterministic multiproduct, multifacility, multiperiod production planning model is analyzed. The model considers concave production costs, which can depend upon the production in several different facilities, and piecewise concave inventory costs. Backlogging of unsatisfied demand is permitted. After determining the general form of the minimum cost production schedule, algorithms to calculate the minimum cost schedule explicitly in certain specific cases are presented.
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Willard I. Zangwill (1966) studied this question.
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