V. I. Tsurkov ,   A. A. Mironov Phys.-Dokl. , vol.39 No.5 , 01.1994 , p. 318-321, language: английский ISSN 1063-7753  Аннотация Consider two problems: (a) a plant with $n$ production units (machines) $P_1,\dots, P_n$, and $m$ consumers (stores) $C_1,\dots, C_m$ must be provided with conveyers that connect producers and consumers, so that the entire volume of production should be consumed; (b) another plant with $n$ objects $O_1,\dots, O_n$, which simultaneously play the roles of producers and consumers, should be provided with conveyers for exchanging materials and intermediate products, so that, for each pair of objects, the volumes of the incoming and outgoing products are equal.\par Let ${\bold A}= \{a_1,\dots, a_n\}$ and ${\bold B}= \{b_1,\dots, b_m\}$ be vectors with nonnegative coordinates, where (a) $a_i$ and $b_j$ are the total widths of the conveyers necessary for the producer $P_i$ and the consumer $C_j$, respectively, with $a_1+\cdots+ a_n= b_1+\cdots+ b_m$; (b) $a_i$ is the total width of the conveyers necessary for an object $O_i$ in order to exchange with other $n- 1$ objects.\par A factory can produce and ship to each plant only conveyers of equal width (or, perhaps, different in the cases (a) and (b)). The problem is to determine the minimal width of conveyers $c({\bold A}, {\bold B})$ in the case (a) and $c({\bold A})$ in the case (b), such that all products by $P_i$, $1\le i\le n$ could be delivered to customers $C_j$, $1\le j\le m$ and the exchange between objects $O_i$, $1\le i\le n$ was possible.\par Below, we formalize these problems and give an algorithm for calculating the values $c({\bold A}, {\bold B})$ and $c({\bold A})$.  Ключевые слова distributive problems, minimax criterion, production planning

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