Geodesic
Approximation solution of the supply management problem
Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 1, pp. 27-39

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The problem is considered of optimizing the product delivery from suppliers to consumers. The size of each open supply is bounded both below and above, the size of consumption for each consumer is bounded below, the supply cost functions are linear for nonzero volumes of supply. A fully polynomial time approximation scheme is proposed for this problem in the case of one consumer, and the complexity of the problem is studied in the general case. 
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A. V. Eremeev; A. A. Romanova; V. V. Servakh; S. S. Chauhan. Approximation solution of the supply management problem. Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 1, pp. 27-39. http://geodesic.mathdoc.fr/item/DA_2006_13_1_a2/