Minimum concave-cost solution of Leontief substitution models of multi- facility inventory systems. (English) Zbl 0175.17602

Veinott, Arthur F. jun.

Oper. Res. 17, 262-291 (1969).

The author shows that a broad class of problems inventory control can be formulated as minimizing a concave function over the solution set of a Leontief substitution system. This class includes deterministic single- and multi-facility economic lot size, lot-size smoothing, warehousing, product-assortment, batch-queuing, capacity-expansion, investment consumption, and reservoir-control problems with concave cost functions. In such problems an optimum occurs at an extreme point of the solution set, and the author utilizes the characterization of the extreme points to obtain most existing qualitative characterizations of optimal policies for inventory models with concave costs in a unified manner. In a number of cases the author gives dynamic programming recursions for searching the extreme points to find an optimal point. The given algorithms are chosen so that computational effort increases algebraically with the size of the problem.

Reviewer: K. Ackermann

MSC:

90B05	Inventory, storage, reservoirs
90C39	Dynamic programming

Keywords:

multi-facility inventory systems; minimum concave-cost solution of Leontief substitution models; dynamic programming recursions