A deterministic inventory system with an inventory-level-dependent demand rate. (English) Zbl 0659.90040

Baker, R. C.; Urban, Timothy L.

J. Oper. Res. Soc. 39, No. 9, 823-831 (1988).

This analysis is concerned with the continuous, deterministic case of an inventory system in which the demand rate of an item is of a polynomial functional form, dependent on the inventory level. Differential and integral calculus are used to find the inventory function with respect to time. From this, the objective function (to maximize average profit per unit time) is developed. For the continuous, multiperiod situation, a nonlinear programming algorithm - separable programming - is utilized to determine the optimal order level (the quantity to order up to) and the order point (the quantity at which an order is placed). A numerical example and a sensitivity analysis are also presented.

MSC:

90B05

Inventory, storage, reservoirs

Keywords:

dependent demand rate; continuous, deterministic case; inventory system; average profit per unit time; separable programming; optimal order level; sensitivity analysis