Optimality of myopic inventory policies for several substitute products.

*(English)*Zbl 0172.44101Summary: Multiproduct inventory systems with proportional ordering costs and stochastic demands are studied. New conditions are obtained under which a myopic ordering policy (a policy of minimizing expected cost in the current period alone) is optimal for a sequence of periods for all initial inventory levels. An important one of these, the substitute property, holds when the myopic policy is such that increasing the initial inventory of one product does not increase the quantity ordered of any product.

Conditions on the one period expected holding and shortage cost function, which are of independent interest in nonlinear programming, are shown to imply the substitute property. Applications of these conditions to models with storage or investment limitations and to a multiechelon model are given.

Under backlogging the usual extension to a fixed delivery lag is obtained. Some non-stationary cases are also treated.

Conditions on the one period expected holding and shortage cost function, which are of independent interest in nonlinear programming, are shown to imply the substitute property. Applications of these conditions to models with storage or investment limitations and to a multiechelon model are given.

Under backlogging the usual extension to a fixed delivery lag is obtained. Some non-stationary cases are also treated.

##### MSC:

90B05 | Inventory, storage, reservoirs |