A two-period stochastic inventory model

Abstract

Even though there is today a multitude of static and dynamic models available to the firm reflecting its perceived economic environment, the number of models including inventories is surprisingly small. These models are roughly divided in two groups: stochastic inventory models, and deterministic inventory models where perfect information is assumed and stochastic functions are replaced by their mean. Formulation of a stochastic inventory model is very dependent upon the specification of the various functions involved, and upon the length of the planning horizon. The demand function usually includes an error term with known stochastic properties. A comprehensive survey of inventory models can be found in Sengupta and Fox (1969). Some simplifying assumptions about the market structure, information available, number of competitors and cost functions have to be made in order to reduce the large number of variables involved, and to obtain some specific results. Among pioneers in the field, Zabel (1970) formulated a model where the demand function has a multiplicative error term, and Mills (1962) formulated a model with an additive error term. We will present in this paper a two period moving horizon (2PMH) model inspired by Mills results, where the demand faced by a firm in each period is uncertain, and where inventories have a dual role; they are held as a buffer against unforeseen fluctuations in demand, and also as an active element in production planning. Mills’ model has been compared to the 2PMH model and the results of the simulations illustrate the benefits of extending the planning horizon from one to two periods.