Econometrica: Oct, 1966, Volume 34, Issue 4
Multi-Item Production and Inventory Management Under Price Uncertainty
B. P. Banerjee, S. S. Sengupta
A model is presented for the derivation and implementation of an optimal linear decision rule for a firm producing and dealing in a number of interacting products, and possessing partial influence on their prices. The behavior of a multi-item production-inventory complex is represented by the dynamics of suitably defined state variables under the influence of decision rules that are linear in the state variables, but otherwise unspecified. The dynamic equations are stochastic owing to the presence of stochastic processes in the forcing terms. The statistical properties of these processes, together with the decision rules, determine the statistics of a functional describing the outcome. The optimum inventory decision is then derived as the "best" linear transformation on the past of the state variables, such that the mean value of the criterion functional is optimized subject to the system of constraints. A mechanism is also developed such that the optimal linear rule may be implemented.