A model is presented for the derivation and implementation of optical 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 as the dynamics of suitably defined state variables under the influence of decision rules that are stable and linear in the state variables, but otherwise unspecified. The dynamical 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 the outcome or the criterion functional 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 constraints.
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