OPTIMAL PRODUCTION IN MONOPOLY PRICING: A STOCHASTIC AND DYNAMIC APPROACH

Abstract

This paper is concerned with a special case of stochastic linear regulator that arises in optima! production planning in monopoly pricing. The state process consists of the inventory level and the demand rate (the latter taken as given). The inventory level involves both the production rate (control variable) and the demand rate. Several stochastic models for the demand are proposed and discussed. The state equation is a linear controlled stochastic equation driven by a Brownian motion. Costs are assumed to be quadratic and the LQG (Linear-Quadratic-Gaussian) approach is used to characterize optimal production-inventory policies. Finally, when possible, closed-form solutions are provided, otherwise approximate solutions are found by means of discrete-time linear systems.