Production Planning for a Stochastic Demand Process

This paper deals with planning production of a single good over a prescribed finite interval of time [0, T]. The costs considered within the problem are production and holding costs; holding costs are incurred for negative inventory (caused by backlogged sales) and positive inventory (caused by production in excess of demand). The demand for the product is treated as a stochastic process. Problem formulation and optimization use tools from continuous-time stochastic variational calculus and control theory. Among its results, the paper proves the uniqueness of the optimal solution and provides an algorithm for the problem.