A Comparative Study of Stochastic Quadratic Programming and Optimal Control Model in Production-Inventory System With Stochastic Demand

Abstract

ABSTRACT. This study compares the optimal control model and stochastic quadratic programming (SQP) model of a production-inventory system. A single product, without shortage in the case of a periodic-review policy with stochastic demand and deterioration rate as a function of time, is discussed. The items are subjected to deterioration via storage and the inventory goal level as a function of production. Demand is represented by a stochastic differential equation, converted to a stochastic constraint, and then to a deterministic constraint. We derive the optimality conditions of optimal control model and formulate three models of SQP. The effect of stochastic demand on the production rate and inventory level is then illustrated. Our numerical results appear to suggest that control of inventory level is better in the case of SQP. Furthermore, the total cost is similar in the three models of SQP -despite a difference in production rates and inventory levels.