Optimal output inventory decisions in stochastic markets

Abstract

Recent economic applications of optimal inventory control models to aggregate industry data (Hay and Holt 1975, Belsley 1969, Sengupta and Sfeir 1979) have been restricted to Linear Quadratic Gaussian (LQG) models and the associated linear decision rules (LDR). For perfect markets with competitive exchange of information, where no individual agent has the monopolistic power to influence the price or the market demand, the LQG model may hold very well as an approximation; this is unlikely to be so for imperfect markets, where imperfection may be due to several sources, e.g., (a) asymmetry in the distribution of market demand, where the third and fourth moments may be as important as the mean and variance, (b) the price may be useable in part as a control variable along with output, (c) the inventory cost function may be partly convex and partly concave and (d) the sensitivity to risk parameters in stochastic demand may modify the LDR and its updating characteristics. Our object here is to formulate in a simplified framework a set of dynamic inventory control models, which incorporates in an approximate sense some of the imperfections of stochastic markets as above. These models are illustrative of the deficiencies of the LDR approach, as they suggest the need for stochastic demand conditions.