In this paper, we use a Markov decision process (MDP) to model the joint inventory-promotion decision problem. The state variable of the MDP represents the demand state brought about by changing environmental factors as well as promotion decisions. The demand state in a period determines the...

A quadratic model for production-inventory planning was made famous by Holt, Modigliani, Muth, and Simon in 1960 in (Holt, C. C., F. Modigliani, J. F. Muth, H. A. Simon. 1960. Planning Production, Inventories, and Work Force. Prentice-Hall, Englewood Cliffs, New Jersey.), especially for its...

We derive a sharp upper bound on the minimal forecast horizon in the discounted dynamic lot size model with constant initial demand. This bound is given by m(m + 1), where m is the EOQ's worth, i.e., the number of periods for which the total demand equals Economic Order Quantity. Our results do...

In this paper, we revisit and clarify the celebrated machine maintenance and sale age model of Kamien and Schwartz (KS) involving a machine subject to failure. KS formulate and solve the problem as a deterministic optimal control problem with the probability of the machine failure as the state...

The purpose of this note is to formulate and solve a dynamic optimization problem based on the Blattberg-Jeuland advertising model. Also examined is the behavior of the optimal long-run equilibrium level of advertising with respect to changes in some important parameters of the problem. In...

Companies spend hundreds of millions of dollars annually on advertising to build and maintain awareness for their brands in competitive markets. However, awareness formation models in the marketing literature ignore the role of competition. Consequently, we lack both the empirical knowledge and...

The following typographical errors appeared in our paper "Planning Horizon Procedures for Machine Replacement Models," Management Science, Vol. 25, No. 2 (February 1979), pp. 140-151.

The following typographical errors appeared in my paper "Optimal Pilfering Policies for Dynamic Continuous Thieves," Management Sci., Vol. 25, No. 6 (1979), pp. 535-542.

This paper considers the problems of a dynamic continuous thief, such as a habitual shoplifter or a gas siphoner, who must choose the pilfering rate (which increases the probability of his arrest over time) to maximize the present value of his total expected gain over a given finite or infinte...

This paper presents a review of recent developments that have taken place in the area of dynamic optimal control models in advertising subsequent to the comprehensive survey of the literature by Sethi in 1977. The basic problem underlying these models is that of determining optimal advertising...