Coordinating inventory control and pricing strategies

Abstract

Traditional inventory models focus on effective replenishment strategies and typically assume that a commodity's price is exogenously determined. In recent years, however, a number of industries have used innovative pricing strategies to manage their inventory effectively. These developments call for models that integrate inventory control and pricing strategies. Such models are clearly important not only in the retail industry, where price-dependent demand plays an important role, but also in manufacturing environments in which production/distribution decisions can be complemented with pricing strategies to improve the firm's bottom line. To date, the literature has confined itself mainly to models with variable ordering costs but no fixed costs. Extending some of these models to include a fixed cost component is the main focus of this thesis. In this thesis, we start by analyzing a single product, periodic review joint inventory control and pricing model, and characterizing the structure of the optimal policy under various conditions. Specifically, for the finite horizon periodic review case, we show, by employing the classical k-convexity concept, that a simple policy, called (s, S, p), is optimal when the demand functions are additive. For the model with more general demand functions, we show that an (s, S, p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-convex functions, and apply it to provide a characterization of the optimal policy. Surprisingly, in the infinite horizon periodic review case, the concept of symmetric k-convex functions allows us to show that a stationary (s, S, p) policy is optimal for both discounted and average profit models even for general demand functions.

(cont.) Our approach developed for the infinite horizon periodic review joint inventory control and pricing problem is then extended to a corresponding continuous review model. In this case, we prove that a stationary (s, S, p) policy is optimal under fairly general assumptions. Finally, the symmetric k-convexity concept developed in this thesis is employed to characterize the optimal policy for the stochastic cash balance problem.