Combined pricing and procurement decisions in stochastic inventory control theory

This thesis attempts to put another building block to the bridge that connects Production/Operations Management, Marketing and Economics disciplines. We consider stochastic inventory control models that combine pricing and procurement decisions. Moreover, we specifically investigate the potential of using product substitution as a sales strategy in one of these models.; The classic Newsvendor Problem considers a single perishable product over a single period model. The per unit revenue, procurement, underage and overage costs are linear. Facing stochastic demand, the objective is to find the optimal procurement quantity so as to maximize the expected profit. It was shown in the literature that if the pricing decision is incorporated into the Newsvendor problem, the expected profit function loses its concavity property, but can be reduced to a single variable function. Moreover, with mild assumptions on the demand distribution, the objective function has at most two stationary points. In this thesis, by taking into account the bounds on the price that is inherent from the linear price-demand relationship, we show that the single variable expected profit function is in fact unimodal. We then extend the same result to a model that incorporates a second category of customers, who buy the end of period excess inventory in bulk and at a fixed discount price. The second extension of the basic Newsvendor with pricing model considers the launching of a new product that can be used to substitute a well-established product. Given the price of the existing product, the objective is to determine the price of the new product, and the procurement quantities of both products so as to maximize the expected profit over a single period. We show that an optimal solution can be found by solving O(n) number of single variable optimization problems, where n is the number of values the demand of the existing product can take. Moreover, under the same mild assumptions on the demand of the new product as the previous two models, each of these single variable functions has at most one stationary point that is a local maximum. We also show that, besides the expected profit, both the price and the procurement quantity of the new product are higher when it is offered as a substitute.; Numerical studies are done to illustrate the potential profit benefit that can be achieved through integrating pricing and substitution decisions into stochastic inventory control models.