An integrated approach to price differentiation and inventory decisions with demand leakage

Price differentiation is among widely practiced tools in Revenue Management (RM) in which a seller offers same or slightly different products (or services) at different prices to its customers. Earlier research studies have shown that the benefits from price differentiation are evident when the market segmentation is assumed to be perfect. In a perfect market segmentation, customers associated with a market segment do not move between market segments. However, it is not uncommon to observe that a market segmentation a firm operates in is seldom prefect, and due to imperfect segmentation customers move between market segments which is also referred to as demand leakage. In addition, the firms predominantly experience stochastic demand and thus a firm experiences both the short sales and leftovers due to demand uncertainty. This research proposes a model to address the issue of an optimal market segmentation using price differentiation as a tool. We also establish an integrated framework for pricing, order and (production) quantity allocation decisions in each market segment when a firm experiences demand leakage from one market segment to another and faces price-dependent stochastic demand. The model is analyzed to determine an optimal decision framework on pricing, order quantity allocation, and market segmentation using the proposed price differentiation. Due to the complexity of the problem, both the hierarchical and joint optimization approaches are developed. A simplified closed-form optimal solution to the problem is outlined in the case of hierarchical approach. The model is also analyzed for a situation in which the distribution of the price-dependent stochastic demand is unknown and a distribution-free approach is utilized to address the problem. It is identified that the use of distribution-free approach also results in a closed-form optimal solution to the problem. A numerical study is presented to demonstrate the performance of the model and solution approaches. The benefits of the optimal market segmentation using a differentiation price are also highlighted along with the proposed integrated optimal decision framework when a firm experiences demand leakage.