Assortment planning in transshipment systems

Assortment planning, i.e., determining the set of products to offer to customers is a challenging task with immediate effects on profitability, market share and customer service. In this thesis, we study a multiple location assortment planning problem in a make-to-order environment. Each location has the exibility to access others' assortments by transshipping products he/she does not keep. This allows them to offer higher variety and increase sales without increasing costs associated with assortment. Customer behavior is defined using exogenous demand model where each arriving customer to a location chooses a product with an exogenous probability among all possible options. In our multiple location setting, we assume that the customer has access to the complete assortment in all locations. If a customer's requested product is not available in that customer's assigned location but available in another location, the firm ships the product to the customer at the same price and incurs a transshipment cost. If his/her first choice product is not offered by any of the locations then he/she switches to a substitute product, which can be either satisfied from customer's assigned location, or by transshipment. Otherwise, it is lost. The problem is then to determine the assortment in each location such that the total expected profit is maximized. We first show that the optimal assortments are nested, i.e., the assortment of a location with a smaller market share is a subset of the assortment of a location with a larger market share. We then show that while the common assortment is in the popular set (i.e., some number of products with highest purchase probabilities), the individual assortments do not necessarily have this property. We also derive a sufficient condition for each assortment to be in the popular set. In the final part of the thesis, we conduct an extensive numerical study to understand the effects of various parameters such as assortment cost and transshipment cost on optimal assortments and effects of allowing transshipments on resulting assortments compared to a no-transshipment system. Finally, we introduce an approximation algorithm that benefits from the structural properties obtained in this study and also test its performance with extensive numerical analyses.