Assortment Planning and Inventory Decisions Under a Locational Choice Model

We consider a single-period assortment planning and inventory management problem for aretailer, using a locational choice model to represent consumer demand. We first determinethe optimal variety, product location, and inventory decisions under static substitution, andshow that the optimal assortment consists of products equally spaced out such that there is nosubstitution among them regardless of the distribution of consumer preferences. The optimalsolution can be such that some customers prefer not to buy any product in the assortment, andsuch that the most popular product is not offered.We then obtain bounds on profit when customers dynamically substitute, using the staticsubstitution for the lower bound, and a retailer-controlled substitution for the upper bound.We thus define two heuristics to solve the problem under dynamic substitution, and numericallyevaluate their performance. This analysis shows the value of modeling dynamic substitution andidentifies conditions in which the static substitution solution serves as a good approximation