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Let N be a finite set and z be a real-valued function defined on the set of subsets of N that satisfies z(S)+z(T)>-z(SUT)+z(SnT) for all S, T in N. Such a function is called submodular. We consider the problem maXscN {z(S): IS[ <-K, z(S) submodular}. Several hard combinatorial optimization problems can be posed in this framework. For example, the problem of… (More)

Assortment planning at a retailer entails both selecting the set of products to be carried and setting inventory levels for each product. We study an assortment planning model in which consumers might accept substitutes when their favorite product is unavailable. We develop an algorithmic process to help retailers compute the best assortment for each store.… (More)

Inventory turnover varies widely across retailers and over time. This variation undermines the usefulness of inventory turnover in performance analysis, benchmarking and working capital management. We develop an empirical model using financial data for 311 public-listed retail firms for the years 1987-2000 to investigate the correlation of inventory… (More)

W e consider the problem of determining (for a short lifecycle) retail product initial and replenishment order quantities that minimize the cost of lost sales, back orders, and obsolete inventory. We model this problem as a two-stage stochastic dynamic program, propose a heuristic, establish conditions under which the heuristic finds an optimal solution,… (More)