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Abstract:
Working in collaboration with Spain-based retailer Zara, we address the problem of distributing over time a limited amount of inventory across all the stores in a fast-fashion retail network. Challenges specific to that environment include very short product life-cycles, and store policies whereby a reference is removed from display whenever one of its key sizes stocks out. We first formulate and analyze a stochastic model predicting the sales of a reference in a single store during a replenishment period as a function of demand forecasts, the inventory of each size initially available and the store inventory management policy just stated. Secondly, we formulate a mixed-integer program embedding a piece-wise linear approximation of the first model applied to every store in the network and allowing to compute store shipment quantities maximizing overall predicted sales, subject to inventory availability and other constraints. We report the implementation of this optimization model by Zara to support its inventory distribution process, and the ensuing controlled field experiment performed to assess the impact of that model relative to the prior procedure used to determine weekly shipment quantities. The results of that experiment suggest that the new allocation process tested increases sales, reduces tran-shipments, and increases the proportion of time that an important category of Zara's products spends on display.

inventory management, retail network

Abstract:
We propose a multi-period extension of the competitive newsvendor model of Lippman and McCardle (1997) to investigate the impact of quick response under competition. For this purpose, we consider two retailers that compete in terms of inventory: customers that face a stockout at their first-choice store will look for the product at the other store. Consequently, the total demand that each retailer faces depends on the competitor's inventory level. We allow for asymmetric reordering capabilities, and we are particularly interested in the case when one of the firms has a lower ordering cost but can only produce at the beginning of the selling season, whereas the second firm has higher costs but can replenish stock in a quick response manner taking advantage of any incremental knowledge about demand (if it is available). We visualize this problem as the competition between a traditional make-to-stock retailer that builds up inventory before the season starts versus a retailer with a responsive supply chain that can react to early demand information. We provide conditions for this game to have a unique pure-strategy subgame-perfect equilibrium, which then allows us to perform numerical comparative statics. Our results confirm in a competitive setting the intuitive fact that quick response is more beneficial when demand uncertainty is higher, or exhibits a higher correlation over time. Finally, we find that part of the competitive advantage from quick response arises from the asymmetry in response capabilities.

Abstract:
This article studies the static pricing problem of a network service provider who has a fixed capacity and faces different types of customers (classes). We consider a single-bandwidth tree network, meaning that each class can have its own capacity constraint but it is assumed that all classes have the same resource requirements. The provider must decide a static price for each class. The customer types are characterized by their arrival process, with a price-dependant arrival rate, and the random time they remain in the system. The goal is to characterize the optimal static prices in order to maximize the provider's revenue. We report new structural findings and insights, illustrative numerical examples, and alternative proofs for some known results. This problem was originally thought for a company that sells phone cards and needs to set the price-per-minute for each destination.

phone cards, Erlang loss system, product-form, stochastic knapsack, quasiconcavity.

Abstract:
Companies such as Zara and World Co. have recently implemented novel product development processes and supply chain architectures enabling them to make more product design and assortment decisions during the selling season, when actual demand information becomes available. How should such retail firms modify their product assortment over time in order to maximize overall profits for a given selling season? Focusing on a stylized version of this problem, we study a finite horizon multiarmed bandit model with several plays per stage and Bayesian learning. Our analysis involves the Lagrangian relaxation of weakly coupled dynamic programs, results contributing to the emerging theory of DP duality, and various approximations. It yields a closed-form dynamic index policy capturing the key exploration vs. exploitation trade-off, and associated suboptimality bounds. While in numerical experiments its performance proves comparable to that of other closed-form heuristics described in the literature, our policy is particularly easy to implement and interpret. This last feature enables extensions to more realistic versions of our motivating dynamic assortment problem that include implementation delays, switching costs and demand substitution effects.

dynamic assortment, demand learning, seasonal consumer goods, DOTM, decisions, operations, technology, management