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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:
Motivated by electronic commerce, this paper is a mechanism design study for sellers of multiple identical items. In the market environment we consider, participants are risk neutral and time-sensitive, with the same discount factor; potential buyers have unit demand and arrive sequentially according to a renewal process; and valuations are drawn independently from the same regular distribution. From the Revelation Principle, we can restrict our attention to direct dynamic mechanisms taking a sequence of valuations and arrival epochs as a strategic input. We define two properties (discreteness and stability), and prove that under a regularity assumption on the inter-arrival time distribution, we may at no cost of generality consider only mechanisms satisfying them. This effectively reduces the mechanism input to a sequence of valuations, allowing us to formulate the problem as a dynamic program (DP). Because this DP is equivalent to a well-known infinite horizon asset-selling problem, we can finally characterize the optimal mechanism as a sequence of posted prices increasing with each sale. Our numerical study indicates that, with uniform valuations, the benefit of dynamic pricing over a fixed posted price may be small. Besides, posted prices are preferable to online auctions for a large number of items or high interest rate, but in other cases auctions are close to optimal and significantly more robust.

Dynamic Pricing, Fixed Posted Price, Online Auctions

Abstract:
Dell's supply chain for desktops involves Asian vendors shipping components by sea to several U.S. plants. While suppliers are responsible for shipping enough inventory, Dell can re-route and expedite their shipments while in transit and also transfer on-hand inventory in order to balance supply across sites. This paper describes the development, implementation and impact of the process and optimization-based control system now used by Dell to address this supply routing challenge for its US-bound monitors. This new methodology is estimated to have reduced Dell's inventory re-positioning costs for monitors by about 60%.

Dell, supply chain, make-to-order manufacturing

Abstract:
Buyout options allow bidders to instantly purchase at a specified price an item listed for sale through an online auction. A temporary buyout option disappears once a regular bid is submitted, while a permanent option remains available until it is exercised or the auction ends; such buyout price may be static and remain constant throughout the auction, or dynamic and vary as the auction progresses. We formulate a game-theoretic model featuring time-sensitive bidders with independent private values and Poisson arrivals but endogenous bidding times to answer the following questions: How should a seller set the buyout price (if at all)? What are the implications of using a temporary buyout option relative to a permanent one? What is the potential benefit associated with using a dynamic buyout price? For all buyout option types we exhibit a Nash equilibrium in bidder strategies, argue that this equilibrium constitutes a plausible outcome prediction, and study the problem of maximizing the corresponding seller revenue. Our numerical experiments suggest that when any of the participants are time-sensitive, the seller may significantly increase his utility by introducing a buyout option, but that dynamic buyout prices may not provide a substantial advantage over static ones. Furthermore, while permanent buyout options yield higher predicted revenue than temporary options, they also provide additional incentives for late bidding and may therefore not be always more desirable.

buyout option, online auction, Nash equilibrium

Abstract:
Wave-based release policies are prevalent in warehouses with an automated sorter, and take different forms depending on how much waves overlap and whether the sorter is split for operating purposes. Waveless release is emerging as an alternative policy adopted by an increasing number of firms. While that new policy presents several advantages relative to waves, it also involves the possibility of gridlock at the sorter. In collaboration with a large US online retailer and using an extensive dataset of detailed flow information, we first develop a model with validated predictive accuracy for its warehouses operating under a waveless release policy. We then use that model to compute operational guidelines for dynamically controlling the main parameter of its waveless policy, with the goal of maximizing throughput while keeping the risk of gridlock under a specified threshold. Secondly, we leverage that model and dataset to perform through simulation a performance comparison of wave-based and waveless policies in this context. Our waveless policy yields larger or equal throughput than the best performing wave-based policy with a lower gridlock probability in all scenarios considered. Waveless release policies thus appear to merit very serious consideration by practitioners. Facilities using a non-overlapping wave policy should also consider overlapping waves or a split sorter policy.

waveless policies

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