Felipe Caro

Dynamic Assortment with Demand Learning for Seasonal Consumer Goods

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 (DPs), results contributing to the emerging theory of DP duality, and various approximations. It yields a closed-form dynamic index policy capturing the key exploration versus exploitation trade-off and associated suboptimality bounds. In numerical experiments its performance proves comparable to that of other closed-form heuristics described in the literature, but this policy is particularly easy to implement and interpret. This last feature enables extensions to more realistic versions of the motivating dynamic assortment problem that include implementation delays, switching costs, and demand substitution effects.

Inventory Management of a Fast-Fashion Retail Network

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 an article is removed from display whenever one of its key sizes stocks out. To solve this problem, we first formulate and analyze a stochastic model predicting the sales of an article 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. We then formulate a mixed-integer program embedding a piecewise-linear approximation of the first model applied to every store in the network, allowing us 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 pilot experiment performed to assess the models impact relative to the prior procedure used to determine weekly shipment quantities. The results of that experiment suggest that the new allocation process increases sales by 3% to 4%, which is equivalent to

School redistricting: embedding GIS tools with integer programming

275 M in additional revenues for 2007, reduces transshipments, and increases the proportion of time that Zaras products spend on display within their life cycle. Zara is currently using this process for all of its products worldwide.

Clearance Pricing Optimization for a Fast-Fashion Retailer

The paper deals with a school redistricting problem in which blocks of a city must be assigned to schools according to diverse criteria. Previous approaches are reviewed and some desired properties of a good school districting plan are established. An optimization model together with a geographic information system environment are then proposed for finding a solution that satisfies these properties. A prototype of the system is described, some implementation issues are discussed, and two real-life examples from the city of Philadelphia are studied, one corresponding to a relatively easy to solve problem, and the other to a much harder one. The trade-offs in the solutions are analysed and feasibility questions are discussed. The results of the study strongly suggest that ill-defined spatial problems, such as school redistricting, can be addressed effectively by an interaction between objective analysis and subjective judgement.

The Impact of Quick Response in Inventory-Based Competition

Fast-fashion retailers such as Zara offer continuously changing assortments and use minimal in-season promotions. Their clearance pricing problem is thus challenging because it involves comparatively more different articles of unsold inventory with less historical price data points. Until 2007, Zara used a manual and informal decision-making process for determining price markdowns. In collaboration with their pricing team, we since designed and implemented an alternative process relying on a formal forecasting model feeding a price optimization model. As part of a controlled field experiment conducted in all Belgian and Irish stores during the 2008 fall-winter season, this new process increased clearance revenues by approximately 6%. Zara is currently using this process worldwide for its markdown decisions during clearance sales.

Double Counting in Supply Chain Carbon Footprinting

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 competitors 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.

Optimizing Long-Term Production Plans in Underground and Open-Pit Copper Mines

Carbon footprinting is a tool for firms to determine the total greenhouse gas GHG emissions associated with their supply chain or with a unit of final product or service. Carbon footprinting typically aims to identify where best to invest in emission reduction efforts, and/or to determine the proportion of total emissions that an individual firm is accountable for, whether financially and/or operationally. A major and underrecognized challenge in determining the appropriate allocation stems from the high degree to which GHG emissions are the result of joint efforts by multiple firms. We introduce a simple but general model of joint production of GHG emissions in general supply chains, decomposing the total footprint into processes, each of which can be influenced by any combination of firms. We analyze two main scenarios. In the first scenario, the social planner allocates emissions to individual firms and imposes a cost on them such as a carbon tax in proportion to the emissions allocated. In the second scenario, a carbon leader voluntarily agrees to offset all emissions in the entire supply chain and then contracts with individual firms to recoup part of the costs of those offsets. In both cases, we find that, to induce the optimal effort levels, the emissions need to be overallocated, even if the carbon tax is the true social cost of carbon. This is in contrast to the usual focus in the life-cycle assessment LCA and carbon footprinting literatures on avoiding double counting. Our work aims to lay the foundation for a framework to integrate the economics-and LCA-based perspectives on supply chain carbon footprinting.

Zara Uses Operations Research to Reengineer Its Global Distribution Process

We present a methodology for long-term mine planning based on a general capacitated multicommodity network flow formulation. It considers underground and open-pit ore deposits sharing multiple downstream processing plants over a long horizon. The purpose of the model is to optimize several mines in an integrated fashion, but real size instances are hard to solve due to the combinatorial nature of the problem. We tackle this by solving the relaxation of a tight linear formulation, and we round the resulting near-integer solution with a customized procedure. The model has been implemented at Codelco, the largest copper producer in the world. Since 2001, the system has been used on a regular basis and has increased the net present value of the production plan for a single mine by 5%. Moreover, integrating multiple mines provided an additional increase of 3%. The system has allowed planners to evaluate more scenarios. In particular, the model was used to study the option of delaying by four years the conversion of Chiquicamata, Codelcos largest open-pit mine, to underground operations.

Fast Fashion: Business Model Overview and Research Opportunities

Overcoming significant technical and human difficulties, Zara recently deployed a new process that relies extensively on sophisticated operations research models to determine each inventory shipment it sends from its two central warehouses to its 1,500 stores worldwide. By taking a retail size-assortment view of a stores inventory, the model incorporates the link between stock levels and demand to select store replenishment quantities. Through a rigorous, controlled field experiment, we estimate that this new process has increased sales by 3--4 percent; this corresponds to estimated profits of approximately

Product and Price Competition with Satiation Effects

233 million and