A. Gürhan Kök

Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application

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. First, we present a procedure for estimating the parameters of substitution behavior and demand for products in each store, including the products that have not been previously carried in that store. Second, we propose an iterative optimization heuristic for solving the assortment planning problem. In a computational study, we find that its solutions, on average, are within 0.5% of the optimal solution. Third, we establish new structural properties (based on the heuristic solution) that relate the products included in the assortment and their inventory levels to product characteristics such as gross margin, case-pack sizes, and demand variability. We applied our method at Albert Heijn, a supermarket chain in The Netherlands. Comparing the recommendations of our system with the existing assortments suggests a more than 50% increase in profits.

Assortment Planning: Review of Literature and Industry Practice

A retailer’s assortment is defined by the set of products carried in each store at each point in time. The goal of assortment planning is to specify an assortment that maximizes sales or gross margin subject to various constraints, such as a limited budget for purchase of products, limited shelf space for displaying products, and a variety of miscellaneous constraints such as a desire to have at least two vendors for each type of product.

Competing Manufacturers in a Retail Supply Chain: On Contractual Form and Coordination

It is common for a retailer to sell products from competing manufacturers. How then should the firms manage their contract negotiations? The supply chain coordination literature focuses either on a single manufacturer selling to a single retailer or one manufacturer selling to many (possibly competing) retailers. We find that some key conclusions from those market structures do not apply in our setting, where multiple manufacturers sell through a single retailer. We allow the manufacturers to compete for the retailers business using one of three types of contracts: a wholesale-price contract, a quantity-discount contract, or a two-part tariff. It is well known that the latter two, more sophisticated contracts enable the manufacturer to coordinate the supply chain, thereby maximizing the profits available to the firms. More importantly, they allow the manufacturer to extract rents from the retailer, in theory allowing the manufacturer to leave the retailer with only her reservation profit. However, we show that in our market structure these two sophisticated contracts force the manufacturers to compete more aggressively relative to when they only offer wholesale-price contracts, and this may leave them worse off and the retailer substantially better off. In other words, although in a serial supply chain a retailer may have just cause to fear quantity discounts and two-part tariffs, a retailer may actually prefer those contracts when offered by competing manufacturers. We conclude that the properties a contractual form exhibits in a one-manufacturer supply chain may not carry over to the realistic setting in which multiple manufacturers must compete to sell their goods through the same retailer.

Inspection and Replenishment Policies for Systems with Inventory Record Inaccuracy

For many companies, inventory record inaccuracy is a major obstacle to achieving operational excellence. In this paper, we consider an inventory system in which inventory records are inaccurate. The manager makes inventory inspection and replenishment decisions at the beginning of each period. There is a cost associated with each inspection. If an inspection is performed, inventory records are aligned with physical inventory. The objective is to develop a joint inspection and replenishment policy that minimizes total costs in a finite horizon. We prove that an inspection adjusted base-stock (IABS) policy is optimal for the single-period problem. In the finite-horizon problem, we show that the IABS policy is near optimal in a numerical study. Under this policy, the manager performs an inspection if the inventory recorded is less than a threshold level, and orders up to a base-stock level that depends on the number of periods since the last inspection. The prevalent approach to deal with inventory inaccuracy in practice is to implement cycle-count programs. Based on the structure of the IABS policy, we propose a new cycle-count policy with state-dependent base-stock levels (CCABS). We show that CCABS is almost as effective as the IABS policy. In addition, we provide guidelines for practitioners to design effective cycle-count programs by conducting sensitivity analyses on the IABS policy. Finally, by comparing the costs associated with these policies and several benchmark systems, we quantify the true value of accurate inventory information, which may be provided by radio-frequency identification (RFID) systems.

Category Management and Coordination in Retail Assortment Planning in the Presence of Basket Shopping Consumers

This paper studies the assortment planning problem with multiple merchandise categories and basket shopping consumers (i.e., consumers who desire to purchase from multiple categories). We present a duopoly model in which retailers choose prices and variety level in each category and consumers make their store choice between retail stores and a no-purchase alternative based on their utilities from each category. The common practice of category management (CM) is an example of a decentralized regime for controlling assortment because each category manager is responsible for maximizing his or her assigned categorys profit. Alternatively, a retailer can make category decisions across the store with a centralized regime. We show that CM never finds the optimal solution and provides both less variety and higher prices than optimal. In a numerical study, we demonstrate that profit loss due to CM can be significant. Finally, we propose a decentralized regime that uses basket profits, a new metric, rather than accounting profits. Basket profits are easily evaluated using point-of-sale data, and the proposed method produces near-optimal solutions.

Implementation of the Newsvendor Model with Clearance Pricing: How to (and How Not to) Estimate a Salvage Value

The newsvendor model is designed to decide how much of a product to order when the product is to be sold over a short selling season with stochastic demand and there are no additional opportunities to replenish inventory. There are many practical situations that reasonably conform to those assumptions, but the traditional newsvendor model also assumes a fixed salvage value: all inventory left over at the end of the season is sold off at a fixed per-unit price. The fixed salvage value assumption is questionable when a clearance price is rationally chosen in response to the events observed during the selling season: a deep discount should be taken if there is plenty of inventory remaining at the end of the season, whereas a shallow discount is appropriate for a product with higher than expected demand. This paper solves for the optimal order quantity in the newsvendor model, assuming rational clearance pricing. We then study the performance of the traditional newsvendor model. The key to effective implementation of the traditional newsvendor model is choosing an appropriate fixed salvage value. (We show that an optimal order quantity cannot be generally achieved by merely enhancing the traditional newsvendor model to include a nonlinear salvage value function.) We demonstrate that several intuitive methods for estimating the salvage value can lead to an excessively large order quantity and a substantial profit loss. Even though the traditional model can result in poor performance, the model seems as if it is working correctly: the order quantity chosen is optimal given the salvage value inputted to the model, and the observed salvage value given the chosen order quantity equals the inputted one. We discuss how to estimate a salvage value that leads the traditional newsvendor model to the optimal or near-optimal order quantity. Our results highlight the importance of understanding how a model can interact with its own inputs: when inputs to a model are influenced by the decisions of the model, care is needed to appreciate how that interaction influences the decisions recommended by the model and how the models inputs should be estimated.

The Effect of Payment Schemes on Inventory Decisions: The Role of Mental Accounting

Does the payment scheme have an effect on inventory decisions in the newsvendor problem? Keeping the net profit structure constant, we examine three payment schemes that can be interpreted as the newsvendors order being financed by the newsvendor herself scheme O, by the supplier through delayed order payment scheme S, and by the customer through advanced revenue scheme C. In a laboratory study, we find that inventory quantities exhibit a consistent decreasing pattern in the order of schemes O, S, and C, with the order quantities of scheme S being close to the expected-profit-maximizing solution. These observations are inconsistent with the expected-profit-maximizing model, contradict what a regular or hyperbolic time-discounting model would predict, and cannot be explained by the loss aversion model. Instead, they are consistent with a model that underweights the order-time payments, which can be explained by the “prospective accounting” theory in the mental accounting literature. A second study shows that the results hold even if all physical payments are conducted at the same time, suggesting that the framing of the payment scheme is sufficient to induce the prospective accounting behavior. We further validate the robustness of our model under different profit conditions. Our findings contribute to the understanding of the psychological processes involved in newsvendor decisions and have implications for supply chain financing and contract design. This paper was accepted by Christian Terwiesch, operations management.

Optimal and Competitive Assortments with Endogenous Pricing Under Hierarchical Consumer Choice Models

This paper studies assortment planning and pricing for a product category with heterogeneous product types from two brands. We model consumer choice using the nested multinomial logit framework with two different hierarchical structures: a brand-primary model in which consumers choose a brand first, then a product type in the chosen brand, and a type-primary model in which consumers choose a product type first, then a brand within that product type. We consider a centralized regime that finds the optimal solution for the whole category and a decentralized regime that finds a competitive equilibrium between two brands. We find that optimal and competitive assortments and prices have quite distinctive properties across different models. Specifically, with the brand-primary model, both the optimal and the competitive assortments for each brand consist of the most popular product types from the brand. With the type-primary choice model, the optimal and the competitive assortments for each brand may not always consist of the most popular product types of the brand. Instead, the overall assortment in the category consists of a set of most popular product types. The price of a product under the centralized regime can be characterized by a sum of a markup that is constant across all products and brands, its procurement cost, and its marginal operational cost, implying a lower price for more popular products. The markup may be different for each brand and product type under the decentralized regime, implying a higher price for brands with a larger market share. These properties of the assortments and prices can be used as effective guidelines for managers to identify and price the best assortments and to rule out nonoptimal assortments. Our results suggest that to offer the right set of products and prices, category and/or brand managers should create an assortment planning process that is aligned with the hierarchical choice process consumers commonly follow to make purchasing decisions. This paper was accepted by Pradeep Chintagunta and Preyas Desai, special issue editors. This paper was accepted by Pradeep Chintagunta and Preyas Desai, special issue editors.

Evaluation of cycle-count policies for supply chains with inventory inaccuracy and implications on RFID investments

Inventory record inaccuracy leads to ineffective replenishment decisions and deteriorates supply chain performance. Conducting cycle counts (i.e., periodic inventory auditing) is a common approach to correcting inventory records. It is not clear, however, how inaccuracy at different locations affects supply chain performance and how an effective cycle-count program for a multi-stage supply chain should be designed. This paper aims to answer these questions by considering a serial supply chain that has inventory record inaccuracy and operates under local base-stock policies. A random error, representing a stock loss, such as shrinkage or spoilage, reduces the physical inventory at each location in each period. The errors are cumulative and are not observed until a location performs a cycle count. We provide a simple recursion to evaluate the system cost and propose a heuristic to obtain effective base-stock levels. For a two-stage system with identical error distributions and counting costs, we prove that it is more effective to conduct more frequent cycle counts at the downstream stage. In a numerical study for more general systems, we find that location (proximity to the customer), error rates, and counting costs are primary factors that determine which stages should get a higher priority when allocating cycle counts. However, it is in general not effective to allocate all cycle counts to the priority stages only. One should balance cycle counts between priority stages and non-priority stages by considering secondary factors such as lead times, holding costs, and the supply chain length. In particular, more cycle counts should be allocated to a stage when the ratio of its lead time to the total system lead time is small and the ratio of its holding cost to the total system holding cost is large. In addition, more cycle counts should be allocated to downstream stages when the number of stages in the supply chain is large. The analysis and insights generated from our study can be used to design guidelines or scorecard systems that help managers design better cycle-count policies. Finally, we discuss implications of our study on RFID investments in a supply chain.

Dynamic Assortment Customization with Limited Inventories

We consider a retailer with limited inventory of identically priced, substitutable products. The retailer faces a market with multiple segments of customers that are heterogeneous with respect to their product preferences. Customers arrive sequentially, and the firm decides which subset of products to offer to each arriving customer depending on the customer’s preferences, the inventory levels, and the remaining time in the season. We show that it is optimal to limit the choice set of some customers (even when the products are in stock), reserving products with low inventory levels for future customers who may have a stronger preference for those products. In certain settings, we prove that it is optimal to follow a threshold policy under which a product is offered to a customer segment if its inventory level is higher than a threshold value. The thresholds are decreasing in time and increasing in the inventory levels of other products. We introduce two heuristics derived by approximating the future marginal expected revenue by the marginal value of a newsvendor function that captures the substitution dynamics between products. We test the impact of assortment customization using data from a fashion retailer. We find that the potential revenue impact of assortment customization can be significant, especially when customer heterogeneity is high and when the products’ inventory-to-demand ratios are asymmetric. Our findings suggest that assortment customization can be used as another lever for revenue maximization in addition to pricing.