Adam J. Mersereau

Retail Inventory Management When Records Are Inaccurate

Inventory record inaccuracy is a significant problem for retailers using automated inventory management systems. In this paper, we consider an intelligent inventory management tool that accounts for record inaccuracy using a Bayesian belief of the physical inventory level. We assume that excess demands are lost and unobserved, in which case sales data reveal information about physical inventory levels. We show that a probability distribution on physical inventory levels is a sufficient summary of past sales and replenishment observations, and that this probability distribution can be efficiently updated in a Bayesian fashion as observations are accumulated. We also demonstrate the use of this distribution as the basis for practical replenishment and inventory audit policies and illustrate how the needed parameters can be estimated using data from a large national retailer. Our replenishment policies avoid the problem of “freezing,” in which a physical inventory position persists at zero while the corresponding record is positive. In addition, simulation studies show that our replenishment policies recoup much of the cost of inventory record inaccuracy, and that our audit policy significantly outperforms the popular “zero balance walk” audit policy.

Relaxations of Weakly Coupled Stochastic Dynamic Programs

We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely, Lagrangian relaxation and the linear programming (LP) approach to approximate dynamic programming. We prove various results comparing the relaxations to each other and to the optimal problem value. We also provide a column generation algorithm for solving the LP-based relaxation to any desired optimality tolerance, and we report on numerical experiments on bandit-like problems. Our results provide insight into the complexity versus quality trade-off when choosing which of these relaxations to implement.

A structured multiarmed bandit problem and the greedy policy

We consider a multiarmed bandit problem where the expected reward of each arm is a linear function of an unknown scalar with a prior distribution. The objective is to choose a sequence of arms that maximizes the expected total (or discounted total) reward. We demonstrate the effectiveness of a greedy policy that takes advantage of the known statistical correlation structure among the arms. In the infinite horizon discounted reward setting, we show that both the greedy and optimal policies eventually coincide and settle on the best arm, in contrast with the Incomplete Learning Theorem for the case of independent arms. In the total reward setting, we show that the cumulative Bayes risk after T periods under the greedy policy is at most O (log T), which is smaller than the lower bound of ¿ (log2 T) established by [1] for a general, but different, class of bandit problems. We also establish the tightness of our bounds. Theoretical and numerical results show that the performance of our policy scales independently of the number of arms.

Markdown Pricing with Unknown Fraction of Strategic Customers

A growing segment of the revenue management and pricing literature assumes “strategic” customers who are forward-looking in their pursuit of utility. Recognizing that such behavior may not be directly observable by a seller, we examine the implications of seller uncertainty over strategic customer behavior in a markdown pricing setting. We assume that some proportion of customers purchase impulsively in the first period if the price is below their willingness to pay, while other customers strategically wait for lower prices in the second period. We consider a two-period selling season in which the seller knows the aggregate demand curve but not the proportion of customers behaving strategically. We show that a robust pricing policy that requires no knowledge of the extent of strategic behavior performs remarkably well. We extend our model to a setting with stochastic demand, and show that the robust pricing policy continues to perform well, particularly as capacity is loosened or the problem is scaled up. Our results underscore the need to recognize strategic behavior, but also suggest that in many cases effective performance is possible without precise knowledge of strategic behavior.

A Learning Approach for Interactive Marketing to a Customer Segment

When a marketer in an interactive environment decides which messages to send to her customers, she may send messages currently thought to be most promising (exploitation) or use poorly understood messages for the purpose of information gathering (exploration). We assume that customers are already clustered into homogeneous segments, and we consider the adaptive learning of message effectiveness within a customer segment. We present a Bayesian formulation of the problem in which decisions are made for batches of customers simultaneously, although decisions may vary within a batch. This extends the classical multiarmed bandit problem for sampling one-by-one from a set of reward populations. Our solution methods include a Lagrangian decomposition-based approximate dynamic programming approach and a heuristic based on a known asymptotic approximation to the multiarmed bandit solution. Computational results show that our methods clearly outperform approaches that ignore the effects of information gain.

Dynamic Capacity Allocation to Customers Who Remember Past Service

We study the problem faced by a supplier deciding how to dynamically allocate limited capacity among a portfolio of customers who remember the fill rates provided to them in the past. A customers order quantity is positively correlated with past fill rates. Customers differ from one another in their contribution margins, their sensitivities to the past, and in their demand volatilities. By analyzing and comparing policies that ignore goodwill with ones that account for it, we investigate when and how customer memory effects impact supplier profits. We develop an approximate dynamic programming policy that dynamically rationalizes the fill rates the firm provides to each customer. This policy achieves higher rewards than margin-greedy and Lagrangian policies and yields insights into how a supplier can effectively manage customer memories to its advantage. This paper was accepted by Martin Lariviere, operations management.

Analytics for Operational Visibility in the Retail Store: The Cases of Censored Demand and Inventory Record Inaccuracy

Armed with a number of modern and emerging visibility technologies and facing increased competition from the internet channel, retail managers are seeking ever deeper visibility into store operations. We review two established streams of operations management research that try to overcome shortcomings of common retail data sources. The first is demand estimation and inventory optimization in the presence of data censoring, where imperfect data may cause significant estimation biases and inventory cost inefficiencies. The second is inventory record inaccuracy, where intelligent replenishment and inspection policies may be able to reduce inventory management costs even without real-time tracking technologies like radio frequency identification (RFID). Common themes of these literatures are that lack of visibility can be costly if not properly accounted for, that intelligent analytical approaches can potentially substitute for visibility provided by technology, and that understanding the best possible policy without visibility is needed to properly evaluate visibility technologies. We include a survey of modern and emerging visibility technologies and a discussion of several new avenues for analytical research.

Initial Shipment Decisions for New Products at Zara

Given uncertain popularity of new products by location, fast fashion retailer Zara faces a trade-off. Large initial shipments to stores reduce lost sales in the critical first days of the product life cycle, but maintaining stock at the warehouse allows restocking flexibility once initial sales are observed. In collaboration with Zara, we develop and test a decision support system featuring a data-driven model of forecast updating and a dynamic optimization formulation for allocating limited stock by location over time. A controlled field experiment run worldwide with 34 articles during the 2012 season showed an increase in total average season sales by approximately 2% and a reduction in the number of unsold units at the end of the regular selling season by approximately 4%.

Demand Estimation from Censored Observations with Inventory Record Inaccuracy

A retailer cannot sell more than it has in stock; therefore, its sales observations are a censored representation of the underlying demand process. When a retailer forecasts demand based on past sales observations, it requires an estimation approach that accounts for this censoring. Several authors have analyzed inventory management with demand learning in environments with censored observations, but the authors assume that inventory levels are known and hence that stockouts are observed. However, firms often do not know how many units of inventory are available to meet demand, a phenomenon known as inventory record inaccuracy. We investigate the impact of this unknown on demand estimation in an environment with censored observations. When the firm does not account for inventory uncertainty when estimating demand, we discover and characterize a systematic downward bias in demand estimation under typical assumptions on the distribution of inventory record inaccuracies. We propose and test a heuristic prescription that relies on a single error statistic and that sharply reduces this bias.

Dynamic Procurement of New Products with Covariate Information: The Residual Tree Method

Problem definition: We study the practice-motivated problem of dynamically procuring a new, short life-cycle product under demand uncertainty. The firm does not know the demand for the new product but has data on similar products sold in the past, including demand histories and covariate information such as product characteristics. Academic/practical relevance: The dynamic procurement problem has long attracted academic and practitioner interest, and we solve it in an innovative data-driven way with proven theoretical guarantees. This work is also the first to leverage the power of covariate data in solving this problem. Methodology: We propose a new, combined forecasting and optimization algorithm called the Residual Tree method, and analyze its performance via epi-convergence theory and computations. Our method generalizes the classical Scenario Tree method by using covariates to link historical data on similar products to construct demand forecasts for the new product. Results: We prove, under fairly mild conditions, that the Residual Tree method is asymptotically optimal as the size of the data set grows. We also numerically validate the method for problem instances derived using data from the global fashion retailer Zara. We find that ignoring covariate information leads to systematic bias in the optimal solution, translating to a 6-15% increase in the total cost for the problem instances under study. We also find that solutions based on trees using just 2-3 branches per node, which is common in the existing literature, are inadequate, resulting in 30-66% higher total costs compared with our best solution. Managerial implications: The Residual Tree is a new and generalizable approach that uses past data on similar products to manage new product inventories. We also quantify the value of covariate information and of granular demand modeling.