Vishal Gaur

An Econometric Analysis of Inventory Turnover Performance in Retail Services

Inventory turnover varies widely across retailers and over time. This variation undermines the usefulness of inventory turnover in performance analysis, benchmarking, and working capital management. We develop an empirical model using financial data for 311 publicly listed retail firms for the years 1987-2000 to investigate the correlation of inventory turnover with gross margin, capital intensity, and sales surprise (the ratio of actual sales to expected sales for the year). The model explains 66.7% of the within-firm variation and 97.2% of the total variation (across and within firms) in inventory turnover. It yields an alternative metric of inventory productivity, adjusted inventory turnover, which empirically adjusts inventory turnover for changes in gross margin, capital intensity, and sales surprise, and can be applied in performance analysis and managerial decision making. We also compute time trends in inventory turnover and adjusted inventory turnover, and find that both have declined in retailing during the 1987-2000 period.

Hedging Inventory Risk Through Market Instruments

We address the problem of hedging inventory risk for a short life cycle or seasonal item when its demand is correlated with the price of a financial asset. We show how to construct optimal hedging transactions that minimize the variance of profit and increase the expected utility for a risk-averse decision maker. We show that for a wide range of hedging strategies and utility functions, a risk-averse decision maker orders more inventory when he or she hedges the inventory risk. Our results are useful to both risk-neutral and risk-averse decision makers because (1) the price information of the financial asset is used to determine both the optimal inventory level and the hedge, (2) this enables the decision maker to update the demand forecast and the financial hedge as more information becomes available, and (3) hedging leads to lower risk and higher return on inventory investment. We illustrate these benefits using data from a retailing firm.

A Periodic Inventory Routing Problem at a Supermarket Chain

Albert Heijn, BV, a supermarket chain in the Netherlands, faces a vehicle routing and delivery scheduling problem once every three to six months. Given hourly demand forecasts for each store, travel times and distances, cost parameters, and various transportation constraints, the firm seeks to determine a weekly delivery schedule specifying the times when each store should be replenished from a central distribution center, and to determine the vehicle routes that service these requirements at minimum cost. We describe the development and implementation of a system to solve this problem at Albert Heijn. The system resulted in savings of 4% of distribution costs in its first year of implementation and is expected to yield 12%-20% savings as the firm expands its usage. It also has tactical and strategic advantages for the firm, such as in assessing the cost impact of various logistics and marketing decisions, in performance measurement, and in competing effectively through reduced lead time and increased frequency of replenishment.

Assortment Planning and Inventory Decisions Under a Locational Choice Model

We consider a single-period assortment planning and inventory management problem for a retailer, using a locational choice model to represent consumer demand. We first determine the optimal variety, product location, and inventory decisions under static substitution, and show that the optimal assortment consists of products equally spaced out such that there is no substitution among them regardless of the distribution of consumer preferences. The optimal solution can be such that some customers prefer not to buy any product in the assortment, and such that the most popular product is not offered. We then obtain bounds on profit when customers dynamically substitute, using the static substitution for the lower bound, and a retailer-controlled substitution for the upper bound. We thus define two heuristics to solve the problem under dynamic substitution and numerically evaluate their performance. This analysis shows the value of modeling dynamic substitution and identifies conditions in which the static substitution solution serves as a good approximation.

Information Sharing in a Supply Chain Under ARMA Demand

In this paper we study how the time-series structure of the demand process affects the value of information sharing in a supply chain. We consider a two-stage supply chain model in which a retailer serves autoregressive moving-average (ARMA) demand and a manufacturer fills the retailers orders. We characterize three types of situations based on the parameters of the demand process: (i) the manufacturer benefits from inferring demand information from the retailers orders; (ii) the manufacturer cannot infer demand, but benefits from sharing demand information; and (iii) the manufacturer is better off neither inferring nor sharing, but instead uses only the most recent orders in its production planning. Using the example of ARMA(1,1) demand, we find that sharing or inferring retail demand leads to a 16.0% average reduction in the manufacturers safety-stock requirement in cases (i) and (ii), but leads to an increase in the manufacturers safety-stock requirement in (iii). Our results apply not only to two-stage but also to multistage supply chains.

Assortment Planning and Inventory Decisions Under Stockout-Based Substitution

We present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single-period problem with stockout-based substitution. In our model, total customer demand is random and comprises fixed proportion of customers of different types. Customer preferences are modeled through the definition of these types. Each customer type corresponds to a specific preference ordering among products. A customer purchases the highest-ranked product, according to his type (if any), that is available at the time of his visit to the store (stockout-based substitution). We solve the optimal assortment problem using a dynamic programming formulation. We establish structural properties of the value function of the dynamic program that, in particular, help to characterize multiple local maxima. We use the properties of the optima to solve the problem in pseudopolynomial time. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known methods, especially when the mean demand is large, the degree of substitutability is high, the population is homogeneous, or prices and/or costs vary across products.

Do Inventory and Gross Margin Data Improve Sales Forecasts for U.S. Public Retailers

Firm-level sales forecasts for retailers can be improved if we incorporate cost of goods sold, inventory, and gross margin (defined by us as the ratio of sales to cost of goods sold) as three endogenous variables. We construct a simultaneous equations model, estimated using public financial and nonfinancial data, to provide joint forecasts of annual cost of goods sold, inventory, and gross margin for retailers using historical data. We show that sales forecasts from this model are more accurate than consensus forecasts from equity analysts. Further, the residuals from this model for one fiscal year are used to predict retailers for whom the relative advantage of model forecasts over consensus forecasts would be large in the next fiscal year. Our results show that historical inventory and gross margin contain information useful to forecast sales, and that equity analysts do not fully utilize this information in their sales forecasts.

Asymmetric Consumer Learning and Inventory Competition

We develop a model of consumer learning and choice behavior in response to uncertain service in the marketplace. Learning could be asymmetric, that is, consumers may associate different weights with positive and negative experiences. Under this consumer model, we characterize the steady-state distribution of demand for retailers given that each retailer holds a constant in-stock service level. We then consider a noncooperative game in steady state between two retailers competing on the basis of their service levels. The demand distributions of retailers in this game are modeled using a multiplicative aggregate market-share model in which the mean demands are obtained from the steady-state results for individual purchases, but the model is simplified in other respects for tractability. Our model yields a unique pure strategy Nash equilibrium. We show that asymmetry in consumer learning has a significant impact on the optimal service levels, market shares, and profits of the retailers. When retailers have different costs, it also determines the extent of competitive advantage enjoyed by the lower-cost retailer.

Does Inventory Productivity Predict Future Stock Returns? A Retailing Industry Perspective

We find that inventory productivity strongly predicts future stock returns among a sample of publicly listed U.S. retailers during the period from 1985 to 2010. A zero-cost portfolio investment strategy, which consists of buying from the two highest and selling from the two lowest quintiles formed on inventory turnover, earns more than 1% average monthly abnormal return benchmarked to the Fama-French-Carhart four-factor model. Our results are robust to different measures of inventory productivity, distinct from the well-known firm characteristics known to generate abnormal returns, and not driven by a particular sub-sample period. A longitudinal analysis of portfolio returns over longer holding periods shows that, while inventory productivity is predictive of stock returns, its information dissipates about 1-2 years after release.

Systematic Risk in Supply Chain Networks

Industrial production output is generally correlated with the state of the economy. Nonetheless, during the times of economic downturn some industries take the biggest hit, while at the times of economic boom they reap most benefits. To provide insight into this phenomenon we map supply networks of industries and firms and investigate how the supply network structure mediates the effect of economy on industry or firm sales. Previous research has shown that retail sales are correlated with the state of the economy. Since retailers source their products from other industries, the sales of their suppliers can also be correlated with the state of the economy. This correlation represents the source of systematic risk for an industry that propagates through a supply chain network. Specifically, we identify the following mechanisms that can affect the correlation between sales and the state of the economy in a supply chain network: propagation of systematic risk into production decisions, aggregation of orders from multiple customers in a supply chain network, and aggregation of orders over time. We find that the first effect does not amplify the correlation, however, the latter two intensify correlation and result in the amplification of correlation upstream in supply networks. We demonstrate three managerial implications of this phenomenon: implications for the cost of capital, for the risk-adjusted valuation of supply chain improvement projects, and for supplier selection and risk.