A Cross-Spectral Analysis of Retail Inventories and Sales

Abstract

The synchronization of inventory and sales is one of the most important activities in retail management. Retailers must continuously adjust their inventory to changes in demand and try to strike a balance between overstocking and understocking. If inventory is excessive, relative to sales, costs go up and profits are reduced. If inventory is too low, stock-outs occur and sales are lost; therefore, profits will not be as high as they might be. Success in managing inventory depends not only on the total stock investment but also on the assortment of products available for sale. In this study attention is focused on inventory investment and the problem of maintaining optimum assortments of products to service demand is not discussed. During recent years, developments in operations research and advances in computer technology have contributed significantly to inventory control capabilities. Models have been developed to calculate economic order quantities and to determine optimum reorder points. Computerized data processing systems have been designed which make it possible to record the details of each sale as the transaction is completed and to update simultaneously the inventory status of each item sold. Generally, these efforts focus on the micro problems of optimal inventory policies for individual firms, assuming different demand conditions and cost structures. Little attention, however, has been given to the aspects of inventory control and relatively less is known about inventory behavior at an aggregate level. Of the studies that do approach inventory problems at the macro level, almost all concentrate on inventory investment by manufacturers and are concerned primarily with explaining the impact of inventory fluctuations on economic conditions. Among the published studies of retail inventories, probably the best known are those that investigate buying practices and inventory levels of department stores.1 This study examines retail inventory-sales behavior at the macro level, using cross-spectral methods. The purpose of the study is to determine the interaction between retail stocks and sales and to define the lead-lag relationships between the two variables. Spectral analysis is well suited to study the oscillations in retail inventory and sales and provides the basis for a more