FORECASTING FOR INVENTORY PLANNING UNDER CORRELATED DEMAND MELIKE BAYKAL-G ¨ URSOY Department of Industrial and Systems Engineering, RUTCOR, CAIT, Rutgers University, New Brunswick, New Jersey NESIM K. ERKIP Department of Industrial Engineering, Bilkent University, Bilkent, Ankara, Turkey INTRODUCTION When selling similar products, mainly due to product substitution by customers in case of stock outs and price/brand concerns, demand for a particular product may depend on the inventory positions of other products. Thus, the effective demand for a particular product is crosscorrelated to the demand of other products. Also, demand for each product might be autocorrelated. Demand created by advertisement or price discounts today might reduce demand in the future. From time to time, the demand might also experience other disturbances that are due to the current economic or political conditions. These dependencies make it challenging for a firm to generate accurate demand forecast for each product and to determine the ‘‘right’’ order quantities so as to maximize its own profit. Survey results reported at the Harvard/Wharton Merchandising Effectiveness Project [1] have found that these subjective forecasts tend to have an average forecasting error of 50% or more. As a result, some firms buy too little of some products resulting in lost sales and profit margin, and some firms buy too much of some products resulting in excess supply that must be marked down after a while, frequently to the point where the product is sold at a loss. A survey conducted by Wiley Encyclopedia of Operations Research and Management Science, edited by James J. Cochran Copyright  2010 John Wiley & Sons, Inc. a major retailer and reported in the New York Times on June 2, 1994, concluded that 50% of customers did not purchase products when they visited the store and of these 40% stated they did so due to their inability to find a given product. Similar under- and oversupply costs have been reported for other products such as automobiles [2] and computers [3]. Demand uncertainty is highest when a new product is introduced against competition. In some industries, for example, in the pharmaceutical industry, firms prefer to be responsive to the customer demand and thus incur high inventory costs to reduce lost sale. This is where accuracy in forecasting becomes crucial. Firms spend a great deal of time and resources trying to predict, as accurately as possible, the future demand for their prod- ucts and services. Clearly, it is beneficial to know about the future, and, in most cases, the near future where accuracy is most needed. Knowing about the future enables making better decisions of ordering when inventories are reviewed—both in pull- and push-type systems. Also, production plans and resource scheduling are done more effectively in push- type systems if we have a good idea about the future. Two issues that are of concern here are forecasting and inventory control for multi- item systems where demand for these items can be correlated, as well as temporally cor- related for each item. Classical forecasting procedures are usually carried out for single items. Standard coverage of well-known text books includes the following topics: times series analysis, exponential smoothing methods (see Holt–Winters Exponential Smoothing), moving average (MA) met- hods, regression with various possible exten- sions [4 – 8]. These references also include the study of nonstationary autoregressive inte- grated moving average (ARIMA) models (see Forecasting Nonstationary Processes). Nevertheless, a number of procedures can be utilized for the forecasting activities under correlated demand. For example, 1