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Modern production planning and inventory control has been developed in order to treat more practical and more complicated circumstances, such as researching supply chain instead of single stock point; multi-items with correlation instead of single item and so on. In this paper, how to classify inventory items which are correlated each other is discussed by using the concept of ‘cross-selling effect’. In history, the ABC classification is usually used for inventory items aggregation because the number of inventory items is so large that it is not computationally feasible to set stock and service control guidelines for each individual item. A fundamental principle in ABC classification is that ranking all inventory items with respect to a notion of profit based on historical transactions. The difficulty is that the profit of one item not only comes from its own sales, but also from its influence on the sales of other items or reverse, i.e., the ‘cross-selling effect’. We had previously developed a classification approach for inventory items by using the association rules to deal with the ‘cross-selling effect’ and found that a very different classification can be obtained when comparing with traditional ABC classification. However, the ‘cross-selling effect’ may be considered in different ways. In this paper, a new consideration of inventory classification based on loss rule is presented. The lost profit of item/itemset with ‘cross-selling effect’ is discussed and defined as criterion for evaluating of importance of item, based on which new algorithms on classifying inventory items, also on discovering maximum profit item selection, are presented. A simple example is used to explain the new algorithm, and large amount of empirical experiments, both on real database collected from Japanese convenient store and on downloaded benchmark database, are implemented to evaluate the performances on effectiveness and utility. The results show that the proposed approach in this paper can gain a well insight into the cross-selling effect among items and is applicable for large-sized transaction database.

In many inventory control systems, it has been considered that the number of items is so large that it is not computationally feasible to set stock and service control guidelines for each individual item. As a result, items are often grouped together and generic inventory control policies (such as service level/order quantity/safety stock coverage) are applied to each item in the same group. The grouping method provides management with more effective means for specifying, monitoring, and controlling system performance, since strategy objectives and organization factors can often be represented more naturally in terms of item groups. Historically, ABC classification scheme is most frequently used for items grouping. It groups items based on the fact that a small fraction of items account for a high percentage of the total dollar usage. The principles of ABC classification have been around a long time, at least since Pareto made his famous observations on the inequality of the distribution of incomes (Silver, Pyke, & Peterson, 1998). Astute managers have continued to apply the principle by concentrating on the “significant few” (the A items) and spending less time on the “trivial many” (the C items). Moreover, to classify the items into the A, B, and C categories, one criterion had to be generally based on, just like as Pareto did. For inventory items, such criterion is often the dollar usage, i.e., the product of unit price and annual demand, of items. For many items, however, ABC classification is sometimes not suitable for inventory control. Managers have to shift some items among categories for a number of reasons. Several researchers considered there might be other criteria that represent important considerations for management. The uncertainty of supply, the rate of obsolescence, the availability of the substitute material, lead time, durability, and the blockade effect of stockout; all of these are examples of such considerations. Some of these may even weigh more heavily than the dollar usage in the management of the items. Several criteria have been identified as important in the management of maintenance inventories (Chase, Aquilano, & Jacobs, 1998). Also several researchers suggested multiple criteria should be used in classification of inventories (Cohen and Ernst, 1988, Flores and Whybark, 1986, Flores and Whybark, 1987 and Lenard and Roy, 1995). Flores and Whybark, 1986 and Flores and Whybark, 1987 firstly considered multiple criteria for ABC analysis on inventory items, including lead time, criticality, commonality, obsolescence and substitutability criteria. The general principal of using multiple criteria for evaluating the importance of item is using the summation of weighted scores in terms of all criteria; e.g., for inventory item i its synthetical score is: View the MathML sourcevi=∑j=1nwjsij, where wj is the weight and sij is the score of item i in terms of j criterion. Ramanathan (2006) proposed an approach, called weighted linear optimization, to aggregate the performance of an inventory item in terms of different criteria to a single synthetical score by using a weighted additive function. Zhou and Fan (2007) proposed an extended version of such weighted linear optimization for multi-criteria inventory classification. The analytic hierarchy process (AHP) ( Vaidya & Kumar, 2006) is a practical methodology that had been used for evaluating the weights of criteria. It prioritizes criteria by comparing each two criteria and calculating scalar weight for each criterion, and was firstly introduced by Partovi and Burton (1993) to do ABC analysis for inventory items based on multi-criteria. Ozan and Mustafa (2008) proposed an inventory classification system based on the fuzzy AHP to assist a sensible multi-criteria inventory classification. Recently, we had proposed a new approach on classification of inventories (Kaku & Xiao, 2008). For some inventory items, evaluating the importance of one item comes not only from its own value, but also from its influence on the other items, i.e., the “cross-selling effect” (Anand, Hughes, Bell, & Patrick, 1997). In such situation, it should be explained clearly whether the cross-selling effects would influence the ranking of items or not, and how to group the items if such effects exist, not concerning what and how many criteria could be used. It is a very important decision making problem in retail stores such as supermarkets and convenience stores, because ordering some items needs to gather some other items related with them. For example, how many bottles of milk should be ordered is dependent on how many pieces of bread are to be ordered. Such situation is not considered in the literatures and it could not be solved by using the traditional classification of inventories. We have developed a classification approach of inventories by using the association rules to deal with the ‘cross-selling effect’ and proposed that a very different ranking of inventory items can be obtained comparing with traditional ABC classification. However, the ‘cross-selling effect’ may be considered in different ways and we refer different considerations of cross-selling effect should lead very different items ranking because they focus on the different sides of management issues. In this paper, a new consideration of inventory classification based on loss rule is presented. Loss rule presents the loss of profit for items if some other items were not considered which have ‘cross-selling effect’ with them (Wong et al., 2003 and Wong et al., 2005). After constructing the framework of new classification and algorithms of ranking inventory item, comparative studies with ABC classification and above ranking method with association rules developed by Kaku and Xiao (2008) are provided by using a numerical example and empirical experiments. The rest of the paper is organized as follows. Section 2 provides an overview of related researches. Section 3 outlines our approach and the issues to be addressed, and provides the detailed descriptions of new algorithm. Sections 4 and 5 present a numeral example and the empirical experiments, respectively. Finally, in Section 6, we conclude the paper and indicate several consequent research topics that we are going to focus on.

In this paper, a new approach of recognizing the importance of inventory items based on loss rule is presented. The loss profit of item (set) in terms of loss rule, namely, the total profit that the item (set) may takes away when it is deleted (or stockout) when the cross-selling effects are taken account of, is introduced to make a new ABC classification of inventories, also to discover the most profitable item selection. We present new algorithms for ranking all of inventory items, to assist inventory manager in truly recognizing low profitable items. A numerical example is presented to illustrate the utility of the new approach. Large amount of empirical experiments are carried out on databases both from benchmark and practice to evaluate the new algorithm’s performance and effectiveness. Experiment results indicate that a considerable large part of inventory items should be reevaluated the importance and therefore change their positions in the ranking list of ABC classification. Many items that traditionally do not belong to the A group have been moved into the A group by the cross-selling effect to reconfigure their inventory policies, and also many items that traditionally belong to C group have been promoted into higher group because of their high loss profits and should not be ignored as they were treated before. Future studies on this topic can be carried out in two aspects. The first is to construct some new framework in which several characteristics of inventory data should be involved such as price, quantity and time series. The second is how to determine the inventory policies when the cross-selling effects were considered. Especially, because the items in a frequent itemset may be from different classes and have cross-selling effects, the inventory policy (when and how many) of such items should be reconsidered.