Inventory Management in e-business: An EOQ Approach with Compensation Policy
Authors: Daewon Sun
Winner of the Best Paper Award for the eBusiness Workshop co-sponsored
by eBRC and the Institute for the Study of Business Markets (ISBM)
In the past several years, we have seen very rapid growth in e-commerce. Even though online retailing was still less than 1% of retail economy in 1999, online retailing is forecasted to be more than $204 billion in 2004 [5]. There are several similarities and differences between online and traditional retailing. One of the significant differences is that there are many online retailers who do not carry any inventory. Obviously, the stockless policy can reduce holding cost, and online retailers can have competitive advantages from the policy.
However, it is obvious that stockouts will hinder consumers' decision making for buying a product. There are many marketing papers studying the relationship between stockouts and consumer response. Fitzsimons argues that when consumers face stockouts, consumers react substantially and negatively to the stockout-they report lower satisfaction with the decision process and show a higher likelihood of switching stores on subsequent shopping trips [3]. Therefore, there exists trade-off between cost savings and lost sales in the stockless policy.
Currently, many traditional retailers keep positive stock on hand except some special cases (e.g., car dealers). However, in e-business, there are many online retailers who are doing business without carrying any stock. They are just accepting backorders. The inventory policies between online and traditional retailers are almost opposite. Then, basic and fundamental questions to ask are "can the stockless policy be an optimal inventory policy?" and "if it can be an optimal inventory policy, what are the sufficient conditions for the optimality?"
It is well known that, under the EOQ model with backorders, accepting only backorders cannot be an optimal solution unless backorder cost is equal to 0 [1, 4]. There are many papers about lost sales cases and partial lost sales cases. However, the stockless policy has not been researched fully yet. This paper's main purpose is to find the stockless policy's sufficient conditions for the optimality and to generate some insights from the sufficient conditions.
To analyze and answer the above basic questions, we introduce a new inventory policy, Compensation policy. In this policy, the only difference from the other inventory policy occurs when we do not have any stock on hand. That means, if we do not have any stock on hand, we will offer a compensation, R, to keep or increase demand rate.
Therefore, we compensate consumer's waiting time with compensation due to stock-outs. From customer's point of view, stock-outs will give a negative effect. Therefore, some customers may postpone the final purchase or stop by the other stores when they notice that they cannot buy what they want immediately. However, with the compensation policy, the customers may still want to buy the product because of the compensation. Furthermore, it is possible that the compensation policy may have higher demand rate compare to the demand rate with stock. From retailer's point of view, as long as they can make profits, they want to increase demand rate. Therefore, this inventory policy is beneficial for both customers and retailers as long as they can get benefits from the policy.
To implementing this policy is not difficult. In traditional retailing, if a store will post its compensation rate with waiting time, it may be attractive some customers who are not interested in purchasing the product at that time. In e-business retailing, the policy can be implemented more easy way. Due to the advanced web-technology, we can change our products price very easily. Therefore, a store will announce the compensation immediately when its inventory is out of stock.
Under this compensation policy, there is also trade-off. Because we will have an additional compensation cost, our total cost will be also increased. However, due to the policy, if the demand rate with stock-outs will be increased, our total profit will be increased also. Furthermore, we may have different optimal inventory policy (e.g., stockless policy) under certain conditions.
In this paper, we consider two types of compensation. One is flat rate and the other is time dependent compensation. Under the flat rate compensation policy, we will offer a fixed compensation regardless of waiting time. Therefore, during the stock-outs period, all customers who placed backorders get same fixed compensation. On the other hand, under the time dependent compensation policy, customers will be compensated according to waiting time.
To investigate and find sufficient conditions for each inventory policies, we formulate Compensation models based on the EOQ model with backorders. However, there are several differences. First, we generalize the assumption about demand rate. Under the EOQ model with backorders, the demand rate is always same. However, in our model, we can have different demand rates between with stock and with stock-outs. Second, if the demand rates are not same, just minimizing average inventory cost will not give us the solution that will maximize profit. Therefore, there are two ways to solve this problem. One is maximizing profit function, and the other is minimizing average inventory cost including the effect of different demand rate. In this paper, we introduce new cost, opportunity cost. This cost represents and takes into account changes of profit due to the difference of demand rate. Therefore, in our model, minimizing the average inventory cost guarantee that the solution from our model is also maximizing the profit function.
Our major findings from our inventory policy and models are as followings. First, the EOQ model with backorders and its solution are special case of our model. This result is obvious. When we will not offer any compensation and have same demand rates between with stock and with stock-outs, our model is exactly same as the EOQ model with backorders. Second, our model also generalizes the EOQ model with backorders in case of partial lost sales. This is also our model's special case when we will not offer any compensation and have partial lost sales. Third, we found that, without any compensation, the stockless policy cannot be an optimal inventory policy unless backorder cost is zero.
Therefore, with no compensation, we can have only positive stock on hand or mixture inventory policy according to our cost structure and demand rates. Fourth, the stockless policy can be an optimal solution only with positive compensation under certain conditions. Fifth, we derive sufficient conditions for the three optimal inventory policies, which are positive stock on hand, mixture inventory, and stockless inventory policy. These sufficient conditions are simple and easy to understand. Finally, we show the optimal solutions for each case. Therefore, given cost structure and demand rates for a product, we can tell what is the optimal inventory policy and what is the exact solution to minimize the average inventory cost which is equivalent to maximizing profit function. Throughout the rest of this paper, we will review the traditional EOQ model with backorders, formulate Compensation models, analyze these Compensation models, find insights from our research, and discuss further research issues. To our knowledge, except the traditional EOQ with backorders, all models are new and also the optimal solutions are new.
