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Article Excerpt
1. Introduction
Stock-outs are endemic in the retail industry. In the supermarket industry alone, stock-outs lead to lost sales of $7-12 billion annually (Ton, 2002). "It's no small secret that retailers are still out of stock on 20% to 30% of the SKUs consumers want almost all the time," according to the Vice President and CIO of Liz Claiborne (Hill, 1998, p. 78).
When stocking out, a retailer is at risk of losing customers to competitors in search for substitutes. A survey by P&G finds about 50% of its customers switching to another retailer after a stock-out (Tierney, 2004). Verbeke et al. (1998) find 34% of Coca Cola customers switch after a store is out of stock. Anticipating this, an option sometimes available to retailers is to arrange in advance to reduce lost sales by the transshipment of inventory or capacity from a competitor. The purpose of this paper is to understand the following: what economic conditions favor a transshipment agreement ex-ante between competing retailers? How are the retailers pricing and inventory decisions affected by such a transshipment agreement? The following examples further motivate this research.
1. In the British Columbia forest industry, a small number of independent trucking companies compete to transport logs from scaling yards, where logging operators have weighed and sorted stems, over public roads to mills. For short periods the capacity of trucking companies can be considered fixed. The demand for transport is quite variable because of terrain, weather and a number of factors beyond their control. Under these circumstances, the cost of the capacity that a transport company deploys in any region and the price it charges determine whether it will survive. Faced with an unmet need to move logs because their usual trucking company is at capacity, a logging operator needs to contact another trucker. However, this creates a problem for the operator as their relationship with the transport provider is much richer than mere transportation: it also includes such services as payment systems and credit arrangements. A working arrangement usually arises among truckers, such that, given unmet demand by one and idle equipment at another, the idle trucks and drivers will be reassigned on a short-term basis. This is not a formal arrangement in the sense of a legal contract, but the terms of trade are common knowledge to all truckers (1) and the "deal" is transparent to loggers, who are charged the same price. They are not concerned if a different logo is on the side of the truck. Thus, an unmet demand from a buyer (logger) is satisfied by sellers (truckers) transshipping their excess capacity (trucks) rather than by the buyer switching to another seller.
2. Most automobile sales are done through dealerships that are independent of (although associated with) manufacturers. It is primarily a decentralized industry. The cars available, possible deviations from the manufacturers' recommended list price, credit terms and a number of other dealer-specified services determine the competitive environment. A customer who desires a brand but simply "must have" a blue car, not the red car on the lot, is almost a daily occurrence for a salesman. Having an inventory of the entire range of models and colors is simply impractical for most dealers. Over time, the practice has arisen of sharing models among dealers. In some cases this is highly formalized with shared web-based inquiry tools; in others, a simple call by the salesman seals the deal. (2) An alternative solution for dealers is to see the customer leave to search others' lots that might stock blue cars.
3. Story three is common to all of us. We enter a store for a fashionable item, only to find it stocked out. We leave and find another store where a reasonable substitute satisfies us. If the store had multiple outlets in the same city, the salesperson might well have been able to find the product in the same chain and transshipped it. but this would be most unusual for independent and competing retailers.
Although the above three stories are from different industries, they have much in common. First, the business entities in all three industries have a choice: they could let the unsatisfied customer "walk away" to find a substitutable product elsewhere, or, they could set up relationships with competitors to transfer unused capacity/inventory to satisfy the extra demand. Of course, more options exist than simply to agree to transship or not. For example, a more laissez-faire approach, without formal prior agreements, could see a combination of customers switching and one-off transshipments between competitors. However, there are many situations where such choices should be made in advance. It might be helpful in this context to keep in mind situations in which up-front investments are needed; for example, some car dealers have built significant IT infrastructure to facilitate transshipment.
Second, all the entities are individually owned and sell substitutable products/services, and operate in the same market boundary. Such entities compete on both price and inventory/capacity. All cases have significant retailer-level differentiation from either value added services or simple parking or location conveniences. Also, in all examples, if transshipment is not available, unsatisfied consumers search for and switch to an alternative--so-called "inventory competition."
Third, all examples can be described by a single-period model. We typically use the newsvendor model to approximate situations where perishable goods are involved. In these examples, truck capacity is highly perishable, this year's model/color of car is reasonably so and the retail fashion item mainly so. In all cases, demand is uncertain, as in the newsvendor paradigm, and capacity or inventory must be in place before demand is known.
Given these considerations, how does the choice of transshipment among competitors affect the underlying pricing and inventory decisions? What drives the strategy to choose transshipment?
Our methodology is to compare two competitive games: a transshipment game where competitors agree to transship in the case that one retailer has surplus inventory and another has extra demand, and a substitution game where, instead, unsatisfied consumers switch to an alternative retailer for a substitute. The following is a summary of our results.
1. We extend the literature on the transshipment game (transshipment among decentralized business units) by considering competition between retailers. In the substitution game we explicitly link consumer switching behavior with imperfect competition between differentiated products.
2. Using a technique developed by Zhao and Atkins (2008), we prove the existence of a pure-strategy Nash equilibrium in retail prices and safety stocks, for both the transshipment game and the substitution game. We further provide conditions for the uniqueness of a pure-strategy Nash equilibrium for both games.
3. Considering a symmetric equilibrium, for the transshipment game, we find that a stronger degree of competition leads to a lower equilibrium retail price and safety stock, which results in more unsatisfied demand and a greater need for transshipment. Furthermore, a larger transshipment price results in a higher retail price and safety stock at equilibrium.
4. When comparing the symmetric equilibria of two games, we find that transshipment between competing retailers never leads to a lower retail price and a higher level of safety stock, so transshipment never leads to a situation that definitely benefits consumers.
5. With low transshipment prices and strong competition (a low level of differentiation), retailers are better off without transshipment. However, with high transshipment prices and weak competition (a high level of differentiation), transshipment benefits retailers. Transshipment is less attractive as the degree of competition increases.
6. We also consider scenarios where retailers transship at either the receiver's or the sender's retail price, in addition to an exogenous transshipment price considered above. With the receiver's price, transshipment again becomes less attractive as the degree of competition increases; however, with the sender's retail price, transshipment is preferred by retailers.
After reviewing the literature in Section 2, we introduce the model in Section 3. We provide equilibrium analyses of the two games in Section 4, and compare them in Section 5. Section 6 provides additional results where the transshipment price is either the receiver's or the sender's retail price, and Section 7 discusses the key results, the contribution and the future research. All proofs appear in the online Appendix.
2. Relationship and contribution to the...
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