قرارداد توزیع برای حمایت از دارایی های موجودی بهینه تحت عدم اطمینان تقاضا

When suppliers produce products for which demand is uncertain, they face a problem of inducing downstream distributors to stock inventory levels that the suppliers prefer. This paper considers a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that linear supply contracts specifying any combination of two of these three instruments can implement the vertical integrated outcome for a monopoly, thereby generating the supplier's preferred inventory configuration and price distribution. We extend our results to differentiated product oligopoly, demonstrating that each supplier obtains its preferred inventory configuration and price distribution, given the choices of its rival. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. Thus, suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion.

Suppliers and the distributors of their products exist in quasi-independent and yet symbiotic relationships with one another. Suppliers determine the amount and composition of their output and then announce contractual terms, which can include, among other terms, wholesale prices, returns policies or buyback allowances, and additional remittances payable contingent on retailer revenues. Distributors, acting in accordance with their knowledge of their local markets, then chose the size and composition of their inventories. These inventories are then priced to consumers, who are subjected to promotion of the supplier's products both by the supplier itself and by its distributors. As both the supplier and its distributors pursue their own interests, contracts can serve to improve the alignments of those interests. Most analysis of such vertical contracts has focused on the promotional issue by considering how vertical restraints can ameliorate free riding. Here, however, we consider contracts to structure inventory holdings. The selection of inventories is perhaps the central function of retailers, whose close proximity to ultimate consumers provides them with insights about what and how much to stock. Using a general model of linear supply contracts, we establish that several commonly observed supply contracts are special cases of our model and thereby establish the equivalence of two common contract variants, revenue sharing and returns policies. Our model emphasizes the central role of demand uncertainty in motivating suppliers to employ supply contracts that are related to inventories. We consider contracts that place the responsibility for choosing appropriate inventories in the hands of retailers, but which provide incentives to hold the level of inventories that the supplier would choose if it possessed the same level of information about demand as that held by its dealers. The contracts in question are contingent on realized demand—they mitigate the dealers' predicament when low demand results in unsold inventories, thereby encouraging larger ex ante orders. The contracts we consider are linear functions of retail inventories, retail sales (quantities or revenues) and unsold inventory. Retailing is taken to be perfectly competitive, so inventories are held and retail prices established so that the expected profits of each retailer are zero. In an earlier paper, (Marvel and Wang, 2007), we have shown that a constant wholesale price together with a buy-back credit for unsold inventories is sufficient to coordinate retailer inventory holdings, generating the distribution of prices and availability that suppliers prefer, even when suppliers do not have access to the information about demand held by their retailers. Perhaps most surprisingly, we demonstrated that buy-backs operate in the same fashion when there are multiple competing suppliers serving the market in question. In this paper, we consider a wide array of alternative supply contracts, each of which consists of a mixture of constant per-unit wholesale prices, buy-back arrangements, and post sale payments contingent on sales made, such as revenue sharing or buybacks. We show that supply contracts that are linear combinations of two of these three categories of contract terms are capable of generating suppliers' preferred inventory holdings and price distributions. We thereby establish that a wide variety of contracts, some of which do not entail buy-backs or returns credits, are equivalent to our original wholesale price plus returns credit contract. Distributors choose optimal inventories from the suppliers' standpoint, even if suppliers do not know the distribution of demand uncertainty, and, given the perfect competition among distributors, all profits in the supply chain are captured by suppliers. We characterize fully three types of optimal contracts available to a monopoly supplier, each of which implements exactly the outcome that would occur if the supplier were integrated forward into distribution. These types include a revenue sharing contract, a generalized consignment sale plan, and a buyback plan. We then extend our results to oligopoly suppliers. We demonstrate that any one of the optimal plans, each supplier is able to obtain its preferred inventory configuration and price distribution, given the choices of its rivals, and we fully characterize the modifications necessary for each of the optimal supply contracts in the oligopoly setting. After presentation of our results, we place them in context, comparing our approach to previous papers such as the Dana, Jr. and Speir (2001) revenue sharing model and the Marvel and Peck (1995) returns model. Our setting differs from these papers, allowing consumers to choose from an array of retailers and analyzing somewhat general demand conditions. In addition to demonstrating in our setting the equivalence of the monopoly supply contracts in these papers, we provide the extension to oligopoly. Suppliers are able to deal with demand uncertainty with remarkably little information about demand, and without the need to control dealer actions in detail. In particular, suppliers need not specify either dealer inventories or resale prices, but instead encourage distributors to order based on information in their possession and to set prices that generate desirable resale price dispersion. Our approach relies on competition among retailers that causes them to select prices that yield zero profits in retail equilibrium. As a result of this competition, retailers that anticipate the possibility that their inventories will turn relatively slowly (that is, that their inventories will not sell if realized demand is low) will only offer their products to the market at comparatively high prices. This effect naturally results in price dispersion in the marketplace. The supplier's problem is to induce its desired degree of price discrimination. The lowest prices are set by retailers who expect to sell out in all demand realizations. When these prices are too low, the supplier throws away surplus and sees insufficient inventory holding for high demand states. But with positive marginal cost of production, the supplier will not wish to provide inventories for very unlikely states of demand. We show that a monopoly supplier can induce its preferred distribution of prices and inventories by relying on retailers to use their superior knowledge of the distribution of demand. We show that the insight extends to the case of oligopoly suppliers. Section 2 analyzes the model when there is a single supplier selling through competitive retailers. We establish the equivalence of revenue sharing, returns, and generalized consignment contracts, and show that with appropriate contracts for competitive retailers, the supplier does not need to know the distribution of demand facing those retailers. In Section 3, we show that the results also apply when oligopoly suppliers compete with one another. The contract equivalence we establish suggests that different supply contracts can coexist in the marketplace, and that, as for the monopoly supplier, oligopoly suppliers do not need to know the distribution of demand, but can instead rely on retailers to use their superior knowledge of the marketplace to set appropriate prices and inventory levels.

This paper provides a general model of contracting to support suppliers' optimal inventory configurations. Our model suggests that in a market where suppliers sell through competitive retailers, the suppliers' optimal revenue sharing, buyback (or returns policy), consignment sales, and other supply contracts can be equivalent in correcting the distortion caused by demand uncertainty. As long as the demand functions are linear, the suppliers do not need to collect information that retailers hold about the nature of demand uncertainty. They do not need to directly control the retailers' inventories or resale prices neither. Retailers can be left free to choose both retail prices and inventories. It is important, however, to consider not only the variety of two-control contracts that work, but also what sort of contracts fail. It is very common for commentators to dismiss inventory concerns simply by saying that a supplier concerned about inventory holding can pay directly for better inventories. This is a quite different approach from the contracts considered here. Suppliers must have considerable information about the conditions facing retailers, and must be able to monitor the retailer inventories to ensure that they are being displayed as the supplier prefers. Note also that the largest payments will need to be made to retailers who are least likely to sell the products. But such payments will only work in concert with specified prices. Retailers who receive an inventory support payment will have a strong incentive to set prices lower than the supplier prefers in order to sell the inventories they have agreed to hold. This is a very different system than the ones we analyze. It is unlikely to work effectively when retailers and suppliers are independent of one another. When suppliers face demand uncertainty and want their retailers to hold inventories that may not sell out in the event of a low demand realization, the suppliers will prefer that prices not be driven to a single level. We have shown that there are a number of contractual paths to the suppliers' preferred price dispersion and inventory holdings. These contracts have the advantage of leaving the decision making on these parameters to retailers who have access to superior information. Our models are simplified by assuming perishable products and ignoring holding costs. Future work will investigate the relaxation of these simplifications with an eye to understanding the wide variety of vertical relationships with which suppliers structure inventory holdings and pricing of their products.