The Allocation of Inventory Risk in a Supply Chain: Push, Pull, and Advance-Purchase Discount Contracts

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Abstract
While every firm in a supply chain bears supply risk (the cost of insufficient supply), some firms may, even with wholesale price contracts, completely avoid inventory risk (the cost of unsold inventory). With a push contract there is a single wholesale price and the retailer, by ordering his entire supply before the selling season, bears all of the supply chain's inventory risk. A pull contract also has a single wholesale price, but the supplier bears the supply chain's inventory risk because only the supplier holds inventory while the retailer replenishes as needed during the season. (Examples include Vendor Managed Inventory with consignment and drop shipping.) An advance-purchase discount has two wholesale prices: a discounted price for inventory purchased before the season, and a regular price for replenishments during the selling season. Advance-purchase discounts allow for intermediate allocations of inventory risk: The retailer bears the risk on inventory ordered before the season while the supplier bears the risk on any production in excess of that amount. This research studies how the allocation of inventory risk (via these three types of wholesale price contracts) impacts supply chain efficiency (the ratio of the supply chain's profit to its maximum profit). It is found that the efficiency of a single wholesale price contract is considerably higher than previously thought as long as firms consider both push and pull contracts. In other words, the literature has exaggerated the value of implementing coordinating contracts (i.e., contracts that achieve 100% efficiency, such as buy-backs or revenue sharing) because coordinating contracts are compared against an inappropriate benchmark (often just a push contract). Furthermore, if firms also consider advance-purchase discounts, which are also simple to administer, then the coordination of the supply chain and the arbitrary allocation of its profit is possible. Several limitations of advance-purchase discounts are discussed.Nash equilibrium, contracting, coordination, bargaining, newsvendor model