Selling a Product Line Through a Retailer When Demand Is Stochastic: Analysis of Price-Only Contracts

Abstract

To expand sales, many manufacturers try to develop and sell product lines. Frequently, however, the operations of distributing a product line creates tension between manufacturers and retailers as they do not necessarily agree on which product versions included in the product line should be sold to consumers. To mitigate this tension, previous literature has shown that if a manufacturer (he) wants to sell his product line through a retailer (she) who faces deterministic demand, then he needs to adjust his product qualities according to her requirements; otherwise she will not carry the entire line. In contrast, this paper shows that if demand is stochastic, then a manufacturer can mitigate the same tension merely by re-allocating inventory risk in the supply chain. This strategy can be so effective that it is possible to find cases where the equilibrium product line is actually longer in a decentralized supply chain than in the direct-selling case. To understand the tradeoff, we consider a supply chain with a manufacturer capable of producing multiple product designs and a retailer who faces stochastic consumer demand. The manufacturer sells his output through the retailer using one of the following variations on the classical wholesale contract: push (PH), pull (PL), or instantaneous fulfillment (IF). With PH and PL (IF), wholesale prices and quantities are decided before (after) demand is revealed. Retail prices are always set after demand is revealed. With PH (PL) the retailer (manufacturer) carries retail inventory. Taking the manufacturer's point of view, we characterize the equilibrium product line length and equilibrium contracting strategy. Our answers are determined by three important drivers: demand variability, product substitutability, and the retailer's outside option. Low outside option and low (high) substitutability imply that the manufacturer maximizes his expected profit offering the retailer longer (shorter) product line using the IF contract. As outside option increases, the equilibrium contract will be either PH or PL. High demand variability and low substitutability imply that the manufacturer should be expected to sell a longer product line with a PH contract. Low demand variability and high substitutability imply that the manufacturer should be expected to sell a shorter product line with a PL contract.

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