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

Abstract

Problem Description: In practice, many consumer products are produced and stocked in product lines rather than in single variants. The issue is that manufacturers and retailers often do not agree on the product line length (number of variants included in the product line). The focus of this study is to understand how product line length and stocking quantities depend on how demand risk is contractually allocated. Academic/Practical Relevance: Our model combines assortment and stocking decisions in the presence of stochastic demand; previous models could address either assortment or stocking issues, but not necessarily both. Methodology: We present a game-theoretic model of a bilateral supply chain in which a manufacturer (he) sells up to two differentiated products through a retailer (she). He decides which products to produce, their wholesale prices, and how to allocate demand risk. We theorize that he can either retain the risk (by adopting a pull contract) or that he can pass it onto the retailer (by adopting a push contract). She responds by choosing assortment, quantities, and retail prices. By solving the model, we develop a descriptive theory that clarifies his incentive to expand his product offering and to reallocate demand risk within the supply chain. Results: Depending on the level of product differentiation, we identify three regions. When product differentiation is either low (commodities) or high (specialized products), the contract choice affects order quantities but not assortment. In these regions, the manufacturer’s contract choice can be explained by looking at elasticity of wholesale demand. For products with some differentiation, the manufacturer’s contract choice affects both order quantities and assortment. In this region, the manufacturer’s contract choice can be explained by looking at the additive effect of demand elasticity and sales expansion from the extended product line net of cannibalization. Managerial Implications: Our paper can be seen as a first step toward developing a link between optimal product line design and optimal risk allocation in a bilateral supply chain.