Competitive multiproduct contracting under multinomial logit demand

Lusheng Shao

Production and Operations Management, 2023, vol. 32, issue 2, 379-396

Abstract: Despite the prevalence of multiproduct firms in many industries, the supply chain contracting literature has predominantly focused on problems where an upstream player offers only one product. This paper studies multiproduct contract design for competing manufacturers each with several products to sell via a common retailer. We consider two contracting schemes under multinomial logit demand (MNL): individual contracting, in which the manufacturers set a wholesale price for each of their products separately; and aggregate contracting, in which the manufacturers set the price as a function of the order quantities for their own products. We find that under individual contracting it is optimal for each manufacturer to offer the full range of his products to the retailer and set an equal wholesale margin for these products. This suggests that the classic result of an equal‐margin policy for the retailer also holds true for the manufacturers. Further, there is an equilibrium characterized by a system of nonlinear equations that can be solved using the standard bisection search method. Under aggregate contracting, a simple cost‐plus contract is optimal for the manufacturers. In equilibrium, each manufacturer charges a markup equal to his marginal contribution to the supply chain, and the supply chain profit is maximized. Comparing these two contracting schemes, we find among other results that the retailer prefers aggregate contracting when there is a large number of products from each manufacturer or when consumer heterogeneity is low, while the opposite is true for the manufacturers. In addition, both the retailer and the manufacturers prefer aggregate contracting when there are few manufacturers in the supply chain. It is also found that as the number of manufacturers or the number of products from each manufacturer increases, the supply chain efficiency loss induced by individual contracting is reduced. Finally, we extend our model to a hybrid setting in which one manufacturer adopts aggregate contracting and the other adopts individual contracting, and demonstrate to the manufacturers the value of aggregate contracting. These results provide useful guidance on optimal contract design for multiproduct firms.

Date: 2023
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