Driving Supply to Marketplaces: Optimal Platform Pricing When Suppliers Share Inventory

Abstract

Problem definition: Marketplace platforms such as Amazon or Farfetch provide a convenient meeting point between customers and suppliers and have become an important element of e-commerce. This sales channel is particularly interesting for suppliers that sell seasonal goods under a tight time frame because they provide expanded reach to potential customers even though it entails lower margins. In this dyadic relationship, a supplier needs to optimize when to share inventory with the platform, and the platform needs to set the right commission structure during the season. Academic/practical relevance: We characterize supplier participation into the platform in a dynamic setting and link it to inventory levels, demand rates, time left in the season, and commission structure. This directly drives the commission structure decision made by the platform. We, thus, provide a framework to evaluate platform commission fee policies, taking into account supplier responses. Methodology: We use an optimal control framework with limited inventory supply and a stochastic demand process. We study the conditions under which the supplier accepts participation and use the platform as a sales channel. We also study the optimal commission structure that the platform should employ and the supplier procurement response. Results: We find that suppliers only participate if inventory is high relative to the time left to sell the items. As a result, the platform can only offer limited supply at the beginning of the season. Given this behavior, we find that the platform and the system are always better off with flexible pricing via fully dynamic commissions, which hurts the supplier the most (better off with less flexible commission fees). Interestingly, when the inventory decision is contingent on the platform pricing policy, the platform often finds it beneficial to commit to a static fee to incentivize the supplier to stock up, highlighting that inability to commit to fixed commissions may destroy value through double marginalization effects. Managerial implications: Our work suggests that short-term profit for the platform is maximized with fully dynamic commission fees at the expense of supplier profit. If inventory is endogenous, suppliers can retaliate by reducing their commitment at the start of the season. Despite the increased revenue obtained with the fully dynamic commission fee, the lost sales from the inventory drop incentivize the platform to opt for supplier-friendly commission fees, which are better for long-term profit.