Risk pooling through physical probabilistic selling

This paper investigates the impacts of a new type of probabilistic selling (PS) where the retailer orders specific products and package some as a discounted physical probabilistic product (PPP) rather than merely a virtual choice. We call this PS strategy as physical probabilistic selling (PPS). The price gap between the specific products and the probabilistic product results in demand reshape, i.e., some customers who originally buy specific products will switch to buying the probabilistic product, which decreases aggregate demand uncertainty. However, the price discount decreases the profit margin. Considering this trade-off, we develop a three-product newsvendor model to address the question of how to set the price for the PPP and make inventory allocation decisions. We prove that there are two effects under PPS, namely the risk pooling effect due to demand reshape and the risk diversification effect due to inventory flexibility. With demand uncertainty, PPS can improve the retailer's profit at lower inventory levels with proper demand reshape induced by the optimal price discount. PPS is more profitable with smaller product differentiation, higher customer price sensitivity, higher demand uncertainty, and lower package cost. With supply uncertainty, we demonstrate through numerical studies that PPS is a viable strategy to combat asymmetrical supply risk that yields higher profits and service levels.