Pricing and inventory management for mixed bundled products with stochastic demand

We analyse optimal pricing for a retailer that sells two products using a mixed price bundling strategy. We consider substitutable products, where there is a disutility associated with jointly consuming both products. Mixed price bundling implies that customers can freely choose to buy one of the two products, both of them, or neither of them. The retailer determines the price of each product when it is sold separately, the bundle discount if these two products are sold in a bundle, and the inventory levels for each product. We first derive the optimal price and bundle discount when the store traffic is deterministic. Our results show that the mixed bundling strategy is the most beneficial to the retailer when substitution is moderate. Then, we move to the stochastic store traffic case and investigate how to jointly optimize prices, bundle discount, and inventory. With backordered unsatisfied demand, the retailer offers a higher individual price and lower bundle discount than it does in the deterministic model. When any unsatisfied demand is lost, we find that the retailer raises the individual price and reduces the bundle discount even further as compared with the backorder case.