Revenue Management Through Dynamic Cross-Selling in E-Commerce Retailing

We consider the problem of dynamically cross-selling products (e.g., books) or services (e.g., travel reservations) in the e-commerce setting. In particular, we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product, packaging complement. Given consumer preferences and product inventories, two issues are analyzed: (1) how to select packaging complements and (2) how to price product packages to maximize profits. We formulate the cross-selling problem as a stochastic dynamic program blended with combinatorial optimization. We demonstrate the state-dependent and dynamic nature of the optimal package selection problem and derive structural properties of the dynamic pricing problem. In particular, we focus on two practical business settings: with (the Emergency Replenishment model) and without (the Lost Sales model) the possibility of inventory replenishment in the case of a product stock-out. For the Emergency Replenishment model, we establish that the problem is separable in the initial inventory of all products and hence the dimensionality of the dynamic program can be significantly reduced. For both models several packaging/pricing heuristics are suggested and their effectiveness is tested numerically