Return or Not? Joint Pricing and Refund Optimization for Omni-Channel Retailing

We study a return problem of a retailer selling multiple substitutable products through an online channel and a physical store. Online purchases can be returned either by mail or to the physical store. The retailer decides each product’s price and refund value in each channel to maximize his expected revenue. We characterize a consumer’s sequential decisions on making a purchase and returning the product using a generalized Markovian logit choice (MLC) model, which allows us to formulate a joint pricing and refund optimization problem. If no constraints on the prices and refund values are imposed, this optimization problem is convex and we obtain analytical expressions of its optimal solution. By allowing products with larger salvage values to be returned or making the return process more convenient, the retailer can increase his revenue. The retailer can also leverage substitution effects to modulate the products’ market shares across the channels. If constraints are imposed on the prices and refund values, the problem may become non-convex and we approximate it using a mixed-integer linear program. Furthermore, the generalized MLC model is flexible and predicts the demand well. Numerical experiments under various parameter settings using synthetic data demonstrate that an estimation-and-optimization framework based on this generalized MLC model yields a revenue close to a theoretical benchmark. The generalized MLC model can be estimated based on partially observable data. A case study using data with some unobservable consumer choices from a major fashion retailer in China demonstrates that our approach is effective