Evaluating the potential effects from probabilistic selling of similar products

In this article, we consider an online retailer who sells two similar products (A and B) over a finite selling period. Any stock left at the end of the period has no value (like clothes going out of fashion at the end of a season). Aside from selling the products at regular prices, he may offer an additional option that sells a probabilistic good, ‘A or B,’ at a discounted price. Whenever a customer buys a probabilistic good, he needs to assign one of the products for the fulfillment. Considering the choice behavior of potential customers, we model the problem using continuous‐time, discrete‐state, finite‐horizon dynamic programming. We study the optimal admission decisions and devise two scenarios, whose value functions can be used as benchmarks to evaluate the demand induction effect and demand dilution effect of probabilistic selling (PS). We further investigate an extension of the base MDP (Markov Decision Process) model in which the fulfillment of probabilistic sales is uncontrollable by the retailer. A special case of the extended model can be used as a benchmark to quantify the potential inventory pooling effect of PS. Finally, numerical experiments are conducted to evaluate the overall profit improvement, and the effects from adopting the PS strategy.