Revenue Management with Product Retirement and Customer Selection

We consider a multi-period, multi-product revenue management problem where in each period the seller has a fixed inventory of multiple substitutable products to sell over a fixed time horizon. In each time period, the seller chooses which subset of products to retire and also selects a customer to visit. When a product is retired, it becomes unavailable to all future customers. When a customer is selected, all available products -- non-retired products with positive remaining inventory -- are offered for the customer to choose from. The objective of the seller is to dynamically retire products and select customers in order to maximize the total expected revenue over a fixed time horizon. Such product retirement decisions are essential when the seller is not able to personalize the set of products offered to each customer.When customers choose according to the same multinomial logit model, we provide an algorithm that is asymptotically optimal as the inventories grow large. For multiple customer types, we give an asymptotically optimal policy when the upper bound linear program has an optimal solution with specific structure. We show that such solution can always be found when there are only two products. In the general case with multiple customer types and products, we design a linear programming-based policy that guarantees a constant fraction of the optimal dynamic retirement-selection policy. Finally, we show that our policies perform well in numerical experiments calibrated with real data, compared to natural benchmarks