Dynamic Inventory-price Control during Opaque Selling of Horizontally-differentiated Products

Abstract

We study a firm that sells two regular horizontally-differentiated products that are similar in major functionalities while retaining minor differences in colors and styles. An arriving buyer may also ask for an opaque product, which can be satisfied by the delivery of either regular product. Such flexibility in rationing is supposed to help the firm overcome the ill effects of inventory imbalances. To help it fully realize this potential, we investigate the firm's operations management in a discounted infinite-horizon criterion. After first gaining insights from the simultaneous control of replenishment and rationing, we then add in pricing to achieve the coordination of all three activities. Optimal policies are found to exhibit an overarching balance-inducing theme. In particular, replenishment should be base-stock with each product's base level decreasing in the other one's inventory; meanwhile, rationing should let an opaque request be satisfied by a product in ampler supply. For the most difficult pricing portion, certain three-dimensional "half-range" properties on profit-to-go functions finally lead us to "negatively feeding-back" policies. Under them, inventory imbalances would induce more opaque requests through lower prices, which in turn help restore the balance of inventory levels. Our numerical experiments find opaque selling to be more competitive when buyers have more homogeneous valuations for the products.

Keywords: Opaque Selling, Replenishment Policy, Rationing Policy, Pricing Policy