Dynamic Mix-Bundling with Limited Inventories

Consider a revenue-maximizing provider who holds inventories for multiple components and adopts mix-bundling to sell a line of products made up of individual components and bundles that comprise these components. Consumers arrive over a finite time horizon up to the time of consumption and each of them requests a component or a bundle. We first study the setting in which the provider holds inventories for two components and adopts quantity-based control to manage selling, whereby she accepts a consumer request for a product if its price is above the associated marginal value. Our results show that a lower inventory level for a component increases the marginal value of a product that comprises this component – the scarcity effect, and a higher inventory level of a component increases the marginal value of the other component – the complementarity effect. The scarcity effect in general outweighs the complementarity effect in influencing optimal policies. While the value of package decreases as time elapses, that of a specific component is not necessarily monotone with time due to inventory imbalance. In the general setting, the provider has inventories for a number of components and adopts price-based control to manage selling. We develop and apply a heuristics to dynamically decide bundle set, component selling prices and bundle discount, to find that the value of mix-bundling in revenue generation depends crucially on the correlation of consumer valuations for components, as well as the availability and dispersion of initial component inventories.