Optimal Allocation of Limited Inventory among Multi-class Customers with Finite Populations

Abstract

We consider the problem of allocating a single type of resource with limited supply to distinct groups, each with a finite population and characterized by unique reward and arrival rate. We consider both deterministic and stochastic settings. In the deterministic model, we formulate the problem as an optimal control problem and derive the analytical optimal allocation policy. In the stochastic model, we formulate the problem as a Markov Decision Process and study the structural properties of the optimal allocation policy. Contrary to the conventional approach of incrementally extending access to groups of lower priority over time, our findings suggest that it is optimal to progressively restrict admission to the lower priority groups.

Keywords: Inventory allocation, finite population, time discounting, optimal control, Markov Decision Process