Optimal Allocation of Limited Inventory Among Multiclass Customers with Finite Populations

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 a unique reward and arrival rate. We develop a stochastic model and formulate the problem as a Markov decision process. We study the structural properties of the optimal value function and derive 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 lower-priority groups. We also present a fluid model with an explicit solution that can serve as a good approximation when the system size is very large.

Funding: P. Ge was partially supported by the Statistical and Applied Mathematical Sciences Institute [Grant NSF-DMS-1929298].

Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2024.0892.