Sequential Resource Allocation for Nonprofit Operations

This paper studies a sequential resource allocation problem motivated by distribution operations of a nonprofit organization. The alternate objectives that arise in nonprofit (as opposed to commercial) operations lead to new variations on traditional problems in operations research and inventory management. Specifically, we consider the problem of distributing a scarce resource to meet customers' demands that are observed sequentially. An allocation policy that seeks to maximize profit may lead to inequitable distributions among customers. Our work in a nonprofit setting solves the sequential resource allocation problem with an objective function aimed at equitable and effective service. We define service in terms of fill rate (the ratio of the allocated amount to observed demand) and develop an objective function to maximize the expected minimum fill rate among customers, which balances equity in fill rates with effectiveness in the use of resources (low waste). Through a dynamic programming framework, we characterize the structure of the optimal allocation policy for a given sequence of customers when demand follows continuous probability distributions. We use that optimal structure to develop a heuristic allocation policy for instances with discrete demand distribution. In addition, we identify customer demand properties to consider when sequencing customer visits to optimize the fill rate objective. For both inventory allocation and customer sequencing decisions, the proposed heuristic methods yield near-optimal solutions.