Managing resource allocation for the recruitment stocking problem

This paper revisits the Recruitment Stocking Problem (RSP), in which a prescribed total number of kits must be allocated across multiple distribution sites, where streams of subjects arrive for kit pickup. A kit can be a test-kit for a new pharmaceutical drug, a medical device, a vaccine, a humanitarian relief survival kit, etc. RSP seeks to minimize the expected recruitment time — the time to recruit a prescribed target number of kits — by identifying an optimal or near-optimal kit allocation across all locations. To this end, we first develop a computational method for evaluating the expected recruitment time using the so-called Randomization Procedure. Specifically, since the recruitment process forms a finite-state continuous-time Markov process, the Randomization Procedure transforms the Markov process with varied transition rates from different states into one with a constant transition rate across all states, and thus substantially simplifies the RSP statistics computation. Further, we develop two search heuristics to efficiently search for optimal or near-optimal kit allocations, especially for large RSP models that are too computationally expensive to optimize by exhaustive search. Finally, we illustrate the efficacy of the proposed heuristics by numerical experiments, and then discuss practical implications and provide managerial insights.