Optimal resource allocation in military hospitals using inverse Erlang-B models

Effective resource allocation is vital for procurement management, optimising assets' use to meet fluctuating demands while minimising operational bottlenecks. This paper advances resource allocation strategies by employing inverse Erlang-B models, specifically applied to military hospitals. Incomplete gamma and Marcum-Q functions are used in novel computational formulations to improve accuracy across various traffic intensities. In contrast, inverse functions offer tight constraints for calculating server requirements under high load. Assuming a 5% rejection rate and an average patient stay of 1.5 days, a case study models daily military hospital ward admissions as an autoregressive process (AR(1)), projecting an average demand of 86 hospital beds, with a minimum of 79 and a maximum of 91 beds per day. The findings demonstrate the effectiveness of inverse Erlang-B models in capacity planning, providing scalable solutions for optimising resource utilisation in healthcare and industrial sectors (Gil et al., 2013; Marinkovic and Stosic, 2023a).