Outpatient capacity allocation considering adding capacity to match high patient demand

Abstract

This paper focuses on an outpatient capacity allocation problem where the patient demand is quite higher than the supply. We study an adding capacity policy to mitigate the mismatch between supply and demand. Under this policy, the doctor is allowed to add capacity if all regular capacity have been booked. A capacity allocation model is formulated for both possible no-show routine patients and all show-up same-day patients. The purpose is to determine the number of capacity can be added and how to allocate regular capacity among routine patients and same-day patients, towards maximizing the expected profit, which is composed of the expected income minus the cost of weighted expected doctor’s overload work caused by the adding capacity policy and the cost of rejecting patients. To achieve the aims, we prove the expected profit monotonously decreases when the number of additional capacity exceeds a threshold, and present a two-tier enumeration search algorithm to find the global optimal solution based on the proof. Numerical results indicate that the proposed policy performs well under different levels of demand higher than supply. The optimal number of the additional capacity is hardly affected by varying total expected patient demand. Additionally, under the change of no-show rate, the number of regular capacity allocated to routine patients becomes more stable, compared with the optimal scheme without considering adding capacity policy.