Optimal outpatient capacity allocation under the capacity-addition policy

Outpatient departments are under great pressure to meet increasing demand with limited medical resources. Facing a high-demand environment, the capacity-addition policy (CAP) has been widely applied, where outpatients allocate additional capacity in a demand-driven approach. Under the CAP, outpatient managers estimate an effective demand. Additional capacity is determined depends on the relationship between the estimate and regular capacity. Moreover, regular capacity is also a decision variable, which leads to great difficulties when conducting capacity allocation. The joint decisions on the optimal regular capacity, its allocation scheme of different phases and proper rule for estimating the effective demand become important concerns for outpatient managers, under uncertainties in demand and patient no-show. This paper addresses the problem towards maximizing the expected profit composed of expected revenue minus the costs of idleness and overwork. Several properties are proposed to address the difficulty in the infinite solution space. Properties help transform the joint decisions into orderly single decisions and prove the unimodality of the objective. Algorithms are designed accordingly. Experiments indicate that it is better to pre-offset the effect of no-show rather than consider its reduction in the determination of additional capacity. Outpatient managers need to enlarge the estimate of effective demand, and 1.1 to 1.2 times of the total expected demand is suggested, where outpatients can balance the expected overload with the expected profit. The optimal regular capacity is stable to the variety of no-show probability.