A comparison of fixed and variable capacity-addition policies for outpatient capacity allocation

Residents of mainland China always come to the first-class hospitals. Facing limitations to medical resources, hospital managers consider adding some potential capacity beyond the regular daily capacity to meet demands and improve the profit. This paper systematically studies the capacity-addition policy, and compares two kinds of them: fixed capacity-addition policy (F-CAP) and variable capacity-addition policy (V-CAP). The former sets the additional capacity by simple calculations according to experiences or history statistics. Under the V-CAP policy, the additional capacity is determined by solving an optimization model rather than a constant. The V-CAP definitely achieves the optimal expected profit, which can be regarded as the benchmark that leads to the best improvement. Since the F-CAP is widely used in many first-class hospitals in practice, this paper attempts to explore in which situations the F-CAP can achieve a similar improvement of the V-CAP, and in what environments the additional capacity should be a variable. In addition to focusing on additional capacity, both policies allocate the regular capacity to two types of patient: routine patients and same-day patients, who have different no-show probabilities. We formulate linear integer programming models of F-CAP and V-CAP to maximize the expected profit. Several propositions and corollaries are proved to cut off the solution space and accelerate the search process. The optimal additional capacity can be directly determined by these properties, and the optimal value is non-decreasing with the regular capacity allocated to routine patients. Numerical experiments indicate that the optimal total supply of regular capacity and additional capacity is always less than the expected total demand. The F-CAP is recommended to the environments with low no-show probabilities of routine patients and same-day patients, moderate expected total demand, correlation coefficient of demands and regular capacity, where the reduction of the expected profit is less than 5% of the F-CAP compared to the V-CAP.