團隊

For a queueing system with multiple customer types differing in service-time distributions and waiting costs, it is well known that the cµ-rule is optimal if costs for waiting are incurred linearly with time. In this paper, we seek to identify policies that minimize the long-run average cost under nonlinear waiting cost functions within the set of fixed priority policies that only use the type identities of customers independently of the system state. For a single-server queueing system with Poisson arrivals and two or more customer types, we first show that some form of the cµ-rule holds with the caveat that the indices are complex, depending on the arrival rate, higher moments of service time, and proportions of customer types. Under quadratic cost functions, we provide a set of conditions that determine whether to give priority to one type over the other or not to give priority but serve them according to first-come, first-served (FCFS). These conditions lead to useful insights into when strict (and fixed) priority policies should be preferred over FCFS and when they should be avoided. For example, we find that, when traffic is heavy, service times are highly variable, and the customer types are not heterogenous, so then prioritizing one type over the other (especially a proportionally dominant type) would be worse than not assigning any priority. By means of a numerical study, we generate further insights into more specific conditions under which fixed priority policies can be considered as an alternative to FCFS.

Emergency department (ED) overcrowding and long patient wait times have become a worldwide problem. We propose a novel approach to assigning physicians to shifts such that ED wait times are reduced without adding new physicians. In particular, we extend the physician rostering problem by including heterogeneity among emergency physicians in terms of their productivity (measured by the number of new patients seen in 1 hour) and by considering the stochastic nature of patient arrivals and physician productivity. We formulate the physician rostering problem as a two-stage stochastic program and solve it with a sample average approximation and the L-shaped method. To formulate the problem, we investigate the major drivers of physician productivity using patient visit data from our partner ED, and find that the individual physician, shift hour, and shift type (e.g., day or night) are the determining factors of ED productivity. A simulation study calibrated using real data shows that the new scheduling method can reduce patient wait times by as much as 13% compared to the current scheduling system at our study ED. We also demonstrate how to incorporate physician preference in scheduling through physician clustering based on productivity. Our simulation results show that EDs can receive almost the full benefit of the new scheduling method even when the number of clusters is small.