Study On Capacity Management Of CT Department With Emergency Non-Preemptive Priority

Healthcare industry faces increasing demand and lengthy waiting time for a wide scope of medical service. The long waits and overcrowded in the large-size hospital makes patients uneasy. Several measures could be employed to solve these problems, such as increasing healthcare industry financial input, carrying out the hierarchical diagnosis system, promoting the utilization of the medical resources. About 20%-40% of the medical resources are wasted according to the conservative estimation of World Health Report (2010). Healthcare managers and policy makers face pressure to manage the medical resources more efficiently and effectively. The core of healthcare operations management is capacity management. Appointment scheduling system is an efficiency lever to manage medical capacity to provide timely access to health services. Appointment scheduling allocates the capacity in advance to effectively utilize the resource, smooth the flow of demand and decrease the waiting time of patients.The radiology department is a key department within the hospital after interviewing the medical staff and administrator in S hospital. CT scan is a bottleneck for providing patients timely service. The backlog of patients and medical resources’ idle time frequently occurred due to the unreasonable capacity management policy. CT department is an appointment-based service system. There are two independent sources of patients: first-come-first-serve regular patient and non-preemptive priority emergency patient.This work focuses on the CT service system which has the above characteristics. The capacity management policies are improved by different methods based on the operation procedure and record data. One assumption that emergency patients have non-preemptive priorities is made throughout this work.Firstly, the direct waiting time of regular patient is considered from appointment rule design and queuing discipline design, respectively. In the appointment rule design, we consider the impact of two decision variables (the quantity of the free slots reserved for emergency patients and the position of these slots) on the expected direct waiting time of regular patients. The waiting time is calculated by mathematical model. Numerical comparisons show that allocating the free slots in the middle of the service session could dramatically decrease the direct waiting time of regular patients. In the queuing discipline design, we construct the M/Ek/1 queueing system with waiting and Geom/NB/1 mixed queueing system, respectively. The analytical results show that the waiting time of the same phase patient in these two queueing systems are the same. However, the waiting time of an arbitrary patient in these two queueing system are different. We also give the values of the patient flow and the upper limit for regular patient so as to let the limit value of loss probability of regular patients be zero in the mixed system.Secondly, the total cost of the service system is considered from appointment rule design and queuing discipline design, respectively. In the appointment rule design, placing the free slots in the end of the session performs best on idle time and overtime of medical resources. The total cost of the service system decreases firstly and then increases as the increases of the number of reserved slots. Allocating the free slots in the middle of the session could effectively reduce the expected total cost. In the queuing discipline design, we construct a nonlinear convex optimization problem which includes the penalty cost of unutilized time of the device and the waiting cost of the regular patients. The optimal arrival rate of regular patients is given by Kuhn-Tucker condition so as to minimize the total cost.Lastly, the regular patients are divided into several classes based on the summed up revenues. Our model describes the direct waiting time of regular patient under emergency random arrival as well as nonlinear relationship between the direct waiting time and the perception of the waiting time. The appointment problem is described as a Markov finite horizon dynamical programming with the goal of improving the total expected reward. Drawing upon the ideas from capacity control theory of revenue management, the booking limit numbers for each patient class are obtained by marginal analysis to ensure the incremental benefit of receiving an appointment is positive. If there is no free slot, some heuristic policies are obtained to improve the total expected reward of hospital. If there are free slots, the booking limit numbers are obtained by two steps marginal analysis. The numerical analysis under different scenarios shows that the total expected reward are improved. It shows that our capacity management policies could achieve trade-off between the summed up revenues for hospital, the direct waiting cost for regular patients, the penalty cost for delaying regular requests, overtime cost for medical resources and penalty cost for idling medical resources.Different appointment scheduling policies for different objective utility functions are given in this work. We expect that this study could apply to the capacity management of the similar medical resources.