An Integrated Approach of Discrete Event Simulation and a Non-Radial Super Efficiency Data Envelopment Analysis for Performance Evaluation of an Emergency Department

An emergency department (ED) has been considered as one of the most congested department in a hospital. The congestion is typically contributed by long waiting time to get medical service, primarily caused by insufficient resource allocation or improper resource configurations. However, how various resource allocation configurations affect ED performance and how their efficiency can correctly be evaluated, using an integrated approach is rarely discussed. This paper thus integrates discrete event simulation (DES) and data envelopment analysis (DEA) to measure ED performance and evaluate the efficiency of potential resource allocation configurations for future performance improvement. For this, a DES model for an ED is first designed and developed. Its performance improvement is then tested using 35 potential resource allocation configurations, and their impacts on the performance are measured. To evaluate their efficiency and identify the optimal configuration, a mixed integer super efficiency of slacks-based measure data envelopment analysis (SE-SBM-DEA) approach dealing with undesirable outputs is proposed. The model utilizes resource allocation as inputs and simulation performance measures as outputs. All inputs were considered as integer, while the outputs were classified into desirable and undesirable in mixed integer-valued data. The desirable real outputs are the utilization of receptionists, nurses and doctors. The undesirable real outputs are the average of patient cycle time and time spent in queues, while the undesirable integer output is average number of patients in queues. The desirable integer output is average number of patients received treatment. The results obtained from the DEA approach show that 21 efficient resource configurations have the capability to increase their inputs, undesirable outputs and/or decrease desirable outputs simultaneously without affecting their efficiency status. The integrated approach helps decision makers manage their healthcare facilities by identifying the sources of inefficiency and (the maximum levels of inputs-undesirable outputs and minimum levels of desirable outputs) to improve and (retain) efficienc

Optimization of Healthcare Delivery System under Uncertainty: Schedule Elective Surgery in an Ambulatory Surgical Center and Schedule Appointment in an Outpatient Clinic

This work investigates two types of scheduling problems in the healthcare industry. One is the elective surgery scheduling problem in an ambulatory center, and the other is the appointment scheduling problem in an outpatient clinic. The ambulatory surgical center is usually equipped with an intake area, several operating rooms (ORs), and a recovery area. The set of surgeries to be scheduled are known in advance. Besides the surgery itself, the sequence-dependent setup time and the surgery recovery are also considered when making the scheduling decision. The scheduling decisions depend on the availability of the ORs, surgeons, and the recovery beds. The objective is to minimize the total cost by making decision in three aspects, number of ORs to open, surgery assignment to ORs, and surgery sequence in each OR. The problem is solved in two steps. In the first step, we propose a constraint programming model and a mixed integer programming model to solve a deterministic version of the problem. In the second step, we consider the variability of the surgery and recovery durations when making scheduling decisions and build a two stage stochastic programming model and solve it by an L-shaped algorithm. The stochastic nature of the outpatient clinic appointment scheduling system, caused by demands, patient arrivals, and service duration, makes it difficult to develop an optimal schedule policy. Once an appointment request is received, decision makers determine whether to accept the appointment and put it into a slot or reject it. Patients may cancel their scheduled appointment or simply not show up. The no-show and cancellation probability of the patients are modeled as the functions of the indirect waiting time of the patients. The performance measure is to maximize the expected net rewards, i.e., the revenue of seeing patients minus the cost of patients\u27 indirect and direct waiting as well as the physician\u27s overtime. We build a Markov Decision Process model and proposed a backward induction algorithm to obtain the optimal policy. The optimal policy is tested on random instances and compared with other heuristic policies. The backward induction algorithm and the heuristic methods are programmed in Matlab