Using simulation and optimisation to characterise durations of emergency department service times with incomplete data

Simulation models of emergency departments (EDs) are often built based on incomplete data, for example, missing arrival times or service-time durations. The difficulty in collecting reliable and complete data can subsequently lead to invalid simulation results. To tackle this problem, we propose a simulation and optimisation method to characterise the unavailable durations of service times. Since many services in an ED are sequential and dependent on each other, this paper considers these multiple process steps cooperatively. We first use lognormal distributions to characterise the key service durations. Then we propose a new meta-heuristic approach, which combines an Improved Adaptive Genetic Algorithm (AGA) and Simulated Annealing (SA), IAGASA, to search for the optimal set of service-time distribution parameters. To address the difficulties of applying IAGASA when noise is involved in the performance measures and improve the simulation efficiency, we jointly apply IAGASA and Optimal Computing Budget Allocation (OCBA) technology. OCBA minimises the total simulation cost for achieving a desired level of probability of correctly selecting the best set of distribution parameters, which improves the search efficiency significantly. The experimental results indicate that our proposed method can find accurate estimates of service-time distribution parameters within a relatively short time.