Development and comparison of two new multi-period queueing reliability models using discrete-event simulation and a simulation–optimization approach

Abstract

This paper aims to develop a new mathematical model for optimizing ambulance deployment and redeployment. For this purpose, two mathematical models have been proposed and compared. The first model is Q-MALP-M1, an extension of the classical model Q-MALP, which is improved by integrating the multi-period redeployment of several types of ambulances. The second model is Q-MALP-M2, a modified version of Q-MALP. In addition to the improvements introduced by the first model, the Q-MALP-M2 overcomes the main Q-MALP model limitation, which is the α-reliability coverage. The Q-MALP-M2 changes the way coverage reliability is considered; instead of maximizing coverage with a fixed reliability level, it maximizes coverage with incremental levels of reliability depending on the number of available ambulances. Also, a discrete-event simulation model was constructed to compare the two mathematical models. A case study was conducted on the Civil Protection services of the Fez-Meknes region, Morocco. A series of scenarios combining various numbers of potential sites and ambulances were solved and simulated. Simulation results proved that the Q-MALP-M2 model, compared to the Q-MALP-M1 model, performs better in terms of coverage and average waiting time. It distributes the ambulances to achieve maximum coverage without necessarily being with the desired level of reliability. Finally, the Q-MALP-M2 model was compared to the simulation–optimization using OptQuest. In terms of coverage, the best-performing solution was sometimes generated by Q-MALP-M2 and other times by OptQuest. However, the Q-MALP-M2 model, in all cases, gives significantly improved results, and its execution time is much shorter than OptQuest. In terms of average waiting time, the results are not conclusive. The best-performing solutions were the results of Q-MALP-M2 in some scenarios and OptQuest in other scenarios. The discrepancies between the generated average waiting times were substantial on both sides.