Integer linear programming models that incorporate probabilistic and stochastic components represent one approach for capturing the stochastic nature of emergency medical service ambulance systems. This includes modeling non-deterministic call arrival and servicing rates and congestion in the ambulance network (i.e., ambulance unavailability). These models focus on maximizing the total population that can find an available ambulance within a set service time standard (s) with a probability of at least α%. In MALP the concept of local vehicle busyness estimates is introduced to estimate the availability of service in a neighborhood given the neighborhood’s level of demand and the number of ambulance vehicles located in the neighborhood. QMALP is an extension of MALP where queue-theory derived parameters are implemented in the MALP model framework in order to relax the assumption that the probability of different ambulances being busy are independent. Despite this considerable development, several concerns remained about MALP and QMALP, namely the districting assumption where its assumed that a neighborhood’s calls for service are served only by an ambulance in the area, that ambulances in a neighborhood only serve calls for service originating within the neighborhood, or that at least the flow of ambulance service to and from external neighborhoods was roughly equal. Questions have been raised about the validity of MALP and QMALP’s reliability estimates, that is, whether a neighborhood actually received α-reliable service.

To address these issues, we developed the Resource-Constrained Queue-based Maximum Availability Location Problem (RC-QMALP). This model is based on a location-allocation framework that (1) assigns workload from neighborhoods to ambulances located within s and ambulance idle capacity to neighborhoods and (2) includes additional constraints designed to help ensure the validity of the original MALP and QMALP constraints used to establish whether a neighborhood can find an available ambulance with α-reliability. We also implemented a secondary minsum objective that minimizes the average travel distance between ambulances and the neighborhoods they service while maintaining the priority of the MALP and QMALP coverage objective.

In this thesis, we validated RC-QMALP by comparing the reliable coverage levels predicted by the RC-QMALP to the ambulance system simulations that used the locational configurations suggested by the RC-QMALP. We found that MALP 2 and QMALP provided higher levels of reliable coverage and that RC-QMALP’s secondary objective has a negligible impact on system performance. However, RC-QMALP-based models provide more accurate estimates of reliable coverage and location solutions whose simulated reliable coverage performance was always within 5% of the optimal solution with the same system parameters (we tested 1,080 different model configurations). Our work suggests that (1) simulation models must be developed to handle the modeling assumptions that underlie location optimization models and that (2) service reliability location models should consider additional factors such as ambulance workloads (and their distribution).