A Markov Chain Model for an EMS System with Repositioning

We propose and analyze a two‐dimensional Markov chain model of an Emergency Medical Services system that repositions ambulances using a compliance table policy, which is commonly used in practice. The model is solved via a fixed‐point iteration. We validate the model against a detailed simulation model for several scenarios. We demonstrate that the model provides accurate approximations to various system performance measures, such as the response time distribution and the distribution of the number of busy ambulances, and that it can be used to identify near‐optimal compliance tables. Our numerical results show that performance depends strongly on the compliance table that is used, indicating the importance of choosing a well‐designed compliance table.     

Social Optimal Location of Facilities with Fixed Servers,Stochastic Demand,and Congestion

We consider two capacity choice scenarios for the optimal location of facilities with fixed servers, stochastic demand, and congestion. Motivating applications include virtual call centers, consisting of geographically dispersed centers, walk‐in health clinics, motor vehicle inspection stations, automobile emissions testing stations, and internal service systems. The choice of locations for such facilities influences both the travel cost and waiting times of users. In contrast to most previous research, we explicitly embed both customer travel/connection and delay costs in the objective function and solve the location–allocation problem and choose facility capacities simultaneously. The choice of capacity for a facility that is viewed as a queueing system with Poisson arrivals and exponential service times could mean choosing a service rate for the servers (Scenario 1) or choosing the number of servers (Scenario 2). We express the optimal service rate in closed form in Scenario 1 and the (asymptotically) optimal number of servers in closed form in Scenario 2. This allows us to eliminate both the number of servers and the service rates from the optimization problems, leading to tractable mixed‐integer nonlinear programs. Our computational results show that both problems can be solved efficiently using a Lagrangian relaxation optimization procedure.