#### Date of Award

8-2013

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Legacy Department

Industrial Engineering

#### Advisor

Mayorga, Maria E

#### Committee Member

Taaffe , Kevin

#### Committee Member

Kurz , Mary E

#### Committee Member

Greenstein , Joel

#### Abstract

Emergency Medical Service (EMS) systems are a service that provides acute care and transportation to a place for definitive care, to people experiencing a medical emergency. The ultimate goal of EMS systems is to save lives. The ability of EMS systems to do this effectively is impacted by several resource allocation decisions including location of servers (ambulances), districting of demand zones and dispatching rules for the servers. The location decision is strategic while the dispatching decision is operational. Those two decisions are usually made separately although both affect typical EMS performance measures. The service from an ambulance is usually time sensitive (patients generally want the ambulances to be available as soon as possible), and the demand for service is stochastic. Regulators also impose availability constraints, the most generally accepted being that 90\% of high priority calls (such as those related to cardiac arrest events) should be attended to within 8 minutes and 59 seconds.

In the case of minimizing the mean response time as the only objective, previous works have shown that there are cases in which it might not be optimal to send the closest available server to achieve the minimum overall response time. Some researchers have proposed integrated models in which the two decisions are made sequentially. The main contribution of this work is precisely in developing the integration of location and dispatching decisions made simultaneously. Combining those decisions leads to complex optimization models in which even the formulation is not straightforward. In addition, given the stochastic nature of the EMS systems the models need to have a way to represent their probabilistic nature. Several researchers agree that the use of queuing theory elements in combination with location, districting and dispatching models is the best way to represent EMS systems. Often heuristic/approximate solution procedures have been proposed and used since the use of exact methods is only suitable for small instances.

Performance indicators other than Response Time can be affected negatively when the dispatching rule is sending the closest server. For instance, there are previous works claiming that when the workload of the servers is taken into account, the nearest dispatching policy can cause workload imbalances. Therefore, researchers mentioned as a potential research direction to develop solution approaches in which location, districting and dispatching could be handled in parallel, due to the effect that all those decisions have on key performance measures for an EMS system. In this work the aim is precisely the development of an optimization framework for the joint problem of location and dispatching in the context of EMS systems. The optimization framework is based on meta heuristics. Fairness performance indicators are also considered, taking into account different points of view about the system, in addition to the standard efficiency criteria.

Initially we cover general aspects related to EMS systems, including an overall description of main characteristics being modeled as well as an initial overview of related literature. We also include an overall description and literature review with focus on solution methodologies for real instances, of two related problems: the $p$-median problem and the maximal covering location problem (MCLP). Those two problems provide much of the basic structure upon which the main mathematical model integrating location and dispatching decisions is built later.

Next we introduce the mathematical model (mixed-integer non-linear problem) which has embedded a queuing component describing the service nature of the system. Given the nature of the resulting model it was necessary to develop a solution algorithm. It was done based on Genetic Algorithms. We have found no benefit on using the joint approach regarding mean Response Time minimization or Expected Coverage maximization. We concluded that minimizing Response Time is a better approach than maximizing Expected Coverage, in terms of the trade-off between those two criteria.

Once the optimization framework was developed we introduced fairness ideas to the location/allocation of servers for EMS systems. Unlike the case of Response Time, we found that the joint approach finds better solutions for the fairness criteria, both from the point of view of internal and external costumers. The importance of that result lies in the fact that people not only expect the service from ambulances to be quick, but also expect it to be fair, at least in the sense that any costumer in the system should have the same chances of receiving quick attention. From the point of view of service providers, balancing ambulance workloads is also desirable. Equity and efficiency criteria are often in conflict with each other, hence analyzing trade-offs is a first step to attempt balancing different points of view from different stakeholders.

The initial modeling and solution approach solve the problem by using a heuristic method for the overall location/allocation decisions and an exact solution to the embedded queuing model. The problem of such an approach is that the embedded queuing model increases its size exponentially with relation to the number of ambulances in the system. Thus the approach is not practical for large scale real systems, say having 10+ ambulances. Therefore we addressed the scalability problem by introducing approximation procedures to solve the embedded queuing model. The approximation procedures are faster than the exact solution method for the embedded sub-problem. Previous works mentioned that the approximated solutions are only marginally apart from the exact solution (1 to 2\%). The mathematical model also changed allowing for several ambulances to be assigned to a single station, which is a typical characteristic of real world large scale EMS systems. To be able to solve bigger instances we also changed the solution procedure, using a Tabu Search based algorithm, with random initialization and dynamic size of the tabu list. The conclusions in terms of benefits of the joint approach are true for bigger systems, i.e. the joint approach allows for finding the best solutions from the point of view of several fairness criteria.

#### Recommended Citation

Toro-diaz, Hector, "Joint Location and Dispatching Decisions for Emergency Medical Service Systems" (2013). *All Dissertations*. 1148.

https://tigerprints.clemson.edu/all_dissertations/1148