Maria E. Mayorga

Joint location and dispatching decisions for Emergency Medical Services

The main purpose of Emergency Medical Service systems is to save lives by providing quick response to emergencies. The performance of these systems is affected by the location of the ambulances and their allocation to the customers. Previous literature has suggested that simultaneously making location and dispatching decisions could potentially improve some performance measures, such as response times. We developed a mathematical formulation that combines an integer programming model representing location and dispatching decisions, with a hypercube model representing the queuing elements and congestion phenomena. Dispatching decisions are modeled as a fixed priority list for each customer. Due to the models complexity, we developed an optimization framework based on Genetic Algorithms. Our results show that minimization of response time and maximization of coverage can be achieved by the commonly used closest dispatching rule. In addition, solutions with minimum response time also yield good values of expected coverage. The optimization framework was able to consistently obtain the best solutions (compared to enumeration procedures), making it suitable to attempt the optimization of alternative optimization criteria. We illustrate the potential benefit of the joint approach by using a fairness performance indicator. We conclude that the joint approach can give insights of the implicit trade-offs between several conflicting optimization criteria.

Improving emergency service in rural areas: a bi-objective covering location model for EMS systems

Emergency medical service (EMS) systems are public services that often provide the first line of response to urgent health care needs within a community. Unfortunately, it has been widely documented that large disparities in access to care exist between rural and urban communities. While rural EMS is provided through a variety of resources (e.g. air ambulances, volunteer corps, etc.), in this paper we focus on ground ambulatory care. In particular our goal is to balance the level of first-response ambulatory service provided to patients in urban and rural areas by locating ambulances at appropriate stations. In traditional covering location models the objective is to maximize demand that can be covered; consequently, these models favor locating ambulances in more densely populated areas, resulting in longer response times for patients in more rural areas. To address the issue of fairness in semi-rural/semi-urban communities, we propose three bi-objective covering location models that directly consider fairness via a secondary objective. Results are discussed and compared which provide a menu of alternatives to policy makers.

Declining liver graft quality threatens the future of liver transplantation in the United States

National liver transplantation (LT) volume has declined since 2006, in part because of worsening donor organ quality. Trends that degrade organ quality are expected to continue over the next 2 decades. We used the United Network for Organ Sharing (UNOS) database to inform a 20‐year discrete event simulation estimating LT volume from 2010 to 2030. Data to inform the model were obtained from deceased organ donors between 2000 and 2009. If donor liver utilization practices remain constant, utilization will fall from 78% to 44% by 2030, resulting in 2230 fewer LTs. If transplant centers increase their risk tolerance for marginal grafts, utilization would decrease to 48%. The institution of “opt‐out” organ donation policies to increase the donor pool would still result in 1380 to 1866 fewer transplants. Ex vivo perfusion techniques that increase the use of marginal donor livers may stabilize LT volume. Otherwise, the number of LTs in the United States will decrease substantially over the next 15 years. In conclusion, the transplant community will need to accept inferior grafts and potentially worse posttransplant outcomes and/or develop new strategies for increasing organ donation and utilization in order to maintain the number of LTs at the current level. Liver Transpl 21:1040‐1050, 2015.

A model for optimally dispatching ambulances to emergency calls with classification errors in patient priorities

The decision of which servers to dispatch to which customers is an important aspect of service systems. Such decisions are complicated when servers have different operating characteristics, customers are prioritized, and there are errors in assessing customer priorities. This article formulates a model for determining how to optimally dispatch servers to prioritized customers given that dispatchers make classification errors in assessing the true customer priorities. These issues are examined through the lens of Emergency Medical Service (EMS) dispatch, for which a Markov Decision Process (MDP) model is developed that captures how to optimally dispatch ambulances (servers) to prioritized patients (customers). It is assumed that patients arrive sequentially, with the location and perceived priority of each patient becoming known upon arrival. The proposed model determines how to optimally dispatch ambulances to patients to maximize the long-run average utility of the system, defined as the expected coverage of true high-risk patients. The utilities and transition probabilities are location dependent, with respect to both the ambulance and patient locations. The analysis considers two cases for approaching the classification errors that correspond to over- and under-responding to perceived patient risk. A computational example is applied to an EMS system. The optimal policies under different classification strategies are compared to a myopic policy and the effect that classification errors have on the performance of these policies is examined. Simulations suggest that the policies remain effective when they are applied to more realistic situations.

A Dispatching Model for Server-to-Customer Systems That Balances Efficiency and Equity

The decision about which servers to dispatch to which customers is an important aspect of service systems. This decision is complicated when servers must be equitably---as well as efficiently---dispatched to customers. In this paper, we formulate a model for determining how to optimally dispatch distinguishable servers to prioritized customers given a set of equity constraints. These issues are examined through the lens of emergency medical service EMS dispatch, for which a Markov decision process model is developed that captures how to dispatch ambulances servers to prioritized patients customers. It is assumed that customers arrive sequentially, with the priority and location of each customer becoming known upon arrival. Four types of equity constraints are considered---two of which reflect customer equity and two of which reflect server equity---all of which draw upon the decision analytic and social science literature to compare the effects of different notions of equity on the resulting dispatching policies. The Markov decision processes are formulated as equity-constrained linear programming models. A computational example is applied to an EMS system to compare the different equity models.

Modeling Equity for Allocating Public Resources

Equity and fairness constitute central concerns in many disciplines, and their relevance to the allocation of public resources is undeniable. However, measures of equity used in the studies of public resource allocation are frequently ad hoc, and no standard measure of equity or process for selecting a measure of equity has emerged. Nevertheless, a burgeoning literature exists that systematically considers how best to model equity with perspectives from many disciplines. The goal of this chapter is to review, synthesize, and critically evaluate key contributions to modeling equity for allocating resources in public service systems. This chapter provides a useful guide to the central issues in the modeling of equity and fairness for operations researchers that reflects a broad, multidisciplinary perspective. Throughout the discussion, the planning and provision of Emergency Medical Services (EMS) resources are used as a microcosm of public services allocation problems, and equity modeling issues are illustrated through problems arising in EMS.

Priority dispatching strategies for EMS systems

Emergency medical service (EMS) systems provide urgent medical care and transport. In this study we implement dispatching policies for EMS systems that incorporate the severity of the call in order to increase the survival probability of patients. A simulation model is developed to evaluate the performance of EMS systems. Performance is measured in terms of patients’ survival probability, since survival probability more directly mirrors patient outcomes. Different response strategies are evaluated utilizing several examples to study the nature of the optimal dispatching policy. The results show that dispatching the closest vehicle is not always optimal and dispatching vehicles considering priority of the call leads to an increase in the average survival probability of patients. A heuristic algorithm, that is easy to implement, is developed to dispatch ambulances for large-scale EMS systems. Computational examples show that the dispatching algorithm is valuable in increasing the patients’ survival probability.

The minimum p-envy location problem: a new model for equitable distribution of emergency resources

Equity is an important consideration in public services such as Emergency Medical Service (EMS) systems. In such systems not only equitability but also performance depends on the spatial distribution of facilities and resources. This paper proposes the minimum p-envy facility location model which aims to find optimal locations for facilities in order to balance customers’ perceptions of equity in receiving service. The model is developed and evaluated through the lens of EMS systems, where ambulances are located at facilities (stations) with the objective of minimizing the sum of “envy” among all demand zones (customer points) with respect to an ordered set of p operating stations weighted by the proportion of demand in each zone. The problem is formulated as an integer program, with priority weights assigned according the probability that an ambulance is available, which is estimated using the hypercube model. Because of the computational effort required to obtain solutions using commercially available software, a tabu search is developed to solve the problem. A case study using real-world data is presented. The performance of the proposed model is tested and compared to other location models such as the p-center and maximal-covering-location problems (MCLP).

Districting and dispatching policies for emergency medical service systems to improve patient survival

The major focus of Emergency Medical Service (EMS) system is to save lives and to minimize the effects of emergency health incidents. Districting, or designing pre-determined response areas, allows an EMS system to reduce the response time of paramedic support to the incident. Furthermore, dispatching policies affect system performance. Thus, in this study we propose integrated dispatching and districting policies to improve the performance of EMS systems. We measure performance in terms of patient survival probability. We propose several policies for districting/dispatching, these are provided as inputs to a simulation model that compares the performance of different policies. Our response areas, or districts, are designed using a constructive heuristic which considers adjusted expected coverage. Intra-district and inter-district dispatching policies are developed considering the degree of the urgency of the call. Computational results show that integrated districting and dispatching policies are vital in increasing patient survivability.

Inventory based allocation policies for flexible servers in serial systems

Motivated by an industry example, we study a two-station serial system in which we allocate flexible servers in order to maximize throughput. We investigate two cases which are different in the way that servers work together when at the same station; namely collaboratively or non-collaboratively. For the collaborative case we prove the optimal policy to be such that the servers work together at a single station at any point in time. In addition to the policy being state-dependent, it also follows a switching-curve structure. In the non-collaborative case, on the other hand, it may be optimal to allocate servers to different stations. Some numerical examples and results regarding policy assignments, switching curves, and system throughput are presented.