A robust counterpart approach to the bi-objective emergency medical service design problem

The paper presents a bi-objective robust program to design a cost-responsiveness efficient emergency medical services (EMS) system under uncertainty. The proposed model simultaneously determines the location of EMS stations, the assignment of demand areas to EMS stations, and the number of EMS vehicles at each station to balance cost and responsiveness. We develop a robust counterpart approach to cope with the uncertain parameters in the EMS system. Extensive numerical studies are performed to demonstrate the benefits of our robust optimization approach.     

Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.     

A stochastic programming approach for multi-period portfolio optimization

This paper extends previous work on the use of stochastic linear programming to solve life-cycle investment problems. We combine the feature of asset return predictability with practically relevant constraints arising in a life-cycle investment context. The objective is to maximize the expected utility of consumption over the lifetime and of bequest at the time of death of the investor. Asset returns and state variables follow a first-order vector auto-regression and the associated uncertainty is described by discrete scenario trees. To deal with the long time intervals involved in life-cycle problems we consider a few short-term decisions (to exploit any short-term return predictability), and incorporate a closed-form solution for the long, subsequent steady-state period to account for end effects.     

Multi-criteria decision analysis for emergency medical service assessment

In emergency management, it is important to arrange the medical resources according to emergency needs. This paper proposes a multi-criteria decision analysis model that combines grey theory and multi-criteria decision making theory to assess the current medical resource situation, find satisfactory solutions, and help the emergency decision makers to take appropriate responses in a timely manner. In addition, the best alternative is identified by the global optimal solution which can provide a theoretical guidance for decision makers to optimize the allocation of medical resources. To validate the proposed model, this paper conducts a case study of medical service assessment in provinces of East China. The results demonstrate that the proposed model can provide objective and comprehensive assessment of medical resources.     

Alternate risk measures for emergency medical service system design

The stochastic nature of emergency service requests and the unavailability of emergency vehicles when requested to serve demands are critical issues in constructing valid models representing real life emergency medical service (EMS) systems. We consider an EMS system design problem with stochastic demand and locate the emergency response facilities and vehicles in order to ensure target levels of coverage, which are quantified using risk measures on random unmet demand. The target service levels for each demand site and also for the entire service area are specified. In order to increase the possibility of representing a wider range of risk preferences we develop two types of stochastic optimization models involving alternate risk measures. The first type of the model includes integrated chance constraints (ICCs ), whereas the second type incorporates ICCs  and a stochastic dominance constraint. We develop solution methods for the proposed single-stage stochastic optimization problems and present extensive numerical results demonstrating their computational effectiveness.     

Reducing disparities in large-scale emergency medical service systems

Emergency Medical Service (EMS) systems operate under the pressure of knowing that human lives might be directly at stake. In the public eye there is a natural expectation of efficient response. There is abundant literature on the topic of efficient planning of EMS systems (maximizing expected coverage or minimizing response time). Other objectives have been considered but the literature available is very sparse compared to efficiency-based works. Furthermore, while real size EMS systems have been studied, the use of exact models is usually hindered by the amount of computational time required to obtain solutions. We approach the planning of large-scale EMS systems including fairness considerations using a Tabu Search-based heuristic with an embedded approximation procedure for the queuing submodel. This allows for the analysis of large-scale real systems, extending the approach in which strategic decisions (location) and operative decisions (dispatching) are combined to balance efficiency and fairness.     

A heuristic approach to the multi-period multi-commodity transportation problem

This paper describes an approach to solving a real-world problem which involves the transportation of multiple types of commodities from a number of sources to a number of destinations in discrete time periods, using a capacitated heterogeneous fleet of vehicles. The preliminary objective is to minimize the total number of discrete periods needed to complete the entire operation. The problem is first formulated as a mixed integer programme and its tractability is then greatly improved by reformulating it through backward decomposition into two separate models and solved iteratively. A heuristic approach harnessing specific features of the second approach is developed for solving large size problems to obtain near-optimal solutions within reasonable time. The design of the heuristic also takes into consideration the secondary objectives of minimizing the total vehicle capacity used and minimizing the total capacity of sources needed to satisfy the demands at the destinations. Computational results are provided for a variety of randomly generated problems as well as problems from the literature. The approach described here may be applied to the multi-period transportation of personnel and goods from multiple starting points to multiple destinations in both military and civilian applications.     

A computational comparison of several formulations for the multi-period incremental service facility location problem

The Multi-period Incremental Service Facility Location Problem, which was recently introduced, is a strategic problem for timing the location of facilities and the assignment of customers to facilities in a multi-period environment. Aiming at finding the strongest formulation for this problem, in this work we study three alternative formulations based on the so-called impulse variables and step variables. To this end, an extensive computational comparison is performed. As a conclusion, the hybrid impulse–step formulation provides better computational results than any of the other two formulations.     

A taxonomy for emergency service station location problem

The emergency service station (ESS) location problem has been widely studied in the literature since 1970s. There has been a growing interest in the subject especially after 1990s. Various models with different objective functions and constraints have been proposed in the academic literature and efficient solution techniques have been developed to provide good solutions in reasonable times. However, there is not any study that systematically classifies different problem types and methodologies to address them. This paper presents a taxonomic framework for the ESS location problem using an operations research perspective. In this framework, we basically consider the type of the emergency, the objective function, constraints, model assumptions, modeling, and solution techniques. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions.     

Optimal hedging strategies for multi-period guarantees in the presence of transaction costs: A stochastic programming approach

Multi-period guarantees are often embedded in life insurance contracts. In this paper we consider the problem of hedging these multi-period guarantees in the presence of transaction costs. We derive the hedging strategies for the cheapest hedge portfolio for a multi-period guarantee that with certainty makes the insurance company able to meet the obligations from the insurance policies it has issued. We find that by imposing transaction costs, the insurance company reduces the rebalancing of the hedge portfolio. The cost of establishing the hedge portfolio also increases as the transaction cost increases. For the multi-period guarantee there is a rather large rebalancing of the hedge portfolio as we go from one period to the next. By introducing transaction costs we find the size of this rebalancing to be reduced. Transaction costs may therefore be one possible explanation for why we do not see the insurance companies performing a large rebalancing of their investment portfolio at the end of each year.     

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144 GB of) available memory in the largest instances.     

A heuristic approach for the double row layout problem

Annals of Operations Research - In the double row layout problem, we wish to position n machines on two parallel rows in order to minimize the cost of material flow among machines. The problem is...     

Analysing emergency medical service ambulance deployment on a Brazilian highway using the hypercube model

In this study we analyse the ambulance deployment of an emergency medical system on a Brazilian highway connecting the cities of São Paulo and Rio de Janeiro. Our focus is on the mean response time of the system to an emergency call, viewed as an important component of the user service. To evaluate the system performance we applied the hypercube model, a well-known tool for planning server-to-customer systems, which is based on spatially distributed queuing theory. The results showed that the model can be effective in supporting design and operational decisions, in particular to reduce the workload unbalancing among the ambulances.     

A unified solving approach for two and three dimensional coverage problems in sensor networks

The problem of designing a wired or a wireless sensor network to cover, monitor and/or control a region of interest has been widely treated in literature. This problem is referred to in literature as the sensor placement problem (SPP) and in the most general case it consists in determining the number and the location of one or more kind of sensors with the aim of covering all the region of interest or a significant part of it. In this paper we propose a unified and stepwise solving approach for two and three dimensional coverage problems to be used in omni-directional and directional sensor networks. The proposed approach is based on schematizing the region of interest and the sensor potential locations by a grid of points and representing the sensor coverage area by a circle or by a circular sector. On this basis, the SPP is reduced to an optimal coverage problem and can be formulated by integer linear programming (ILP) models. We will resume the main ILP models used in our approach, highlighting, for each of them, the specific target to be achieved and the design constraints taken into account. The paper concludes with an application of the proposed approach to a real test case and a discussion of the obtained results.     

A review on initiatives for the management of daily medical emergencies prior to the arrival of emergency medical services

Central European Journal of Operations Research - Emergency services worldwide face increasing cost pressure that potentially limits their existing resources. In many countries, emergency services...     

A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs

A common assumption in the literature on mixed-model assembly line balancing is that a task that is common to multiple models must be assigned to a single station. In this paper, we relax this restriction, and allow a common task to be assigned to different stations for different models. We seek to minimize the sum of costs of the stations and the task duplication. We develop an optimal solution procedure based on a backtracking branch-and-bound algorithm and evaluate its performance via a large set of experiments. A branch-and-bound based heuristic is then developed for solving large-scale problems. The heuristic solutions are compared with a lower bound and experiments show that the heuristic provides much better solutions than those obtained by traditional approaches.     

A nonsmooth version of the univariate optimization algorithm for locating the nearest extremum (locating extremum in nonsmooth univariate optimization)

An algorithm for univariate optimization using a linear lower bounding function is extended to a nonsmooth case by using the generalized gradient instead of the derivative. A convergence theorem is proved under the condition of semismoothness. This approach gives a globally superlinear convergence of algorithm, which is a generalized Newton-type method.