A Chance Constrained Programming Model for Reliable Emergency Vehicles Relocation Problem

AbstractEmergency vehicles relocation is one mechanism of increasing preparedness for potential emergencies. This paper addresses the problem of designing reliable emergency vehicles relocation system. Under this respect, we extend the DYNACO model with chance-constrained programming framework for the optimal redeployment of emergency vehicles. The model deals with the availability of emergency vehicles by approximate hypercube. In addition, other random elements including travel time and emergency demand are taken into account in the model. Solution procedure based on genetic algorithm and Monte-Carlo simulation is developed to solve the stochastic model. Computational experiences are reported to illustrate the performance and the effectiveness of the proposed solution

Optimization and Spatial Queueing Models to Support Multi-Server Dispatching Policies with Multiple Servers per Station

In this thesis, we propose novel optimization and spatial queueing models that expand the currently existing methods by allowing multiple servers to be located at the same station and multiple servers to be dispatched to a single call. In particular, a mixed integer linear programming (MILP) model is introduced that determines how to locate and dispatch ambulances such that the coverage level is maximized. The model allows multiple servers to be located at the same station and balances the workload among them while maintaining contiguous first priority response districts. We also propose an extension to the approximate Hypercube queueing model by allowing multi-server dispatches. Computational results suggest that both models are effective in optimizing and analyzing the emergency systems. We also introduce the M[G]/M/s/s queueing model as an extension to the M/M/s/s model which allows for multiple servers to be assigned to a single customer

DISTRICTING AND DISPATCHING POLICIES TO IMPROVE THE EFFICIENCY OF EMERGENCY MEDICAL SERVICE (EMS) SYSTEMS

The major focus of Emergency Medical Service (EMS) systems is to save lives and to minimize the effects of emergency health incidents. The efficiency of the EMS systems is a major public concern. Thus, over the past three decades a significant amount of research studies have been conducted to improve the performance of EMS systems. The purpose of this study is also to improve the performance of EMS system. The contribution of this research towards improving the performance of EMS systems is twofold. One area is to implement optimal or near optimal dispatching strategies for EMS systems and the other is to determine the response boundaries for EMS vehicles. Proposed dispatching strategies are implemented incorporating the degree of the urgency of the call. A Markov decision process (MDP) model is developed to obtain optimal dispatching strategies in less complex models. A heuristic algorithm is proposed to dispatch ambulances for more complex models. In this study, an integer programming formulation and a constructive heuristic are proposed to determine response areas or districts for each ambulance. Additionally, dispatching rules to dispatch paramedic units within districts and out of districts are examined. Simulation is used to evaluate the performance of the EMS system after introducing proposed dispatching policies. Performance is measured in terms of patients\u27 survival probability rather than measuring the response time thresholds, since survival probability reflects the patients\u27 outcome directly. Results are illustrated using real-data collected from Hanover county Virginia. Results show that proposed dispatching rules are valuable in increasing patients\u27 survivabilit

Using Markov Decision Processes with Heterogeneous Queueing Systems to Examine Military MEDEVAC Dispatching Policies

major focus of the Military Health System is to provide efficient and timely medical evacuation (MEDEVAC) to battlefield casualties. Medical planners are responsible for developing dispatching policies that dictate how aerial military MEDEVAC units are utilized during major combat operations. The objective of this research is to determine how to optimally dispatch MEDEVAC units in response to 9-line MEDEVAC requests to maximize MEDEVAC system performance. A discounted, infinite horizon Markov decision process (MDP) model is developed to examine the MEDEVAC dispatching problem. The MDP model allows the dispatching authority to accept, reject, or queue incoming requests based on the request\u27s classification (i.e., zone and precedence level) and the state of the MEDEVAC system. Rejected requests are rerouted to be serviced by other, non-medical military organizations in theater. Performance is measured in terms of casualty survivability rather than a response time threshold since survival probability more accurately represents casualty outcomes. A representative planning scenario based on contingency operations in southern Afghanistan is utilized to investigate the differences between the optimal dispatching policy and three practitioner-friendly myopic baseline policies. Two computational experiments, a two-level, five-factor screening design and a subsequent three-level, three-factor full factorial design, are conducted to examine the impact of selected MEDEVAC problem features on the optimal policy and the system level performance measure. Results indicate that dispatching the closest available MEDEVAC unit is not always optimal and that dispatching MEDEVAC units considering the precedence level of requests and the locations of busy MEDEVAC units increases the performance of the MEDEVAC system. These results inform the development and implementation of MEDEVAC tactics, techniques, and procedures by military medical planners. Moreover, an open question exists concerning the best exact solution approach for solving Markov decision problems due to recent advances in performance by commercial linear programming (LP) solvers. An analysis of solution approaches for the MEDEVAC dispatching problem reveals that the policy iteration algorithm substantially outperforms the LP algorithms executed by CPLEX 12.6 in regards to computational effort. This result supports the claim that policy iteration remains the superlative solution algorithm for exactly solving computationally tractable Markov decision problems

Studies on Management of Emergency Service Systems

RÉSUMÉ: Forts des outils de la théorie des files d’attente, de la géométrie stochastique et des extensions développées en cours de route, nous présentons des modèles descriptifs de systèmes de services d’urgence organisés en fonction du potentiel de limitation explicite des distances de dispatching avec une fidélité accrue du modèle et une stratégie de dispatching pour atteindre des performances maximales avec des ressources limitées. En utilisant le terme «sauvegardes partielles» pour faire référence à des règles d’expédition avec des limites explicites sur les distances d’expédition, nous étendons d’abord le modèle classique de mise en file d’attente hypercube pour inclure des sauvegardes partielles avec des priorités. La procédure étendue pourra représenter les systèmes de services d’urgence dans lesquels le sous-ensemble de serveurs pouvant être envoyés à une demande d’intervention d’urgence dépend de l’origine et du niveau de service demandé. Cela permet de développer des modèles d’optimisation dans lesquels le concepteur du système laisse le choix des unités de réponse pouvant être envoyées dans chaque zone de demande et peut être intégré à l’espace de la solution avec d’autres variables de décision d’emplacement ou d’allocation. La nouvelle méthode descriptive et les modèles d’optimisation sur lesquels reposent les plans de répartition et de répartition optimaux correspondants devraient indiscutablement améliorer les performances et mieux refléter le comportement réel des répartiteurs lorsque la configuration instantanée du système constitue un facteur majeur dans la prise de décision. Par la suite, nous étendons notre analyse. des déploiements statiques couverts par le premier modèle vers des systèmes à relocalisation dynamique. En faisant des hypothèses d’uniformité sur les origines des demandes de service et les emplacements des unités d’intervention, nous développons un cadre théorique pour une évaluation rapide et aléatoire de la performance du système avec une politique de sauvegarde partielle donnée et des résultats donnés spécifiés en fonction du temps de réponse. Le modèle général permet de révéler tout potentiel théorique d’amélioration des performances du système en utilisant des stratégies de dispatching de secours partielles aux stratégies tactiques ou opérationnelles, sans connaître les détails de la méthode de relocalisation dynamique utilisée ni même de la distribution de la demande au-delà du taux total d’arrivée et de la densité. Nous présentons des résultats auxiliaires et des outils à l’appui de notre traitement des systèmes de service d’urgence avec sauvegardes partielles, notamment des notes sur les distributions de distance avec des effets liés et quelques lois de conservation du débit liées aux situations de file d’attente rencontrées dans le cadre de ce travail.----------ABSTRACT: Armed with tools in queuing theory, stochastic geometry, and extensions developed along the way, we present descriptive models of emergency service systems organized around and emphasizing the potential of explicitly limiting dispatch distances in increasing model fidelity and as a dispatching strategy to achieve maximal performance with limited resources. Borrowing the term ”partial backups” to refer to dispatch policies with explicit limits on the dispatch distances, we first extend the classic hypercube queuing model to incorporate partial backups with priorities. The extended procedure will be able to represent emergency service systems where the subset of servers that can be dispatched to a request for emergency intervention depend on the origin and level of service requested. This allows for development of optimization models where the choice of response units eligible for dispatch to each demand zone is left to the system designer and can be integrated into the solution space along with other location or allocation decision variables. The new descriptive method and thus the optimization models built upon and the corresponding optimal location and dispatch plans, should arguably lead to better performance and better reflect the actual dispatchers’ behavior where the instantaneous system configuration constitutes a major factor in making assignment decisions. We next extend our analysis of static deployments covered by the first model to systems with dynamic relocation. Making uniformity assumptions on the origins of service requests and locations of the response units, we develop a theoretical framework for quick and dirty evaluation of the system performance with a given partial backup policy and a given outcome specified as a function of response time. The general model, makes it possible to reveal any theoretical potential to improve system performance by employing partial backup dispatching strategies at tactical or operational, without knowing the details of the dynamic relocation method used or even the demand distribution beyond the total arrival rate and the density per area. Finally, auxiliary results and tools supporting our treatment of emergency service systems with partial backups are presented, which include notes on distance distributions with boundary effects and a few rate conservation laws related to the queuing situations we encountered in this work

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models