Fernando Y. Chiyoshi

Towards unified formulations and extensions of two classical probabilistic location models

We give a unified view of Daskins Maximum Expected Covering Location Problem (MEXCLP) and ReVelle and Hogans Maximum Availability Location Problem (MALP), identifying similarities and dissimilarities between these models and showing how they relate to each other. These models arise in the location of servers in congested emergency systems. An existing extension of MEXCLP is reviewed; we then develop an extension of MALP and give the corresponding mathematical formulation. These two extensions are obtained when the simplifying assumptions of the original models are dropped and Larsons hypercube model is embedded into local search methods. In this paper these methods are further enhanced by the use of simulated annealing. Computational results are given for problems available in the literature.

A statistical analysis of simulated annealing applied to the p-median problem

We present a statistical analysis of simulated annealing applied to the p-median problem. The algorithm we use combines elements of the vertex substitution method of Teitz and Bart with the general methodology of simulated annealing. The cooling schedule adopted incorporates the notion of temperature adjustments rather than just temperature reductions. Computational results are given for test problems ranging from 100 to 900 vertices, retrieved from Beasleys OR-Library for combinatorial problems. Each problem was run for a maximum of 100 different streams of random numbers. Optimal solutions were found for 26 of the 40 problems tested, although high optimum hitting rates were obtained for only 20 of them. The worst gap in relation to the optimal solution was 1.62%, after all runs for each of the test problems were computed.

A note on solutions to the maximal expected covering location problem

The maximal expected covering location problem (MEXCLP) and its adjusted counterpart (AMEXCLP) compute expected coverage arising only from unqueued calls, whereas the interactive use of the hypercube queueing model (HQM) considers both unqueued and queued calls in this computation. In this note we show that the three models are not strictly comparable because of the structural differences in their objective functions and that, when using HQM, it is important to state clearly the factor being used to express traveling time in terms of service time units.

O uso do modelo hipercubo na solução de problemas de localização probabilísticos

The hypercube model is revisited regarding its use in solution methods for probabilistic location problems. This use of the model is relevant in situations in which the randomness in the availability of servers is an important factor to be considered; in some circumstances this randomness can be represented by spatially distributed queues. The model is presented through an illustrative example, for which the equilibrium equations are derived; some measures of performance are also defined. This is followed by the description of an exact and an approximate method for the calculation of these measures. Several probabilistic location models are then studied, which is followed by the analysis of solution methods for these models, with special emphasis given to methods that embed the hypercube model. Although incipient at present, the use of the hypercube model in probabilistic location problems has good potential, for example if embedded into metaheuristics such as simulated annealing and tabu search.

Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil

Emergency medical services (EMS) assist different classes of patients according to their medical seriousness. In this study, we extended the well-known hypercube model, based on the theory of spatially distributed queues, to analyze systems with multiple priority classes and a queue for waiting customers. Then, we analyzed the computational results obtained when applying this approach to a case study from an urban EMS in the city of Ribeirao Preto, Brazil. We also investigated some scenarios for this system studying different periods of the day and the impact of increasing the demands of the patient classes. The results showed that relevant performance measures can be obtained to analyze such a system by using the analytical model extended to deal with queuing priority. In particular, it can accurately evaluate the average response time for each class of emergency calls individually, paying particular attention to high priority calls.

Solução do problema de localização de máxima disponibolidade utilizando o modelo hipercubo

The Maximum Availability Location Problem (MALP) seeks to locate m servers so that the maximum number of calls for an emergency service has a server available within a predefined critical distance S,with reliability a . In this paper MALP is extended for the case where the busy fractions are calculated individually, for each server. This is achieved through the use of the Hypercube Model, embedded into a single vertex substitution heuristic. Computational results are given for networks of up to 150 vertices available in the literature.

A tutorial on hypercube queueing models and some practical applications in Emergency Service Systems

This paper presents some extensions and applications of hypercube queueing models todescribe server-to-customer type Emergency Service Systems. The classical hypercube is a well-known spatially distributed queueing model effective in analyzing these systems, based on Markovian analysis approximations. Experience has shown that each real life Emergency Service System may have its own unique characteristics so that each system may require a particular hypercube queueing model incorporating those characteristics. Some of these distinctive characteristics are considered in the extensions presented in this tutorial such as dispatch policy based on random selection of the server to take an incoming call; partial cooperation among servers whereby depending on where the call is coming from, some servers cannot take the call; servers with additional workload coming from walk-in nonemergency customers such as in customer-to-server systems; existence of calls requiring the dispatch of more than one server; existence of more than one type of servers in the system, for instance paramedical and medical units in emergency medical systems. In this study, we present a set of these models based on the smallest non-trivial service systems. For each model, the construction of the system of equations for equilibrium hypercube state probabilities and the evaluation of particular operational characteristics are described.

MODELO HIPERCUBO: ANÁLISE E RESULTADOS PARA O CASO DE SERVIDORES NÃO-HOMOGÊNEOS

The objective of the present paper is to analyze the use and solution of the hypercube model for the case of non-homogeneous servers (servers with different mean service times). Systems with nonhomogeneous servers can be found in several real world applications, such as for example in the provision of Emergency Medical Services (EMS) in some Brazilian cities. The importance of explicitly considering non-homogeneous servers in the hypercube model is initially demonstrated through an illustrative example. It is then shown that the solution for the non-homogeneous case can be advantageously obtained by the method of Gauss-Siedel. This method was tested for a network of 55 nodes, in models with between 10 and 17 servers, with the total system workload varying between 0.1 and 0.9. Finally, a regression model is proposed to estimate the computing time required to solve a specific problem.

Towards hypercube queuing models for dispatch policies with priority in queue and partial backup

This work extends the hypercube queuing model to address users in-queue priorities.The extended model also considers the partial backup of servers.It is motivated by an emergency maintenance service of an agro-industry in Brazil.To reduce the computational burden an approximate method is also developed.The findings suggest promising perspectives for real-life applications. This work extends the hypercube queuing model to explicitly address users in-queue priorities, as well as the partial backup of servers. To reduce the computational burden an approximate method is also developed. The study is motivated by an emergency maintenance service system found within the agricultural stage of the sugarcane agro-industry in Brazil. An example is used to illustrate the issues of priority in queue and partial backup. In order to show the importance and effectiveness of our proposed models we conducted additional experiments by varying the user arrival rates as well as eliminating the in-queue priorities. The study shows that selected adaptations and extensions of both the hypercube model and the approximate method are capable of representing similar emergency systems. The findings from the illustrative examples suggest promising perspectives for real-life applications in sugar and ethanol plants, and other agro-industries.

Extensão do modelo hipercubo para análise de sistemas de atendimento médico emergencial com prioridade na fila

Em alguns sistemas de atendimento medico emergencial, a demanda pelo servico pode ser alta devido ao atendimento a pacientes em diferentes estados, desde mais graves ate mais leves. Nesses sistemas, pode haver formacao de filas de usuarios aguardando atendimento, e a necessidade de se considerar explicitamente politicas de prioridade nesse atendimento torna-se importante. Neste trabalho propoe-se uma extensao do classico modelo hipercubo de filas espacialmente distribuidas para considerar fila com prioridade. Para verificar a viabilidade e a aplicabilidade dessa abordagem, utilizam-se dados de um estudo de caso realizado no SAMU de Ribeirao Preto-SP. Foram analisados dois cenarios que consideram dois aspectos relevantes: o impacto dos atendimentos de remocao de pacientes e o aumento da demanda nas diversas classes de chamados dos usuarios do sistema. O foco e no tempo medio de resposta aos chamados dos usuarios, considerado como uma medida de desempenho importante do sistema, principalmente aos chamados de classes com alta prioridade. Os resultados mostram que a abordagem pode ser utilizada para analisar satisfatoriamente sistemas com prioridade de fila.