Location of single-server immobile facilities subject to a loss constraint

• Published in: The Journal of the Operational Research Society Vol. 61; no. 6; pp. 987 - 999
• Main Authors: Boffey, B, Galvão, R D, Marianov, V
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.06.2010; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Applied sciences; Average travel speed; Biological and medical sciences; Business and Management; Case-Oriented Paper; Case-oriented Papers; Clinics; Coefficients; Datasets; Density distributions; Erlang distribution; Exact sciences and technology; General aspects; Health services; Integers; Linearization; location; Location analysis; Logistics; loss; Management; Mathematical programming; Medical sciences; Network servers; Operational research and scientific management; Operational research. Management science; Operations research; Operations Research/Decision Theory; Planification. Prevention (methods). Intervention. Evaluation; Public health. Hygiene; Public health. Hygiene-occupational medicine; queues; Queuing theory; Queuing theory. Traffic theory; Random variables; Studies; Travel time; Uniqueness; Brazil; loss; location; queues; Erlang distribution; Neonatal; Mergers and Acquisitions; Exponential distribution; Transit time; Time allowed; Queueing network; Single server queue; Modeling; Location problem; Variance; Facility location; Emergency department; Model matching; Hospital; Deterministic approach; Queue; Linearization; Human; Travel time; Linear programming; Mean value; Integer programming; Time distribution; Service time; Newborn; Queueing system; Time average; Service quality
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2009.12

Waiting may be unacceptable, even a short time, at a facility providing a service involving medical or other emergencies. Hence, it is appropriate to locate such facilities so that the rate at which users are lost is limited. Each facility will here be modelled as an M/E r /m/N queueing system subject to a loss restriction constraint and the single-server case (m=1) will be treated in detail. Introduction of the Erlang distribution for service times allows a better fit of the model to actual values of both mean and variance than do currently available models that use an exponential distribution. Location of facilities will be such that the average travel time to a facility is minimized. It is shown how a deterministic constraint, equivalent to the loss constraint, can be generated resulting in an integer linear program, and values of a parameter ρ c which facilitates this linearization are tabulated for various values of r, N and service level demanded. Numerical experiments are performed including an application loosely related to the location of neonatal clinics in the Municipality of Rio de Janeiro. Finally, there is a discussion of how further improved modelling of the service time distribution might be effected.