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Allocating servers to facilities, when demand is elastic to travel and waiting times

Published online by Cambridge University Press:  25 January 2006

Vladimir Marianov ,
Miguel Rios  and
Francisco Javier Barros
Vladimir Marianov
Affiliation:
Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Vicuna Mackenna 4860, Santiago, Chile; marianov@ing.puc.cl; mrios@ing.puc.cl
Miguel Rios
Affiliation:
Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Vicuna Mackenna 4860, Santiago, Chile; marianov@ing.puc.cl; mrios@ing.puc.cl
Francisco Javier Barros
Affiliation:
Graduate Program, Department of Systems Engineering, Pontificia Universidad Catolica de Chile, Vicuna Mackenna 4860, Santiago, Chile; FBarros@sqm.cl
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Abstract

Public inoculation centers are examples of facilities providing service to customers whose demand is elastic to travel and waiting time. That is, people will not travel too far, or stay in line for too long to obtain the service. The goal, when planning such services, is to maximize the demand they attract, by locating centers and staffing them so as to reduce customers' travel time and time spent in queue. In the case of inoculation centers, the goal is to maximize the people that travel to the centers and stay in line until inoculated. We propose a procedure for the allocation of multiple servers to centers, so that this goal is achieved. An integer programming model is formulated. Since demand is elastic, a supply-demand equilibrium equation must be explicitly included in the optimization model, which then becomes nonlinear. As there are no exact procedures to solve such problems, we propose a heuristic procedure, based on Heuristic Concentration, which finds a good solution to this problem. Numerical examples are presented.

Keywords

Facility locationresource allocationnonlinearoptimizationinteger programmingheuristics.
Type
Research Article
Information
RAIRO - Operations Research , Volume 39 , Issue 3 , July 2005 , pp. 143 - 162
Copyright
© EDP Sciences, 2006

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References

F.J. Barros, Asignacion de Recursos en una Red Congestionada y con Demanda Elastica. Unpublished Master's Thesis, Pontificia Universidad Catolica de Chile (2004).
O. Berman and D. Krass, Facility Location Problems with Stochastic demands and Congestion, in Facility Location: Applications and Theory, edited by Z. Drezner and H.W. Hamacher. Springer-Verlag, New York (2002) 329–371.
Berman, O. and Larson, R., Optimal 2-Facility Network Districting in the Presence of Queuing. Transportation Science 19 (1985) 261–277. CrossRef
O. Berman and S. Vasudeva, Approximating Performance Measures for Public Services, working paper, Joseph L. Rotman School of Management, University of Toronto, Canada (2000).
Berman, O., Larson, R. and Parkan, C., The Stochastic Queue P-Median Location Problem. Transportation Science 21 (1987) 207–216. CrossRef
Berman, O. and Mandowsky, R., Location-Allocation on Congested Networks. Eur. J. Oper. Res. 26 (1986) 238–250. CrossRef
M. Brandeau, S. Chiu, S. Kumar and T. Grossman, Location with Market Externalities, in Facility Location: A Survey of Applications and Methods, edited by Z. Drezner. Springer-Verlag, New York (1995) 121–150.
M. Daskin, Networks and Discrete Location: Models, Algorithms and Applications. Wiley-Interscience Series in discrete Mathematics and Optimization, John Wiley (1995).
Hakimi, L., Optimal Location of Switching Centers and the absolute centers and medians of a graph. Oper. Res. 12 (1964) 450–459. CrossRef
F. Hillier and G. Lieberman, Introduction to Operations Research. Holden-Day Inc., Oakland, CA (1986).
Kariv, O. and Hakimi, L., An algorithmic approach to network location problems, part ii: The p-medians. SIAM J. Appl. Math. 37 (1979) 539–560. CrossRef
Laporte, G., Louveaux, F. and Van Hamme, L., Exact solution to a location problem with stochastic demands. Transportation Science 28 (1994) 95–103. CrossRef
V. Marianov and C. ReVelle, The standard response fire protection siting problem, INFOR: The Canadian J. Oper. Res. 29 (1991) 116–129.
Marianov, V. and ReVelle, C., The capacitated standard response fire protection siting problem: deterministic and probabilistic models. Ann. Oper. Res. 40 (1992) 303–322. CrossRef
Marianov, V., Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential. Ann. Oper. Res. 123 (2003) 125–141. CrossRef
V. Marianov and D. Serra, Location Problems in the Public Sector, in Facility Location: Applications and Theory, edited by Z. Drezner and H.W. Hamacher. Springer-Verlag, New York (2002) 119–150.
Marianov, V. and Serra, D., Location-Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times. Ann. Oper. Res. 111 (2002) 35–50. CrossRef
Marianov, V. and Serra, D., Location models for airline hubs behaving as M/D/c queues. Comput. Oper. Res. 30 (2003) 983–1003. CrossRef
V. Marianov and D. Serra, Location of Multiple-Server Common Service Centers or Public Facilities, for Minimizing General Congestion and Travel Cost Functions. Research Report, Department of Electrical Engineering, Pontificia Universidad Catolica de Chile.
ReVelle, C. and Swain, R., Central Facility Location. Geographical Analysis 2 (1970) 30–42. CrossRef
K. Rosing, Heuristic concentration: A study of stage one, Tinbergen Institute Discussion Papers. Tinbergen Institute, Amsterdam/Rotterdam (1998).
Rosing, K., Heuristic concentration: a study of stage one. Environment and Planning B 27 (2000) 137–150. CrossRef
Rosing, K. and Hodgson, M.J., Heuristic concentration for the p-median: an example demonstrating how and why it works. Comput. Oper. Res. 29 (2002) 1317–1330. CrossRef
Rosing, K. and ReVelle, C., Heuristic Concentration: Two stage solution construction. Eur. J. Oper. Res. 97 (1997) 75–86. CrossRef
Rosing, K., ReVelle, C. and Schilling, D., Gamma Heuristic, A for the P-Median. Eur. J. Oper. Res. 117 (1999) 522–532. CrossRef
Teitz, M. and Bart, P., Heuristic methods for estimating the generalized vertex median on a weighted graph. Oper. Res. 16 (1968) 955–965. CrossRef
Zhou, J. and Baoding, L., New stochastic models for capacitated location-allocation problem. Comput. Industrial Eng. 45 (2003) 111–125. CrossRef