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.
Mots clés : facility location, resource allocation, nonlinear optimization, integer programming, heuristics
@article{RO_2005__39_3_143_0,
author = {Marianov, Vladimir and Rios, Miguel and Barros, Francisco Javier},
title = {Allocating servers to facilities, when demand is elastic to travel and waiting times},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {143--162},
publisher = {EDP-Sciences},
volume = {39},
number = {3},
year = {2005},
doi = {10.1051/ro:2006002},
mrnumber = {2205668},
zbl = {1103.90059},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro:2006002/}
}
TY - JOUR AU - Marianov, Vladimir AU - Rios, Miguel AU - Barros, Francisco Javier TI - Allocating servers to facilities, when demand is elastic to travel and waiting times JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2005 SP - 143 EP - 162 VL - 39 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro:2006002/ DO - 10.1051/ro:2006002 LA - en ID - RO_2005__39_3_143_0 ER -
%0 Journal Article %A Marianov, Vladimir %A Rios, Miguel %A Barros, Francisco Javier %T Allocating servers to facilities, when demand is elastic to travel and waiting times %J RAIRO - Operations Research - Recherche Opérationnelle %D 2005 %P 143-162 %V 39 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro:2006002/ %R 10.1051/ro:2006002 %G en %F RO_2005__39_3_143_0
Marianov, Vladimir; Rios, Miguel; Barros, Francisco Javier. Allocating servers to facilities, when demand is elastic to travel and waiting times. RAIRO - Operations Research - Recherche Opérationnelle, Tome 39 (2005) no. 3, pp. 143-162. doi : 10.1051/ro:2006002. http://www.numdam.org/articles/10.1051/ro:2006002/
[1] , Asignacion de Recursos en una Red Congestionada y con Demanda Elastica. Unpublished Master's Thesis, Pontificia Universidad Catolica de Chile (2004).
[2] and, 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. | Zbl
[3] and, Optimal 2-Facility Network Districting in the Presence of Queuing. Transportation Science 19 (1985) 261-277. | Zbl
[4] and, Approximating Performance Measures for Public Services, working paper, Joseph L. Rotman School of Management, University of Toronto, Canada (2000).
[5] , and, The Stochastic Queue P-Median Location Problem. Transportation Science 21 (1987) 207-216. | Zbl
[6] and, Location-Allocation on Congested Networks. Eur. J. Oper. Res. 26 (1986) 238-250. | Zbl
[7] ,, and, Location with Market Externalities, in Facility Location: A Survey of Applications and Methods, edited by Z. Drezner. Springer-Verlag, New York (1995) 121-150.
[8] , Networks and Discrete Location: Models, Algorithms and Applications. Wiley-Interscience Series in discrete Mathematics and Optimization, John Wiley (1995). | MR | Zbl
[9] , Optimal Location of Switching Centers and the absolute centers and medians of a graph. Oper. Res. 12 (1964) 450-459. | Zbl
[10] and, Introduction to Operations Research. Holden-Day Inc., Oakland, CA (1986). | MR | Zbl
[11] and, An algorithmic approach to network location problems, part ii: The p-medians. SIAM J. Appl. Math. 37 (1979) 539-560. | Zbl
[12] , and, Exact solution to a location problem with stochastic demands. Transportation Science 28 (1994) 95-103. | Zbl
[13] and, The standard response fire protection siting problem, INFOR: The Canadian J. Oper. Res. 29 (1991) 116-129. | Zbl
[14] and, The capacitated standard response fire protection siting problem: deterministic and probabilistic models. Ann. Oper. Res. 40 (1992) 303-322. | Zbl
[15] , Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential. Ann. Oper. Res. 123 (2003) 125-141. | Zbl
[16] and, 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. | Zbl
[17] and, Location-Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times. Ann. Oper. Res. 111 (2002) 35-50. | Zbl
[18] and, Location models for airline hubs behaving as M/D/c queues. Comput. Oper. Res. 30 (2003) 983-1003. | Zbl
[19] and, 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.
[20] and, Central Facility Location. Geographical Analysis 2 (1970) 30-42.
[21] , Heuristic concentration: A study of stage one, Tinbergen Institute Discussion Papers. Tinbergen Institute, Amsterdam/Rotterdam (1998).
[22] , Heuristic concentration: a study of stage one. Environment and Planning B 27 (2000) 137-150.
[23] and, Heuristic concentration for the p-median: an example demonstrating how and why it works. Comput. Oper. Res. 29 (2002) 1317-1330. | Zbl
[24] and, Heuristic Concentration: Two stage solution construction. Eur. J. Oper. Res. 97 (1997) 75-86. | Zbl
[25] , and, A Gamma Heuristic for the P-Median. Eur. J. Oper. Res. 117 (1999) 522-532. | Zbl
[26] and, Heuristic methods for estimating the generalized vertex median on a weighted graph. Oper. Res. 16 (1968) 955-965. | Zbl
[27] and, New stochastic models for capacitated location-allocation problem. Comput. Industrial Eng. 45 (2003) 111-125.
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