Allocating servers to facilities, when demand is elastic to travel and waiting times
RAIRO - Operations Research - Recherche Opérationnelle, Volume 39 (2005) no. 3, pp. 143-162.

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.

DOI: 10.1051/ro:2006002
Classification: 90B80, 90B22
Keywords: facility location, resource allocation, nonlinear optimization, integer programming, heuristics
Marianov, Vladimir ; Rios, Miguel ; Barros, Francisco Javier 1

1 Graduate Program, Department of Systems Engineering, Pontificia Universidad Catolica de Chile, Vicuna Mackenna 4860, Santiago, Chile
@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://archive.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://archive.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://archive.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, Volume 39 (2005) no. 3, pp. 143-162. doi : 10.1051/ro:2006002. http://archive.numdam.org/articles/10.1051/ro:2006002/

[1] F.J. Barros, Asignacion de Recursos en una Red Congestionada y con Demanda Elastica. Unpublished Master's Thesis, Pontificia Universidad Catolica de Chile (2004).

[2] 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. | Zbl

[3] O. Berman and R. Larson, Optimal 2-Facility Network Districting in the Presence of Queuing. Transportation Science 19 (1985) 261-277. | Zbl

[4] O. Berman and S. Vasudeva, Approximating Performance Measures for Public Services, working paper, Joseph L. Rotman School of Management, University of Toronto, Canada (2000).

[5] O. Berman, R. Larson and C. Parkan, The Stochastic Queue P-Median Location Problem. Transportation Science 21 (1987) 207-216. | Zbl

[6] O. Berman and R. Mandowsky, Location-Allocation on Congested Networks. Eur. J. Oper. Res. 26 (1986) 238-250. | Zbl

[7] 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.

[8] M. Daskin, Networks and Discrete Location: Models, Algorithms and Applications. Wiley-Interscience Series in discrete Mathematics and Optimization, John Wiley (1995). | MR | Zbl

[9] L. Hakimi, Optimal Location of Switching Centers and the absolute centers and medians of a graph. Oper. Res. 12 (1964) 450-459. | Zbl

[10] F. Hillier and G. Lieberman, Introduction to Operations Research. Holden-Day Inc., Oakland, CA (1986). | MR | Zbl

[11] O. Kariv and L. Hakimi, An algorithmic approach to network location problems, part ii: The p-medians. SIAM J. Appl. Math. 37 (1979) 539-560. | Zbl

[12] G. Laporte, F. Louveaux and L. Van Hamme, Exact solution to a location problem with stochastic demands. Transportation Science 28 (1994) 95-103. | Zbl

[13] V. Marianov and C. Revelle, The standard response fire protection siting problem, INFOR: The Canadian J. Oper. Res. 29 (1991) 116-129. | Zbl

[14] V. Marianov and C. Revelle, The capacitated standard response fire protection siting problem: deterministic and probabilistic models. Ann. Oper. Res. 40 (1992) 303-322. | Zbl

[15] V. Marianov, Location of Multiple-Server Congestible Facilities for Maximizing Expected Demand, when Services are Non-Essential. Ann. Oper. Res. 123 (2003) 125-141. | Zbl

[16] 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. | Zbl

[17] V. Marianov and D. Serra, Location-Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times. Ann. Oper. Res. 111 (2002) 35-50. | Zbl

[18] V. Marianov and D. Serra, Location models for airline hubs behaving as M/D/c queues. Comput. Oper. Res. 30 (2003) 983-1003. | Zbl

[19] 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.

[20] C. Revelle and R. Swain, Central Facility Location. Geographical Analysis 2 (1970) 30-42.

[21] K. Rosing, Heuristic concentration: A study of stage one, Tinbergen Institute Discussion Papers. Tinbergen Institute, Amsterdam/Rotterdam (1998).

[22] K. Rosing, Heuristic concentration: a study of stage one. Environment and Planning B 27 (2000) 137-150.

[23] K. Rosing and M.J. Hodgson, Heuristic concentration for the p-median: an example demonstrating how and why it works. Comput. Oper. Res. 29 (2002) 1317-1330. | Zbl

[24] K. Rosing and C. Revelle, Heuristic Concentration: Two stage solution construction. Eur. J. Oper. Res. 97 (1997) 75-86. | Zbl

[25] K. Rosing, C. Revelle and D. Schilling, A Gamma Heuristic for the P-Median. Eur. J. Oper. Res. 117 (1999) 522-532. | Zbl

[26] M. Teitz and P. Bart, Heuristic methods for estimating the generalized vertex median on a weighted graph. Oper. Res. 16 (1968) 955-965. | Zbl

[27] J. Zhou and L. Baoding, New stochastic models for capacitated location-allocation problem. Comput. Industrial Eng. 45 (2003) 111-125.

Cited by Sources: