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

Vladimir Marianov; Miguel Rios; Francisco Javier Barros[1]

  • [1] Graduate Program, Department of Systems Engineering, Pontificia Universidad Catolica de Chile, Vicuna Mackenna 4860, Santiago, Chile

RAIRO - Operations Research - Recherche Opérationnelle (2005)

  • Volume: 39, Issue: 3, page 143-162
  • ISSN: 0399-0559

Abstract

top
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.

How to cite

top

Marianov, Vladimir, Rios, Miguel, and Barros, Francisco Javier. "Allocating servers to facilities, when demand is elastic to travel and waiting times." RAIRO - Operations Research - Recherche Opérationnelle 39.3 (2005): 143-162. <http://eudml.org/doc/245181>.

@article{Marianov2005,
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.},
affiliation = {Graduate Program, Department of Systems Engineering, Pontificia Universidad Catolica de Chile, Vicuna Mackenna 4860, Santiago, Chile},
author = {Marianov, Vladimir, Rios, Miguel, Barros, Francisco Javier},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {facility location; resource allocation; nonlinear optimization; integer programming; heuristics},
language = {eng},
number = {3},
pages = {143-162},
publisher = {EDP-Sciences},
title = {Allocating servers to facilities, when demand is elastic to travel and waiting times},
url = {http://eudml.org/doc/245181},
volume = {39},
year = {2005},
}

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
PB - EDP-Sciences
VL - 39
IS - 3
SP - 143
EP - 162
AB - 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.
LA - eng
KW - facility location; resource allocation; nonlinear optimization; integer programming; heuristics
UR - http://eudml.org/doc/245181
ER -

References

top
  1. [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. [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. Zbl1061.90068
  3. [3] O. Berman and R. Larson, Optimal 2-Facility Network Districting in the Presence of Queuing. Transportation Science 19 (1985) 261–277. Zbl0606.90053
  4. [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. [5] O. Berman, R. Larson and C. Parkan, The Stochastic Queue P-Median Location Problem. Transportation Science 21 (1987) 207–216. Zbl0624.90025
  6. [6] O. Berman and R. Mandowsky, Location-Allocation on Congested Networks. Eur. J. Oper. Res. 26 (1986) 238–250. Zbl0595.90013
  7. [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. [8] M. Daskin, Networks and Discrete Location: Models, Algorithms and Applications. Wiley-Interscience Series in discrete Mathematics and Optimization, John Wiley (1995). Zbl0870.90076MR1326602
  9. [9] L. Hakimi, Optimal Location of Switching Centers and the absolute centers and medians of a graph. Oper. Res. 12 (1964) 450–459. Zbl0123.00305
  10. [10] F. Hillier and G. Lieberman, Introduction to Operations Research. Holden-Day Inc., Oakland, CA (1986). Zbl0641.90047MR569591
  11. [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. Zbl0432.90075
  12. [12] G. Laporte, F. Louveaux and L. Van Hamme, Exact solution to a location problem with stochastic demands. Transportation Science 28 (1994) 95–103. Zbl0821.90077
  13. [13] V. Marianov and C. ReVelle, The standard response fire protection siting problem, INFOR: The Canadian J. Oper. Res. 29 (1991) 116–129. Zbl0732.90052
  14. [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. Zbl0784.90045
  15. [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. Zbl1053.90081
  16. [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. Zbl1061.90073
  17. [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. Zbl1013.90024
  18. [18] V. Marianov and D. Serra, Location models for airline hubs behaving as M/D/c queues. Comput. Oper. Res. 30 (2003) 983–1003. Zbl1039.90029
  19. [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. [20] C. ReVelle and R. Swain, Central Facility Location. Geographical Analysis 2 (1970) 30–42. 
  21. [21] K. Rosing, Heuristic concentration: A study of stage one, Tinbergen Institute Discussion Papers. Tinbergen Institute, Amsterdam/Rotterdam (1998). 
  22. [22] K. Rosing, Heuristic concentration: a study of stage one. Environment and Planning B 27 (2000) 137–150. 
  23. [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. Zbl0994.90113
  24. [24] K. Rosing and C. ReVelle, Heuristic Concentration: Two stage solution construction. Eur. J. Oper. Res. 97 (1997) 75–86. Zbl0923.90107
  25. [25] K. Rosing, C. ReVelle and D. Schilling, A Gamma Heuristic for the P-Median. Eur. J. Oper. Res. 117 (1999) 522–532. Zbl0937.90055
  26. [26] M. Teitz and P. Bart, Heuristic methods for estimating the generalized vertex median on a weighted graph. Oper. Res. 16 (1968) 955–965. Zbl0165.22804
  27. [27] J. Zhou and L. Baoding, New stochastic models for capacitated location-allocation problem. Comput. Industrial Eng. 45 (2003) 111–125. 

NotesEmbed ?

top

You must be logged in to post comments.