Optimized Design of Large-Scale Social Welfare Supporting Systems on Complex Networks

  • Jaroslav Janáček
  • Ľudmila Jánošíková
  • Ľuboš Buzna
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 57)

Abstract

Our contemporary societies are supported by several systems of high importance providing large-scale services substantial for citizens everyday life. Typically, these systems are built or rely on various types of complex networks such as road networks, railway networks, electricity networks, communication networks etc. Examples of such systems are a set of emergency medical stations, fire or police stations covering the area of a state, social or administration infrastructure. The problem of how to design these systems efficiently, fairly, and reliably is still timely and it brings along many new research challenges. This book chapter presents a brief survey of optimization models and approaches applicable to the problem. We pay special attention to the methods based on the branch and bound principle and show how their computational properties can be improved. Furthermore, we discuss how some of these models can be rearranged in order to allow using the existing solving techniques as approximative methods. The presented numerical experiments are conducted on realistic data describing the topology of the Slovak road network. On the one hand, we hope that this chapter can come handy to researchers working in the area of complex networks, as it presents efficient methods to design public service systems on the networks. On the other hand, we can picture the benefits potentially resulting from the knowledge of the network properties and possibly being utilized in the algorithms design.

Keywords

Public service systems Large-scale emergency systems 

Notes

Acknowledgements

The authors are grateful for the financial support provided by the Ministry of Education of the Slovak Republic (project VEGA 1/0361/10) and thank J. Slavík, P. Tarábek, M. Koháni, and two anonymous reviewers for thorough reading of the manuscript and the valuable comments.

References

  1. 1.
    Ahuja, R.K., Magnanti, T., Orlin, J.: Network flows: Theory, algorithms, and applications, Prentice Hall, (1993).Google Scholar
  2. 2.
    Balinski, M.: Integer programming: methods, uses computation, Management Science, 12, pp. 254–313, (1965).MathSciNetCrossRefGoogle Scholar
  3. 3.
    Beltran-Royo, C., Vial J.P., Alonso-Ayuso, A.: Semi-Lagrangian relaxation applied to the uncapacitated facility location problem, Computational Optimization and Applications, Online First, DOI: 10.1007/s10589-010-9338-2, (2010).Google Scholar
  4. 4.
    Bertsimas, D., Farias, V.F., Trichakis, N.: The price of fairness, Operations Research, (forthcoming).Google Scholar
  5. 5.
    Bilde, O., Krarup, J.: Sharp lower bounds and efficient algorithms for the simple plant location problem. Annals of Discrete Mathematics, 1, pp. 77–97, (1977).MathSciNetCrossRefGoogle Scholar
  6. 6.
    Brandeau, M.L., Chiu, S.S., Kumar, S., Grossmann, T.A.: Location with Market Externalities, In: Z., Drezner, ed., Facility Location: A Survey of Applications and Methods, Springer Verlag, New York, (1995).Google Scholar
  7. 7.
    Brandes, U., Erlenbach, T.: Network Analysis: Methodological Foundations, Springer-Verlag Berlin Heidelberg, (2005).Google Scholar
  8. 8.
    Budge, S., Erkut, E., Ingolfsson, A.: Optimal Ambulance Location with Random Delays and Travel Times. Working paper, University of Alberta School of Business, (2005).Google Scholar
  9. 9.
    Butler, M., Wiliams, H.P.: Fairness versus efficiency in charging for the use of common facilities. Journal of Operational Research Society, 53, pp. 1324–1329, (2002).MATHCrossRefGoogle Scholar
  10. 10.
    Butler, M., Wiliams, H., P.: The allocation of shared fixed costs, European Journal of Operational Research 170, pp. 391–397, (2006).Google Scholar
  11. 11.
    Caprara A., Toth, P., Fischetti, M.: Algorithms for the set covering problem, Annals of Operations Research 98, pp. 353–371, (2000).MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Crainic, T.G.: Long-haul freight transportation. In Handbook of transportation science, New York: Springer, (2003).Google Scholar
  13. 13.
    Daganzo, C.F.: Logistics System Analysis, Springer Verlag Berlin, (1996).Google Scholar
  14. 14.
    Daskin, M.S.: Network and Discrete Location. Models, Algorithms, and Applications. John Wiley & Sons, New York, NY, (1995).Google Scholar
  15. 15.
    Dorogovtsev, S., Mendes, J.: Evolution of networks: From biological nets to the Internet and WWW, Oxford University Press, Oxford (2003).MATHGoogle Scholar
  16. 16.
    Eiselt, H.A., Laporte, G.: Objectives in Location Problems, In: Drezner, Z., ed., Facility Location: A Survey of Applications and Methods, Springer Verlag, New York, (1995).Google Scholar
  17. 17.
    Erlenkotter, D.: A dual-based procedure for uncapacitated facility location. Operations Research, 26, 6, pp. 992–1009, (1978).MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Frank, H., Frisch, I.T.: Communication, Transmission and Transportation Networks, Addison Wesley, Series in Electrical Engineering, (1971).Google Scholar
  19. 19.
    Galvao, R.D., Nascimento, E.M.: The location of benefit-distributing facilities in the Brazilian social security system. Operational Research’90 (Proceedings of the IFORS 1990 Conference), pp. 433–443, (1990).Google Scholar
  20. 20.
    Galvao, R.D.: Uncapacitated facility location problems: contributions, Pesqui. Oper. 2004, 24, 1, pp. 7–38. ISSN 0101–7438, (2004).Google Scholar
  21. 21.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the theory of NP Completeness, San Francisco, Freeman and Co., (1979).Google Scholar
  22. 22.
    Hakimi, S.L.: Optimum location of switching centers and the absolute centers and medians of a graph, Operations Research, 12, pp. 450–459, (1964).MATHCrossRefGoogle Scholar
  23. 23.
    Janáček, J., Kováčiková, J.: Exact solution techniques for large location problems. In Proceedings of the International Conference: Mathematical Methods in Economics, pp. 80–84, Ostrava, (1997).Google Scholar
  24. 24.
    Janáček, J., Buzna, Ľ.: A comparison of continuous approximation with mathematical programming approach to location problems, Central European Journal of Operation Research, 12, 3, pp. 295–305, (2004).MATHGoogle Scholar
  25. 25.
    Janáček, J., Buzna, Ľ.: An acceleration of Erlenkotter-Koerkels algorithms for the uncapacitated facility location problem. Ann. Oper. Res. 164, pp. 97–109, (2008).MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Janáček, J., Gábrišová, L.: A two-phase method for the capacitated facility problem of compact customer subsets. Transport, 24, 4, pp. 274–282, (2009).CrossRefGoogle Scholar
  27. 27.
    J. Janáček, B., Linda, E., Ritschelová: Optimization of municipalities with extended competence selection, Prague economic papers: quarterly journal of economic theory and policy, 19, 1 pp. 21–34, (2010).Google Scholar
  28. 28.
    Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.L.: The large-scale organization of metabolic networks, Nature, 407, (2000).Google Scholar
  29. 29.
    Karp, R.M.: Reducibility among Combinatorial Problems: In Complexity of Computer Computations, Miller, E.W., Tatcher J.W. eds., New York, Plenum Press, pp. 85–104, (1972)Google Scholar
  30. 30.
    Koerkel, M.: On the exact solution of large-scale simple plant location problems. Eur. J. Oper. Res. 39, 2, pp. 157–173, (1989).MATHCrossRefGoogle Scholar
  31. 31.
    Lämmer, S., Gehlsen, B., Helbing, D.:Scaling laws in the spatial structure of urban road networks, Physica A, 363, 1, pp. 89–65, (2006).Google Scholar
  32. 32.
    Mladenovic, N., Brimberg, J., Hansen, P.: A note on duality gap in the simple plant location problem. European Journal of Operational Research, 174, pp. 11–22, (2006).MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Nace, D., Doan, L.N., Klopfenstein, O., Bashllari, A.: Max-min fairness in multi-commodity flows, Computers & Operations Research 35, pp. 557–573. (2008).MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Nogueirai, T., Mendes, R., Valie, Z., Cardoso, J. C.: Optimal Location of Natural Gas Sources in the Iberian System, Proceedings of the 6th WSEAS International Conference on Power Systems, Lisbon, Portugal, September 22–24, (2006).Google Scholar
  35. 35.
    Pioro, M., Medhi, D.: Routing, flow, and capacity design in communication and computer networks, Morgan Kaufmann Publishers, (2004).Google Scholar
  36. 36.
    Rawls, J.: A Theory of justice. Harward University Press, (1971).Google Scholar
  37. 37.
    Resende, M.G.C., Pardalos, P.M.: Handbook of optimization in telecommunications, Springer Science+Business Media, Inc., (2006).Google Scholar
  38. 38.
    Silva, F., Serra, D.: Locating Emergency Services with Different Priorities: The Priority Queuing Covering Location Problem, The Journal of the Operational Research Society, 59, 9, pp. 1229–1238, (2008).MATHCrossRefGoogle Scholar
  39. 39.
    Srinivasan, U.T., Dunne, J.A., Harte, J., Martinez, N.D.: Response of complex food webs to realistic extinction sequences, Ecology 88, 617, (2007).CrossRefGoogle Scholar
  40. 40.
    Sripetch, A., Saengudomlert, P.: Topology Design of Optical Networks Based on Existing Power Grids, Fifth Annual Conference on Communication Networks and Services Research(CNSR’07), (2007).Google Scholar
  41. 41.
    Toregas, C., Swain, R., ReVelle C., Bergman, L.: The location of emergency service facilities, Operations Research, 19, pp. 1363–1373, (1973).CrossRefGoogle Scholar
  42. 42.
    Whittle, P., Networks optimization and evolution, Cambridge University Press, (2007).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Jaroslav Janáček
    • 1
  • Ľudmila Jánošíková
    • 1
  • Ľuboš Buzna
    • 1
  1. 1.Faculty of Management Science and Informatics, Department of Transportation NetworksUniversity of ŽilinaŽilinaSlovak Republic

Personalised recommendations