BazEkon - Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie

BazEkon home page

Meny główne

Redmer Adam (Poznan University of Technology, Poland)
Facility Location Problem Mathematical Models - Supply Chain Perspective
LogForum, 2022, vol. 18, nr 4, s. 379-395, tab., bibliogr. 40 poz.
Słowa kluczowe
Logistyka, Łańcuch dostaw, Modelowanie matematyczne, Dystrybucja
Logistics, Supply chain, Mathematical modeling, Distribution
Background: Supply chains are the networks linking sources of supply with demand points and composed of so-called actors, i.e., producers, distributors/wholesalers, retailers, and customers/consumers. As in every network, supply chains contain vertices and arcs, the former represented by factories and warehouses (including distribution centers). Such facilities cause long-term and expensive investments. As a result, decisions on location and number of them belong to the strategic level of management and require quantitative analysis. To do this, mathematical models of the Facility Location Problem (FLP) are constructed to allow an application of optimization methods. Methods: Mathematical optimization or programming is the selection of the best solution, with regard to some criterion, from a set of feasible alternatives. The fundamental of mathematical optimization is the formulation of mathematical models of analyzed problems. Mathematical models are composed of objective function, decision variables, constraints, and parameters. These components are presented and compared in the paper concerning FLP from a supply chain perspective. Results: The ten mathematical models of the FLP are presented, including the two original ones. The models are classified according to such features as facility type they concern, including the desirable, neutral, and undesirable ones. The models and their components are characterized. In addition, their applicability and elasticity are analyzed. Finally, the models are compared and discussed from the supply chain point of view. Conclusions: However, the FLP mathematical models are relatively similar; the most important element of them for supply chain appropriate representation is an objective function. It strongly influences the possible applicability of FLP models and their solutions, as well. The objective functions having broader applicability turned out to be the maximized number of supply/demand points covered by facilities and the minimized number of facilities necessary to cover supply/demand points. However, not to locate all allowed facilities (use all the location sites) or as many as supply/demand points, but an appropriate number of them, it is necessary to take into account facility fixed costs. Thus, when locating logistics facilities, the minimized total cost of serving supply/demand points is the most appropriate objective function. (original abstract)
Pełny tekst
  1. Ahmadi-Javid, A., Seyedi, P., Syam, S.S., 2017. A survey of health care facility location. Computers & Operations Research, 79, 223-263.
  2. Ambrosino, D., Scutellà, M.G., 2005. Distribution network design: New problems and related models. European Journal of Operational Research, 165(3), 610-624.
  3. Berman, O., Drezner, Z., Wesolowsky, G.O., 1996. Minimum covering criterion for obnoxious facility location on a network. Networks, 28(1), 1-5. 1::AID-NET1 3.0.CO;2-J
  4. Boloori Arabani, A., Farahani, R.Z., 2012. Facility location dynamics: An overview of classifications and applications. Computers & Industrial Engineering, 62, 408-420.
  5. Boonmee, Ch., Arimura, M., Asada, T., 2017. Facility location optimization model for emergency humanitarian logistics. International Journal of Disaster Risk Reduction, 24, 485-498.
  6. Brimberg, J., 1995. The Fermat-Weber location problem revisited. Mathematical Programming, 71(1, Ser. A), 71-76, MR 1362958.
  7. Bruno, G., Genovese, A., Improta, G., 2014. A historical perspective on location problems. BSHM Bulletin: Journal of the British Society for the History of Mathematics, 29(2), 83-97.
  8. Church, R.L., Garfinkel, R.S., 1978. Locating an obnoxious facility on a network. Transportation Science, 12(2), 107-118.
  9. Conceição, S., Pedrosa, L., Neto, A., Vinagre, M., Wolff, E., 2012. The facility location problem in the steel industry: A case study in Latin America. Production Planning & Control, 23(1), 26-46.
  10. Cornuejols, G., Nemhauser, G.L., Wolsey, L.A., 1990. The uncapacitated facility location problem. In: Francis, R.L., Mirchandani, P.B. (Eds.): Discrete location theory. New York, Wiley-Interscience, 119-171.
  11. Dorrie, H., 1965. 100 great problems of elementary mathematics: their history and solution. New York, NY: Dover Publications.
  12. Drezner, Z., Hamacher, H.W., 2004. Facility location: applications and theory. Springer.
  13. Drezner, Z., Wesolowsky, G.O., 1980. A maximin location problem with maximum distance constraints. AIIE Transactions, 12(3), 249-252.
  14. Eiselt, H., Marianov, V., 2011. Foundations of location analysis. International Series in Operations Research & Management Science. New York, Springer.
  15. Eiselt, H.A., Laporte, G., 1995. Facility location: A survey of application and methods. Springer, New York.
  16. Farahani, R.Z., Hekmatfar, M., Fahimnia, B., Kazemzadeh, N., 2014. Hierarchical facility location problem: Models, classifications, techniques, and applications. Computers & Industrial Engineering, 68, 104-117.
  17. Farahani, R.Z., Steadie Seifi, M., Asgari, N., 2010. Multiple criteria facility location problems: A survey. Applied Mathematical Modelling, 34, 1689-1709.
  18. Galli, L., Letchford, A.N., Miller, S., 2018. New valid inequalities and facets for the simple plant location problem. European Journal of Operational Research, 269(3), 824-833.
  19. Guastaroba, G., Speranza, M.G., 2014. A heuristic for BILP problems. The single source capacitated facility location problem. European Journal of Operational Research, 238, 438-450.
  20. Gupta, A., Könemann, J., 2011. Approximation algorithms for network design: A survey. Surveys in Operations Research and Management Science, 16, 3-20.
  21. Hakimi, S.L., 1964. Optimum locations of switching centers and the absolute centers and medians of a graph. Operations Research, 12(3), 450-459.
  22. Hale, T.S., Moberg, C.R., 2003. Location science research: A review. Annals of Operations Research, 123, 21-35.
  23. Jayaraman, V., 1998. Transportation, facility location and inventory issues in distribution network design: An investigation. International Journal of Operations & Production Management, 18(5), 471-494.
  24. Kauf, S., Laskowska-Rutkowska, A., 2019. The location of an international logistics center in Poland as a part of the One Belt One Road initiative. LogForum, 15(1). 71-83.
  25. Klamroth, K., 2002. Single facility location problems with barriers. Berlin, Springer Verlag Telos.
  26. Klose, A., Drexl, A., 2005. Facility location models for distribution system design. European Journal of Operational Research, 162(1), 4-29.
  27. Korupolu, M.R., Plaxton, C.G., Rajaraman, R., 2000. Analysis of a local search heuristic for facility location problems. Journal of Algorithms, 37(1), 146-188.
  28. Kuby, M.J., 1987. Programming models for facility dispersion: The p-dispersion and maxisum dispersion problems. Geographical Analysis, 19(4), 315-329.
  29. Kuhn, H.W., Kuenne, R.E., 1962. An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics. Journal of Regional Science, 4, 21-34.
  30. Lin, C.-C., Lin, C.-C., 2018. The p-Center flow-refueling facility location problem. Transportation Research Part B, 118, 124-142.
  31. Magnanti, T.L., Wong, R.T., 1984. Network design and transportation planning: Models and algorithms. Transportation Science, 18(1), 1-55.
  32. Mangiaracina, R., Song, G., Perego, A., 2015. Distribution network design: A literature review and a research agenda. International Journal of Physical Distribution & Logistics Management, 45(5), 506-531.
  33. Or, I., Pierskalla, W.P., 1979. A transportation location-allocation model for regional blood banking. AIIE Transactions, 11(2), 86-95.
  34. Owen, S.H., Daskin, M.S., 1998. Strategic facility location: A review. European Journal of Operational Research, 111(3), 423-447.
  35. Rahmani, R., MirHassani, S.A., 2014. A hybrid Firefly-Genetic algorithm for the capacitated facility location problem. Information Sciences, 283, 70-78.
  36. Sliva, F., Serra, D., 2007. A capacitated facility location problem with constrained backlogging probabilities. International Journal of Production Research, 45(21), 5117-5134.
  37. Sridharan, R., 1995. The capacitated plant location problem. European Journal of Operational Research, 87, 203-213.
  38. Turkoglu, D.C., Genevois, M.E., 2020. A comparative survey of service facility location problems. Annals of Operations Research, 292, 399-468.
  39. Vygen, J., 2005. Approximation algorithms for facility location problems. Bonn, Germany: Research Institute for Discrete Mathematics.
  40. Weiszfeld, E., 1937. Sur le point par lequel la somme des distances den points donnés est minimum. Tohoku Mathematics Journal, 43, 355-386.
Cytowane przez
Udostępnij na Facebooku Udostępnij na Twitterze Udostępnij na Google+ Udostępnij na Pinterest Udostępnij na LinkedIn Wyślij znajomemu