Zadanie lokalizacji o szczególnej strukturze

• Autorzy: Zofia Jankowska-Zorychta

Warianty tytułu

An Assignment Problem of Specific Structure

• Języki publikacji: PL

Abstrakty

Autor zajmuje się problemem optymalnego (w odniesieniu do kosztów inwestycji i transportu) położenia m obiektów w n dopuszczalnych punktach przy założeniu, że m ≤ n oraz przy założeniu, że nie każdy obiekt może znajdować się w każdym punkcie.

EN

The author deals with the problem of optimal (with reference to the investment and transportation costs) location of m objects in n acceptable points under the assumption that m ≤ n and the restriction that not each object can be located in each point. It is shown that such a problem can be described by means cf well-known models, f.e. the Koopmans-Beckmann quadratic assignment problem or the Lawler 0-1 linear programming problem. Basing on the specific structure of this problem a mathematical model is formulated. It is of smaller size as compared to the models mentioned above. This fact is illustrated by an example. The author also shows that it is possible to include into the model the transportation connections between objects to be located and already existing ones. (original abstract)

Słowa kluczowe

PL

Modele lokalizacji; Programowanie matematyczne; Modele matematyczne

EN

Location models; Mathematical programming; Mathematical models

• Czasopismo: Przegląd Statystyczny
• Rocznik: 1985
• Tom: 32
• Numer: z. 3
• Strony: 255--262

Twórcy

autor

Zofia Jankowska-Zorychta

Bibliografia

• [1] Bazaraa M. S., Sherali H. D., Benders' partitioning scheme applied to a new formulation of the quadratic assignment problem, Naval Research Logistics Quarterly 27 (1980), s. 29-41.
• [2] Benders J. F., Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematic 4 (1962), s. 238 - 252.
• [3] Burkard R. E., Some recent advances in quadratic assignment problems, Raport 81 - 16, Mathematiches Institut, Technische Universitat zu Köln, August 1981 (Paper presented at the International Congres on Mathematical Programming, held in Rio de Janeiro, April 6-8 1981).
• [4] Burkard R. E., Quadratic assignment problems Bericht, 83-20, September 1983, Technische Universitat Graz, Institute für Mathematik, Opening Lecture delivered at the 5th Mathematical Programming Seminar, held in Zaborów (Poland), May 31 June 3, 1983.
• [5] Burkard R. E., Bönniger T., A heuristic for quadratic Boolean programs with applications to quadratic assignment problems, European Journal, of Operations Research 13 (1983), s. 274 -386.
• [6] Burkard R. E., Stratmann K. H., Numerical investigations on quadratic assignment problems, Naval Research Logistics Quarterly 25 (1978), s. 129 - 148.
• [7] Elshafei A. N., Hospital layout as a quadratic assignment problem, Operational Research Quarterly 28 (1977), s. 167 - 179.
• [8] Frieze A. M., Yadegar J., On the quadratic assignment problem Discrete Applied Mathematics 5 (1983), s. 89 - 98.
• [9] Gavett J. W., Plyter N. V, The optimal assignment of facilities to locations by branch and bound, Operations Research 14 (1966), s. 210 - 232.
• [10] Geoffrion A. M., Graves G. W., Multicommodity distribution system design by Benders' decomposition, Management Science 20 (1974), s. 822 - 844.
• [11] Glover F., Woolsey R. E., Further reduction of zero-one polynomial programming problems to 0-1 line programming problems, Operations Research 21 (1973), s. 156 - 161.
• [12] Graves G. W., Whinston A. B., An algorithm for the quadratic assignment problem, Management Science 16 (1970), s. 453 - 472.
• [13] Kaufman L., Broeckx F., An algorithm for the quadratic assignment problem using Benders decomposition, European Journal of Operational Research 2 (1978), s. 207 - 211.
• [14] Koopmans T. C., Beckmann M., Assignment problems and the location of economic activities, Econometria 25 (1957), s. 53 - 76.
• [15] Lawler E. L., The quadratic assignment problem, Management Science 9 (1963), s. 586 - 599.
• [16] Nugent C. E., Wollmann T. E., Rumi J., An experimental comparison of techniques for the assignment of facilities to locations, Operations Research 16 (1968), s. 150 - 173.
• [17] Ogryczak W., Zagadnienia lokalizacyjne w programowaniu matematycznym, Sprawozdanie Instytutu Informatyki UW 115 (1982), s. 1-40.
• [18] Pierce J. F., Crowston W. B., Tree search algorithms for quadratic assignment problems, Naval Research Logistics Quarterly 18 (1971), s. 1 - 36.
• [19] Słomiński L., Kwadratowe zadanie rozmieszczenia jako liniowe zadanie programowania zero-jedynkowego. Archiwum Automatyki i Telemechaniki, 20 (1975), s. 89 - 115.
• [20] Zorychta K., On Converting the 0-1 Linear Programming Problem to a Set-Covering Problem, Bull. Acad. Pol. Math. XXV, 9 (1977), s. 919 - 923.