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The Quadratic Assignment Problem

  • Chapter
Handbook of Combinatorial Optimization

Abstract

The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. Specifically, we are given three n x n input matrices with real elements F = (f ij ), D = (d kl ) and B = (b ik ), where f ij is the flow between the facility i and facility j, d kl is the distance between the location k and location l, and b ik is the cost of placing facility i at location k. The Koopmans-Beckmann version of the QAP can be formulated as follows: Let n be the number of facilities and locations and denote by N the set N = {1, 2,..., n}.

These authors have been supported by the Spezialforschungsbereich F 003 “Optimierung und Kontrolle”, Projektbereich Diskrete Optimierung.

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Authors and Affiliations

  1. Institute of Mathematics, Technical University Graz, Steyrergasse 30, 8010, Graz, Austria

    Rainer E. Burkard & Eranda Çela

  2. Center for Applied Optimization, Industrial and Systems Engineering Department, University of Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos & Leonidas S. Pitsoulis

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  1. Rainer E. Burkard
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  2. Eranda Çela
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  3. Panos M. Pardalos
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  4. Leonidas S. Pitsoulis
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Editors and Affiliations

  1. University of Minnesota, Minneapolis, USA

    Ding-Zhu Du

  2. University of Florida, Gainesville, USA

    Panos M. Pardalos

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Burkard, R.E., Çela, E., Pardalos, P.M., Pitsoulis, L.S. (1998). The Quadratic Assignment Problem. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_27

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