Abstract
One of the most notorious network design problems is the Quadratic Assignment Problem (QAP). We develop an heuristic algorithm for QAPs along with an M/G/C/C state dependent queueing model for capturing congestion in the traffic system interconnecting the nodes in the network. Computational results are also presented.
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References
R.E. Burkard, “Locations with spatial interaction-Quadratic Assignment Problem,” in Discrete Location Theory, R.L. Francis and P.B. Mirchandani (Eds.), Academic Press: New York, 1984.
R.E. Burkard, E. Cela, P.M. Pardalos, and L. Pitsoulis, in Handbook of Combinatorial Optimization, Ding-Zhu Du and P.M. Pardalos (Eds.), Kluwer Academic Publishers: Dordrecht, vol. 3, 241–337, 1999.
Cheah, Jenyeng, “State dependent queueing models,” Masters Thesis. Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, MA, 01003. Spring 1990.
Cheah, Jenyeng and J. MacGregor Smith, “Generalized M/G/C/C state dependent queueing models and pedestrian traffic flows,” Queueing Systems and Their Applications (QUESTA), vol. 15 pp. 365–386, 1994.
D. Chhajed, B. Montreuil, and T. Lowe, “Flow network design for manufacturing system layout,” European Journal of Operational Research, vol. 57, pp. 145–161, 1992.
A.J. Duncan, Quality Control and Industrial Statistics, Richard D. Irwin: Homewood, Il., 1986.
G. Finke and R.E. Burkard, Surveys in Combinatorial Optimization, North-Holland: Amsterdam, 1987, pp. 61–82.
J.J. Fruin, Pedestrian Planning and Design, Metropolitan Assoc. of Urban Des. and Env. Plng: New York NY 10008, 1971.
R.J. Gaskins and J.M.A. Tanchoco, “Flowpath design for automated guided vehicle system,” International Journal of Production Research, vol. 25, no. 5, pp. 667–676, 1987.
D. Gross and C.M. Harris, Fundamentals of Queueing Theory, John Wiley and Son, New York. 1985.
Jain, Rajat and J. MacGregor Smith, “Modelling vehicular traffic flow using M/G/C/C state dependent queueing models,” Transportation Science, vol. 31, no. 4, pp. 324–336, 1997.
T.C. Koopmans and M. Beckman, “Assignment problems and the location of economic activities,” Econometric, vol. 25, pp. 53–76, 1957.
A. Kusiak and S.S. Heragu, “The facility layout problem,” European Journal of Operational Research, vol. 29, pp. 229–251, 1987.
Wu-Ji Li, “Deming's methodolog in inspection criteria,” Master's Project. Department of Industrial Engineering and Operations Research, University of Massachusetts, Amherst, MA, 01003, 1988.
Wu-Ji Li and J. MacGregor Smith, “An algorithm for quadratic assignment problems,” The European Journal of Operational Research, vol. 81, pp. 205–216, 1995.
Wu-Ji Li and J.M. Smith, “Star, grid, and ring topologies in facility location and network design,” in Network De-sign: Connectivity and Facilities Location, P. Pardalos and D.Z. Du (Eds.), Dimacs Series in Discrete Mathemtics and Theoretical Computer Science, vol. 40, pp. 219–246, 1997.
Adolf, D. May, Traffic Flow Fundamentals, Prentice-Hall, Inc.: New York, 1990.
T. Muller, Automated Guided Vehicles, IFS Publications: Kempston, Bedford, 1983.
P.M. Pardalos, M.G.C. Resende, and Y. Li, “Algorithm 754: FORTRAN subroutines for approximate solution of dense quadratic assignment problems using GRASP,” ACM Transactions on Mathematical Software, vol. 22, no. 1, pp. 104–118, 1996.
P.M. Pardalos, M.G.C. Resende, and L. Pitsoulis, “Algorithm 769: FORTRANsubroutines for approximate solution of sparsemquadratic assignment problems using GRASP,” ACMTransactions on Mathematical Software, vol. 23, no. 2, pp. 196–208, 1997.
Pardalos, P.M. and L. Pitsoulis (Eds.), Nonlinear Assignment Problems: Algorithms and Applications. Kluwer Academic Publishers: Dordrecht, 2000.
P.M. Pardalos and H. Wolkowicz (Eds.). Quadratic Assignment Problems: Algorithms and Applictions, DIMACS Series, vol. 16, American Mathematical Society, 1995.
S. Ross, Stochastic Process, John Wiley & Sons: New York, 1983.
S. Sahni and T. Gonzalez, “P-complete approximation problems,” J. ACM, vol. 23, pp. 555–565, 1976.
R. Sharpe and J. Brochie, “An urban systems study,” R. Aust. Plann. Inst. J., vol. 10, pp. 3–12, 1972.
J.M. Smith and N.B. Rouse, “Application of queueing network models to optimization of resource allocation within libraries,” Journal of The American Society for Information Science, vol. 30, no. 5, pp. 250–263, 1978.
J.M. Smith and R. Macleod, “A relaxed assignment algorithm for the quadratic assignment problem,” INFOR, vol. 26, no. 3, 1988.
J.M. Smith, “Cellular arrangement problems with random flows,” Engineering Optimization, vol. 24, pp. 59–74, 1995.
J.M. Smith and D. Towsley, “The use of queueing network in the evaluation of egress from buildings,” Environment and Planning, vol. B-8, pp. 125–139, 1981.
L. Steinberg, “The backboard wiring problem: A placement algorithm,” SIAM Rev., vol. 3, pp. 37–50, 1961.
P. Tregenza, The Design of Interior Circulation, Van Norstand Reinhold Company: New York, 1976.
S. Yuhaski and J.M. Smith, “Modeling circulation systems in buildings using state dependent queueing models,” Queueing System, vol. 4, pp. 319–338, 1989.
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Smith, J.M., Li, WJ. Quadratic Assignment Problems and M/G/C/C/ State Dependent Network Flows. Journal of Combinatorial Optimization 5, 421–443 (2001). https://doi.org/10.1023/A:1011624708694
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DOI: https://doi.org/10.1023/A:1011624708694