Abstract
We consider linear programs in which the objective function (cost) coefficients are independent non-negative random variables, and give upper bounds for the random minimum cost. One application shows that for quadratic assignment problems with such costs certain branch-and-bound algorithms usually take more than exponential time.
Similar content being viewed by others
References
R.E. Burkard, “Locations with spatial interactions—Quadratic assignment problem“, in: R.L. Francis and Mirchandani, eds.,Discrete location theory (Academic Press, New York, 1984).
R.E. Burkard and U. Fincke, “The asymptotic probabilistic behaviour of quadratic sum assignment problems“,Zeitschrift für Operations Research 27 (1983) 73–81.
A.M. Frieze, “Complexity of a 3-dimensional assignment problem“,European Journal of Operational Research 13 (1983) 161–164.
A.M. Frieze and J. Yadegar, “On the quadratic assignment problem“,Discrete Applied Mathematics 5 (1983) 89–98.
M.R. Garey and D. S. Johnson,Computers and intractability (Freeman, San Francisco, 1979).
W. Hoeffding, “Probability inequalities for sums of bounded random variables“,Journal of the American Statistical Association 58 (1963) 13–30.
R.M. Karp, Lecture at the NIHE Summer School on Combinatorial Optimisation, Dublin, 1983.
C.J.H. McDiarmid, “On the greedy algorithm with random costs”, to appear.
D.W. Walkup, “On the expected value of a random assignment problem“,SIAM Journal on Computing 8 (1979) 440–442.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dyer, M.E., Frieze, A.M. & Mcdiarmid, C.J.H. On linear programs with random costs. Mathematical Programming 35, 3–16 (1986). https://doi.org/10.1007/BF01589437
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01589437