Abstract
Two schemes of the branch-and-bound method for a flow shop total weighted tardiness minimization problem are proposed that differ in that a schedule in one scheme is constructed in a natural order (first, one chooses the first job in the schedule, then the second, etc.), whereas, in the second scheme, a schedule is constructed in the reverse order (first, one chooses the last job in the schedule, then the penultimate job, etc.). It is shown by numerical experiments that the efficiency of the methods essentially depends on the parameters of the problem, which can be easily calculated from the initial data. A criterion for choosing the most efficient method (from among the two) is proposed for any particular problem.
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References
K. R. Baker, Introduction to Sequencing and Scheduling (New York: Wiley, 1974).
W. Bozejko, M. Uchronski, and M. Wodecki, “Scatter search for a weighted tardiness flow shop problem,” in Multidisciplinary Int. Scheduling Conf. MISTA 2009, Dublin, Ireland, 10–12 August 2009; URL: http://staff.iiar.pwr.wroc.pl/wojciech.bozejko/papers/2009/MISTA-4pages.pdf, open access.
W. Bozejko and M. Wodecki, “Population-based heuristics for hard permutational optimization problems,” Int. J. Comput. Intell. Res. 2(2), 151 (2006).
K. Bulbul, Ph. Kaminsky, and C. Yano, “Flow shop scheduling with earliness, tardiness, and intermediate inventory holding costs,” Nav. Res. Logist. 51(3), 407 (2004).
V. A. Cicirello, “On the design of an adaptive simulated annealing algorithm,” First Workshop on Autonomous Search, Rhode Island, USA, 23 September 2007; URL: http://www.forevermar.com/SimA.pdf, open access.
A. R. Rahimi-Vahed and S. M. Mirghorbani, “A multi-objective particle swarm for a flow shop scheduling problem,” J. Combin. Optim. 13(1), 79 (2007).
T. Sen, J. M. Sulek, and P. Dileepan, “Static scheduling research to minimize total weighted and unweighted tardiness: A state-of-the-art survey,” Int. J. Prod. Econ. 3(1), 1 (2003).
J. K. Lenstra and A.H.G. Rinnooy Kan, “Complexity results for scheduling chains on a single machine,” Eur. J. Oper. Res. 96, 270 (1980).
O. Engin and A. Doyen, “A new approach to solve flowshop scheduling problems by artificial immune systems,” Future Gener. Comput. Syst. 20(6), 1083 (2004).
I. K. Agapeevich, V. R. Fazylov, “Generator of initial data for the total weighted tardiness minimization problem in flow shop systems,” in Issled. Prikl. Mat. Inf. (Kazan: Kazan Gos. Univ., 2011), Issue 27, pp. 3–7.
R. W. Conway, W. L. Maxwell, L. W. Miller, Theory of Scheduling (Reading: Addison-Wesley, 1967; Moscow: Nauka, 1975).
E. Ignall and L. Shrage, “Application of the Branch-and-Bound Technique to Some Flow-Shop Scheduling Problems,” Oper. Res. 13(3), 400 (1965).
V. R. Fazylov, Problem of a Manipulator of a Galvanic Line (Kazan: Kazan. Mat. O-vo, 2000).
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Original Russian Text © I.K. Agapeevich, V.R. Fazylov, 2012, published in Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, Vol. 154, No. 3, pp. 180–189.
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Agapeevich, I.K., Fazylov, V.R. Two schemes of the branch-and-bound method for a flow shop total weighted tardiness minimization problem. Lobachevskii J Math 34, 359–367 (2013). https://doi.org/10.1134/S199508021304001X
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DOI: https://doi.org/10.1134/S199508021304001X