A Feasible Method for a Class of Mathematical Problems in Manufacturing System

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Abstract:

In this paper a feasible method is proposed for solving a class of mathematical problems in manufacturing system and production system. By utilizing linearization technique the relaxation programming problem about the original problem is constructed. The proposed branch and bound algorithm is convergent to the global minimum of original problem through the successive refinement linear relaxation of the feasible region of objective function and solutions of a series of relaxation linear programming problem. And large number of experiments results show feasibility of presented method.

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Key Engineering Materials (Volumes 460-461)

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806-809

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January 2011

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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[1] S. Schaible, J. Shi, Recent developments in fractional programming: single ratio and maxmin cale, Proc. 3rd Intl. Conf. Nonlinear Anal. Convex Anal. 2003: 493-506.

Google Scholar

[2] I. Ahmad, Z. Husain, Duality in nondifferentiable minimax fractional programming with generalized convexity, Appl. Math. Comput., 2006, 176: 545-551.

DOI: 10.1016/j.amc.2005.10.002

Google Scholar

[3] S. Schaible, Fractional programming, in R. Horst and P.M. Pardalos (eds. ), Handbook of Global Optimization, Kluwer Academic Publishers, Dordrecht-Boston-London, 1995, 168: 495-608.

Google Scholar

[4] K. Sekitani, J. Shi and Y. Yamamoto, General fractional programming: min-max convexconvex quadratic case, in M. Fushimi and K. Tone (eds), Proceedings of APORS'94, Development in Diversity and Harmony, World Scientific, Singapore, 1995, 505-514.

DOI: 10.1142/9789814533102

Google Scholar

[5] H.P. Benson. On the global optimization of sums of linear fractional functions over a convex set. J. Optim. Theory Appl., 2004, 121: 19-39.

DOI: 10.1023/b:jota.0000026129.07165.5a

Google Scholar

[6] H. Konno, K. Fukaisi. A branch and bound algorithm for solving low rank linear multiplicative and fractional programming problems. J. Glob. Optim., 2000, 18: 283-299.

Google Scholar

[7] Y. Wang, P. Shen, Liang Z A. A branch-and-bound algorithm to globally solve the sum of several linear ratios, Appl. Math. Comput., 2005, 168: 89-101.

DOI: 10.1016/j.amc.2004.08.016

Google Scholar

[8] T. N. Hoai-Phung, H. Tuy. A unified monotonic approach to generalized linear fractional programming. J. Glob. Optim., 2003, 26: 229-259.

Google Scholar