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On Optimal Non-Overlapping Segmentation and Solutions of Three-Dimensional Linear Programming Problems through the Super Convergent Line Series
Department of Statistics, University of Calabar, Calabar, Nigeria
Deparment of Statistics, University of Nigeria, Nsukka, Nigeria
- 1 Department of Statistics, University of Calabar, Calabar, Nigeria
- 2 Deparment of Statistics, University of Nigeria, Nsukka, Nigeria
American Journal of Operations Research·Volume 07 (2017)·Pages 225–238·Published 4 May 2017·DOI10.4236/ajor.2017.73015
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Abstract
The solutions of Linear Programming Problems by the segmentation of the cuboidal response surface through the Super Convergent Line Series methodologies were obtained. The cuboidal response surface was segmented up to four segments, and explored. It was verified that the number of segments, S, for which optimal solutions are obtained is two (S = 2). Illustrative examples and a real-life problem were also given and solved.
KeywordsAverage Information MatrixExperimental SpaceLine Search AlgorithmSupport PointsOptimal Solution
- Gass, S.I. (1958) Linear Programming Methods and Applications. McGraw-Hill, New York.
- Dantzig, G.B. (1963) Linear Programming and Extension. Princeton University Press, Princeton. https://doi.org/10.1515/9781400884179
- Philip, D.T., Walter, M. and Wright, M.H. (1981) Practical Optimization. Academic Press, London.
- Wilde, D.J. and Beightler, C.S. (1967) Foundations of Optimization. Prentice Hall Inc., Upper Saddle River.
- Myers, R.H. (1971) Response Surface Methodology. Allyn & Bacon, Boston.
- Onukogu, I.B. and Chigbu, P.E. (2002) Super Convergent Line Series (in Optimal Design of Experiment and Mathematical Programming). AP Express Publishing, Nsukka.
- Chigbu, P.E. and Ugbe, T.A. (2002) On the Segmentation of the Response Surfaces for Super Convergent Line Series Optimal Solutions of Constrained Linear and Quadratic Programming Problem. Global Journal of Mathematical Sciences, 1, 27-34.
- Chigbu, P.E. and Ukaegbu, E.C. (2007) On the Precision and Mean Square Error Matrices Approaches in Obtaining the Average Information Matrices via the Super Convergent Line Series. Journal of Nigerian Statistical Association, 19, 4-18.
- Etukudo, I.A. and Umoren, M.U. (2008) A Modified Super Convergent Line Series Algorithm for Solving Linear Programming Problems. Journal of Mathematical Sciences, 19, 73-88.
- Iwundu, M.P. and Hezekiah, J.E. (2014) Algorithmic Approach to Solving Linear Programming Problems on Segmented Regions. Asian Journal of Mathematics and Statistics, 7, 40-59. https://doi.org/10.3923/ajms.2014.40.59
- Iwundu, M.P. and Ebong, D.W. (2014) Modified Quick Convergent Inflow Algorithm for Solving Linear Programming Problems. International Journal of Probability and Statistics, 3, 54-66. https://doi.org/10.5539/ijsp.v3n4p54
- Ugbe, T.A. and Chigbu, P.E. (2014) On Non-Overlapping Segmentation of the Response Surfaces for Solving Constrained Programming Problems through Super Convergent Line Series. Communications in Statistics—Theory and Methods, 43, 306-320. https://doi.org/10.1080/03610926.2012.661510
- Grosan, C. and Abraham, A. (2007) Modified Line Search Method for Global Optimization. Proceeding of the 1st Asia International Conference of Modeling and Simulation, Phuket, 27-30 March 2007, 415-420. https://doi.org/10.1109/AMS.2007.68
- Andrei, N. (2008) Performance Profiles of Line Search Algorithm for Unconstrained Optimization. Research Institute for Informatics. Centre for Advance Modeling and Optimization, ICI Technical report. https://www.ici.ro/neculai/p12a08