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A Primal Simplex Algorithm for Solving Linear Programming Problem with Grey Cost Coefficients | ||
| Journal of New Researches in Mathematics | ||
| همکاران ، دوره 1، شماره 4، اردیبهشت 2016، صفحه 115-135 اصل مقاله (672.5 K) | ||
| نویسندگان | ||
| S.H. Nasseri* 1؛ A. Yazdani2؛ D. Darvishi Salokolaei2 | ||
| 1Faculty of Mathematical Sciences, Mazandaran University, Babolsar, Iran Corresponding author | ||
| 2Faculty of Mathematical Sciences, Mazandaran University, Babolsar, Iran | ||
| چکیده | ||
| an extension of the classical linear programming problem to an inexact environment as well as fuzzy and stochastic environment. Hence, here a new approach for solving interval grey number linear programming problems is introduced without converting them to classical linear programming problems. The proposed method is established based on the primal simplex algorithm where the cost coefficient row includes grey numbers. As an essential tool in the solving process, a theoretical discussion on grey arithmetic and in particular an ordering role for grey numbers is necessary to evaluate the optimality conditions of a candidate feasible solution. It is also emphasized that the discussed model and the solution process is useful for real situations and practical cases, when a kind of the grey number linear programming is appeared, such as Water Resource Management and Planning, Economics, etc. Finally, the proposed approach is illustrated by a numerical example. | ||
| کلیدواژهها | ||
| Grey linear programming؛ Grey System Theory؛ Interval Grey number؛ Primal simplex algorithm؛ Uncertainty | ||
| مراجع | ||
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[1] Bai, Y., Wang, P. and Xie, J. (2014). Optimization of Urban Water Supply Schemes based on Grey System Theory. International Journal of Control and Automation, 7(9), 239-246. [2] Bhattacharyya, R. (2015). A grey theory based multiple attribute approach for R & D project portfolio selection. Fuzzy Information and Engineering, 7, 211-225. [3] Chang, N.B. and Wang, S.F. (1995). A grey nonlinear programming approach for planning coastal waste water treatment and disposal systems. Water Science Technology, 32, 19–29. [4] Chang, N.B., Wen, G.G., Cheng, Y.L. and Yong, Y.C. (1996). A grey fuzzy mutiobjective programming approach for the optimal planning of a reservoir watershed part a: theoretical development. Water Research, 30, 2329–2324. [5] Chen, Z., Chen, Q., Chen, W. and Wang, Y. (2004). Grey linear programming. Kybernetes, 33(2), 238-246. [6] Chen, M.Y. and Wu, S.H. (1993). Linear programming with grey forecasting. Proceedings of International AMSE Conference, Applied Modeling and Simulation, 3-8. | ||
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