A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

Sultan, T. I.; Emam, O. E.; Abohany, A. A.
September 2014
Applied Mathematics & Information Sciences;2014, Vol. 8 Issue 5, p2217
Academic Journal
This paper presents a three level large scale linear programming problem in which the objective functions at every level are to be maximized. A three level programming problem can be thought as a static version of the Stackelberg strategy. An algorithm for solving a three planner model and a solution method for treating this problem are suggested. At each level we attempt to optimize its problem separately as a large scale programming problem using Dantzig and Wolfe decomposition method. Therefore, we handle the optimization process through a series of sub problems that can be solved independently. Finally, a numerical example is given to clarify the main results developed in this paper.


Related Articles

  • An optimization algorithm for solving a class of multiplicative problems. Hongwei Jiao; Kun Li; Jianping Wang // Journal of Chemical & Pharmaceutical Research;2014, Vol. 6 Issue 1, p271 

    In this paper, by using new linearization method we present an optimization algorithm for globally solving a class of multiplicative problems which have a broad application in computational chemistry, information technology, and so on. By utilizing characteristic of quadratic function, a series...

  • Chaotic Harmony Search Algorithm with Different Chaotic Maps for Solving Assignment Problems. Abdel-Raouf, Osama; El-henawy, Ibrahim; Abdel-Baset, Mohamed // International Journal of Computer Applications;Jan2014, Vol. 86, p8 

    This paper presents an improved version of a harmony meta-heuristic algorithm with different chaotic maps, (IHSCH), for solving the linear assignment problem. The proposed algorithm uses chaotic behavior to generation a candidate solution in a behavior similar to acoustic monophony. Numerical...

  • Outcome Space Branch and Bound Algorithm for Globally Solving A Class of Linear Multiplicative Programming. Jingben Yin; Jing Chen // International Journal of Digital Content Technology & its Applic;Jan2013, Vol. 7 Issue 1, p167 

    This article present an outcome space branch and bound algorithm for globally solving a class of multiplicative programming problems. The main computation involve in solving the series of linear programming problems, and the algorithm economizes the required computations by conducting the branch...

  • Relaxation Method for Globally Solving a Class of Multiplicative Programming Problems. Yunrui Guo; Jing Chen; Jingben Yin // International Journal of Digital Content Technology & its Applic;Jan2013, Vol. 7 Issue 1, p178 

    This article present a branch and bound algorithm for globally solving a class of multiplicative problems by using relaxation method. By utilizing character of bilinear function, a sequence of linear relaxation programming of the initial non-convex programming problem are derived which are...

  • Multiattribute decision making models and methods using interval-valued fuzzy sets. Hongmei Ju; Fenghua Qi // Journal of Chemical & Pharmaceutical Research;2014, Vol. 6 Issue 7, p465 

    The concept of interval-valued fuzzy sets is the generalization of the concept of fuzzy sets. The theory of interval-valued fuzzy sets is well suited to dealing with vagueness. Recently, interval-valued fuzzy sets have been used to build soft decision making models that can accommodate imprecise...


    This paper describes a numerical method to optimize elastic bodies featuring a locally periodic microscopic pattern. A new idea, of optimizing the periodicity cell itself, is considered. In previously published works, the authors have found that optimizing the shape and topology of the model...

  • A algorithm based on the PSS splitting for saddle-point problems. Tong Qiujuan // Journal of Chemical & Pharmaceutical Research;2014, Vol. 6 Issue 7, p503 

    We present a algorithm based on the PSS splitting for the saddle-point problems in this paper, and analysis the convergence of the new method. The results supported by numerical experiments show that the new method outperform the existing classical iterative methods.

  • A two-stage and bi-level stochastic programming for customer involvement in engineer-to-order product design decision. Kristianto, Yohanes // Annual International Conference on Operations Research & Statist;2013, p44 

    A product configuration needs to consider the stochastic of customer decision process. However, it is a challenge to tackle this issue in an Engineer-to-order (ETO) manufacturing. The objective of this article is to construct generic product and routing (GPR) for manufacturing the ETO products...

  • Polynomially Computable Bounds for the Probability of the Union of Events. Boros, Endre; Scozzari, Andrea; Tardella, Fabio; Veneziani, Pierangela // Mathematics of Operations Research;Nov2014, Vol. 39 Issue 4, p1311 

    We consider the problem of finding upper and lower bounds for the probability of the union of events when the probabilities of the single events and the probabilities of the intersections of up to m events are given. It is known that the best possible bounds can be obtained by solving linear...


Other Topics