Multi-Objective Programming and Goal Programming: Theories and Applications


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European Jour- nal of Operational Research, , Economica, 32, European Journal of Operational Research, 1, Journal of the Operational Research Society, 36, Bulletin of the Malaysian Mathematical Sciences Society, 26, Applied Mathematical Sciences, 6, Journal of Uncertainty Analysis and Applications, 2, 2- Omega, 29, Share This Article:. The paper is not in the journal. Go Back HomePage. DOI: Muhamad Safiih , A. Ateq Mezral. ABSTRACT This study introduces an alternative through two phases of goal programming to overcome the existing membership model problem that does not have a specific mathematical method to examine whether the receipt number of members is compatible with the criteria or characteristics that apply for membership through the lexicographic goal programming LGP and multi-choice goal programming with utility function MCGP-U.

It is applied for membership artificial data. The results indicate that both goal programming methods could meet the retail loyalty program membership modus operandi. Introduction The rising cost of living in Malaysia is not a foreign thing.

Multi-Objective Programming and Goal Programming

Equation 4 were subject to a utility function, , which could be written as: 5 where , membership size, , membership profile for i-th member, , reward redemption service provider profile. Membership Model Examination 3. Goal Programming Goal programming GP is a method that often used by the decision makers to solve their problem since introduced by Charnes and Cooper, [10]. The classic LGP model was introduced by Ignizio [12] are defined as follows: Definition Tamiz, [18] : A lexicographic minimization defined as a sequential minimization of each priority whilst maintaining the minimal values reached by all higher priority level minimizations.

The algebraic representation of LGP is given as: 6 subject to 7 where , j-th decision making variable, , coefficients in i-th goals or rigid constraint, and are respectively the negative and positive deviation for goal i, is the right hand side rigid constraint for i oraspiration goal for i, a is the achievement vector for the LGP and is where is usually a linear function of the weighted, unwanted deviation variables at priority level k and K is the lowest priority level.

Right linear utility function RLUF used in this study [8] could be depicted as follows: Proposition 1: P1 and the level of utility achieved in the RLUF Figure 1 are equivalent or have same optimal solutions. This case can be formulated as follows: Figure 1. Conflicts of Interest The authors declare no conflicts of interest. Cite this paper Safiih, L. Theoretical Economics Letters , 6 , References [ 1 ] Ateq Mezral, A.

Integration of Two-Phase Goal Programming to Examine the Effectiveness of Membership Model

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Multi-Objective Problems

TEL Most popular papers. History Issue. Frequently Asked Questions. Recommend to Peers. Recommend to Library. Contact Us. All Rights Reserved. Ateq Mezral, A. Konishi, H. Sandler, T. Abbas, A. Yang, J. Ignizio, J. Chang, C. Buchanan, J. Charnes, A. Badri, M. Norsida, H.

Theory and Applications

Hassan, N. Maity, G. Romero, C. Tamiz, M.

Beyond the Numbers

Submission System Login. There are also algorithms to determine the set of all maximal efficient faces [2]. Based on these goals, the set of all efficient extreme points can seen to be the solution of MOLP. This type of solution concept is called decision set based [3]. It is not compatible with an optimal solution of a linear program but rather parallels the set of all optimal solutions of a linear program which is more difficult to determine. Efficient points are frequently called efficient solutions. This term is misleading because a single efficient point can be already obtained by solving one linear program, such as the linear program with the same feasible set and the objective function being the sum of the objectives of MOLP [4].

More recent references consider outcome set based solution concepts [5] and corresponding algorithms [6] [3]. Assume MOLP is bounded, i. A formal definition of a solution [5] [7] is as follows:.


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If MOLP is not bounded, a solution consists not only of points but of points and directions [7] [8]. Multiobjective variants of the simplex algorithm are used to compute decision set based solutions [1] [2] [9] and objective set based solutions. Objective set based solutions can be obtained by Benson's algorithm. Multiobjective linear programming is equivalent to polyhedral projection. From Wikipedia, the free encyclopedia. Mathematical Programming.

Journal of Optimization Theory and Applications.


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