TOPSIS Approach for Solving Bi-Level Non-Linear Fractional MODM Problems

TOPSIS (technique for order preference similarity to ideal solution) is considered one of the known classical multiple criteria decision making (MCDM) methods to solve bi-level non-linear fractional multi-objective decision making (BL-NFMODM) problems, and in which the objective function at each level is considered nonlinear and maximization type fractional functions. The proposed approach presents the basic terminology of TOPSIS approach and the construction of membership function for the upper level decision variable vectors, the membership functions of the distance functions from the positive ideal solution (PIS) and of the distance functions from the negative ideal solution (NIS). Thereafter a fuzzy goal programming model is adopted to obtain compromise optimal solution of BL-NFMODM problems. The proposed approach avoids the decision deadlock situations in decision making process and possibility of rejecting the solution again and again by lower level decision makers. The presented TOPSIS technique for BL-NFMODM problems is a new fuzzy extension form of TOPSIS approach suggested by Baky and Abo-Sinna (2013) (Applied Mathematical Modelling, 37, 1004-1015, 2013) which dealt with bi -level multi-objective decision making (BL-MODM) problems. Also, an algorithm is presented of the new fuzzy TOPSIS approach for solving BL-NFMODM problems. Finally, an illustrative numerical example is given to demonstrate the approach

Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy Parameters: A FGP Approach

The motivation behind this paper is to present multi-level multi-objective quadratic fractional programming (ML-MOQFP) problem with fuzzy parameters in the constraints. ML-MOQFP problem is an important class of non-linear fractional programming problem. These type of problems arise in many fields such as production planning, financial and corporative planning, health care and hospital planning. Firstly, the concept of the -cut and fuzzy partial order relation are applied to transform the set of fuzzy constraints into a common crisp set. Then, the quadratic fractional objective functions in each level are transformed into non-linear objective functions based on a proposed transformation. Secondly, in the proposed model, separate non-linear membership functions for each objective function of the ML-MOQFP problem are defined. Then, the fuzzy goal programming (FGP) approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach

A fuzzy goal programming approach to solving decentralized bi-level multi-objective linear fractional programming problems

This paper presents a new approach for solving decentralized bi-level multi-objective linear fractional programming problems. The main goal was to find a simple algorithm with high confidence of decision-makers in the results. First, all the linear fractional programming models on the given set of constraints were solved separately. Next, all the linear fractional objective functions were linearized, membership functions of objective functions and decision variables controlled by decision-makers at the highest level calculated, and a fuzzy multi-objective linear programming model formed and solved as linear goal programming problem by using simplex algorithm. The efficiency of the proposed algorithm was investigated using an economic example, and the obtained results compared with those obtained using an existing method

Integration of an Improved Grey-Based Method and Fuzzy Multi-Objective Model for Supplier Selection and Order Allocation

For multi-attribute decision making (MADM) problems, a grey based approach (LI) had been developed to evaluate, rank and select the best suppliers. The method calculates a grey possibility degree between compared suppliers alternatives set and positive ideal referential alternative. The drawback of the method is that the negative ideal referential alternative is not considered in evaluating and ranking of the alternatives. Moreover, the method can only consider interval fuzzy number as input data and real number is neglected. Based on this model and other MADM methods, all demand was sold by the best supplier. In other cases, if the best supplier cannot satisfy all demand, multi-objective programming is used to formulate the problem and assign optimum order quantities to the best suppliers (multi-sourcing). Some techniques, such as goal programming (GP) approach, ε-Constraint method, Reservation level (RL) driven Tchebycheff procedure (RLTP) method had been proposed to solve the multi-objective models. It may be a problem that these techniques traced back to more than 10 years ago. Therefore, there may be still the need to produce a new technique in order to solve the multi-objective models. In this study, to overcome the first drawback, the LI method was improved based on the concepts of technique for order preference by similarity to ideal solution (TOPSIS) to consider both the positive and the negative ideal referential alternative for evaluation of the suppliers. The improved version of the LI method is called the I.LI method. Based on the concepts of TOPSIS, the chosen alternative should have the shortest distance from the positive ideal solution and the farthest from the negative ideal solution. Moreover, in order to solve the problems, a new grey based method (NG) based on the TOPSIS concepts was proposed that can easily consider both interval fuzzy number and real number simultaneously. Afterwards, an innovative comparative approach was proposed to compare the three MADM methods, the LI, the I.LI and the NG methods, and to show that which method is more optimal than the other methods. Subsequently, in this thesis, an integration of the NG method and fuzzy multi-objective model was suggested for multi-sourcing and multi-product supplier selection problem. The score of suppliers calculated by the NG method was served as coefficients in one objective function of the multi-objective model. In this fuzzy multi-objective model, the products are divided into two independent and dependent products so that (1) the price breaks (discounts) depend on the size of the order quantities, (2) independent products’ sales volume affect the prices and discounts of the dependent products and (3) all products must be sold as a bundle. Finally, to overcome the third problem, a new weighted additive function, which is able to consider relative importance of each objective as well as condition of fuzzy situation, is proposed to solve the fuzzy multi-objective model and assign optimum order quantities to the suppliers evaluated and ranked by the NG method. The results of the innovative comparative approach showed that the result of the NG method is more optimal than the I.LI method and the latter is more optimal than the LI method. Therefore, the NG method was selected to be integrated with the fuzzy multi-objective model. Also, the fuzzy multi-objective model was solved by the new weighted additive function, and the results demonstrated that besides considering the relative importance of the objectives, the new technique is also able to consider the condition of fuzzy situation

Penghasilan manual rjngkas penggunaan alat Total Station Sokkia Set5f dan Perisian Sdr Mapping & Design untuk automasi ukur topografi

Projek ini dilaksanakan untuk menghasilkan manual ringkas penggunaan alat Total Station Sokkia SET5F dan Perisian SDR Mapping & Design dalam menghasilkan pelan topografi yang lengkap mengikut konsep field to finish. Manual telah dihasilkan dalam dua bentuk iaitu buku dan CD-ROM. Manual ini telah dinilai berdasarkan data yang diperolehi daripada 7 orang responden melalui kaedah Borang Penilaian Manual. Analisis data dilakukan menggunakan perisian SPSS versi 11.0. Hasil analisis skor min menunjukkan kesemua responden bersetuju bahawa manual dalam bentuk buku ini menarik Min ( M ) ^ ^ dan Sisihan Piawai (SD) = .535 tetapi kurang interaktif (M) = 2.29 dan (SD) = 0.488. Berbanding dengan manual dalam format CD-ROM yang mencatat nilai (M) = 3.57 dan (SD) = 0.535 semua responden bersetuju bahawa manual ini mesra pengguna dan lebih interakti

The Project Scheduling Problem with Non-Deterministic Activities Duration: A Literature Review

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration.Peer Reviewe