A New Approximate Algorithm for Solving Multiple Objective Linear Programming with Fuzzy Parameters

Many business decisions can be modeled as multiple objective linear programming (MOLP) problems. When formulating a MOLP problem, objective functions and constraints involve many parameters which possible values are assigned by the experts who are often imprecisely or ambiguously known. So, it would be certainly more appropriate to interpret the experts’ understanding of the parameters as fuzzy numerical data which can be represented by fuzzy numbers. This paper focuses on fuzzy multiple objective linear programming (FMOLP) problems with fuzzy parameters in any form of membership function in both objective functions and constraints. Based on the related results of fuzzy linear programming (FLP) and linear programming problems with fuzzy equality and inequality constraints proposed by Zhang et al, this paper firstly proposes related definitions and concepts about FMOLP problems with fuzzy parameters. It then proposes a new approximate algorithm developed for solving the corresponding MOLP problems and the FMOLP problems. Finally, the use of related concepts, theorems, and the proposed approximate algorithm is illustrated by an example involving different cases which include setting various iterate steps, tolerances, weights, and satisfaction levels

Crisp-linear-and Models in Fuzzy Multiple Objective Linear Fractional Programming

The aim of this paper is to introduce two crisp linear models to solve fuzzy multiple objective linear fractional programming problems. In a novel manner we construct two piece-wise linear membership functions to describe the fuzzy goal linked to a linear fractional objective. They are related to the numerator and denominator of the fractional objective function; and we show that using the fuzzy-and operator to aggregate them a convenient description of the original fractional fuzzy goal is obtained. Further on, with the help of the fuzzy-and operator we aggregate all fuzzy goals and constraints, formulate a crisp linear model, and use it to provide a solution to the initial fuzzy multiple objective linear fractional programming problem. The second model embeds in distinct ways the positive and negative information, the desires and restrictions respectively; and aggregates in a bipolar manner the goals and constraints. The main advantage of using the new models lies in the fact that they are linear, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals

A λ-cut and goal-programming-based algorithm for fuzzy-linear multiple-objective bilevel optimization

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a λ-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using λ-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a λ-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a λ-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm. © 2006 IEEE

A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

This paper presents a modification of Pal, Moitra and Maulik\u27s goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP) problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example

Fuzzy multi-objective optimisation for master planning in a ceramic supply chain

This is an Accepted Manuscript of an article published in International Journal of Production Research on 2012, available online: http://www.tandfonline.com/10.1080/00207543.2011.588267.In this paper, we consider the master planning problem for a centralised replenishment, production and distribution ceramic tile supply chain. A fuzzy multi-objective linear programming (FMOLP) approach is presented which considers the maximisation of the fuzzy gross margin, the minimisation of the fuzzy idle time and the minimisation of the fuzzy backorder quantities. By using an interactive solution methodology to convert this FMOLP model into an auxiliary crisp single-objective linear model, a preferred compromise solution is obtained. For illustration purposes, an example based on modifications of real-world industrial problems is used.This research has been carried out in the framework of a project funded by the Science and Technology Ministry of the Spanish Government, entitled 'Project of reinforcement of the competitiveness of the Spanish managerial fabric through the logistics as a strategic factor in a global environment' (Ref. PSE-370000-2008-8).Peidro Payá, D.; Mula, J.; Alemany Díaz, MDM.; Lario Esteban, FC. (2012). Fuzzy multi-objective optimisation for master planning in a ceramic supply chain. International Journal of Production Research. 50(11):3011-3020. https://doi.org/10.1080/00207543.2011.588267S301130205011Alemany, M.M.E.et al., 2010. Mathematical programming model for centralized master planning in ceramic tile supply chains.International Journal of Production Research, 48 (17), 5053–5074Beamon, B. M. (1998). Supply chain design and analysis: International Journal of Production Economics, 55(3), 281-294. doi:10.1016/s0925-5273(98)00079-6Chen, C.-L., & Lee, W.-C. (2004). Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices. Computers & Chemical Engineering, 28(6-7), 1131-1144. doi:10.1016/j.compchemeng.2003.09.014Chern, C.-C., & Hsieh, J.-S. (2007). A heuristic algorithm for master planning that satisfies multiple objectives. Computers & Operations Research, 34(11), 3491-3513. doi:10.1016/j.cor.2006.02.022Kreipl, S., & Pinedo, M. (2009). Planning and Scheduling in Supply Chains: An Overview of Issues in Practice. Production and Operations Management, 13(1), 77-92. doi:10.1111/j.1937-5956.2004.tb00146.xLai, Y.-J., & Hwang, C.-L. (1993). Possibilistic linear programming for managing interest rate risk. Fuzzy Sets and Systems, 54(2), 135-146. doi:10.1016/0165-0114(93)90271-iLi, X., Zhang, B., & Li, H. (2006). Computing efficient solutions to fuzzy multiple objective linear programming problems. Fuzzy Sets and Systems, 157(10), 1328-1332. doi:10.1016/j.fss.2005.12.003Mula, J., Peidro, D., Díaz-Madroñero, M., & Vicens, E. (2010). Mathematical programming models for supply chain production and transport planning. European Journal of Operational Research, 204(3), 377-390. doi:10.1016/j.ejor.2009.09.008Mula, J., Peidro, D., and Poler, R., 2010b. The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand.International Journal of Production Economics, In pressPark *, Y. B. (2005). An integrated approach for production and distribution planning in supply chain management. International Journal of Production Research, 43(6), 1205-1224. doi:10.1080/00207540412331327718Peidro, D., Mula, J., Poler, R., & Lario, F.-C. (2008). Quantitative models for supply chain planning under uncertainty: a review. The International Journal of Advanced Manufacturing Technology, 43(3-4), 400-420. doi:10.1007/s00170-008-1715-yPeidro, D., Mula, J., Poler, R., & Verdegay, J.-L. (2009). Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets and Systems, 160(18), 2640-2657. doi:10.1016/j.fss.2009.02.021Selim, H., Araz, C., & Ozkarahan, I. (2008). Collaborative production–distribution planning in supply chain: A fuzzy goal programming approach. Transportation Research Part E: Logistics and Transportation Review, 44(3), 396-419. doi:10.1016/j.tre.2006.11.001Selim, H., & Ozkarahan, I. (2006). A supply chain distribution network design model: An interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3-4), 401-418. doi:10.1007/s00170-006-0842-6Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193-214. doi:10.1016/j.fss.2007.08.010Haehling von Lanzenauer, C., & Pilz-Glombik, K. (2002). Coordinating supply chain decisions: an optimization model. OR Spectrum, 24(1), 59-78. doi:10.1007/s291-002-8200-3Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55. doi:10.1016/0165-0114(78)90031-

An integrated model for solving production planning and production capacity problems using an improved fuzzy model for multiple linear programming according to Angelov's method

Decision making has become a part of our everyday lives. The main apprehension is that almost all decision difficulties include certain criteria, which usually can be multiple or conflicting. Certainly, the production planning and production capacity development includes several parameters uncertainty such as fuzzy resource capacity, fuzzy demand and fuzzy production rate. This situation makes decision maker challenging to describe the objective crisply and at the end the real optimum solution cannot attained correctly. The Fuzzy model for multi-objective linear programming should be an suitable approach for dealing with the production planning and production capacity (PP& PC) problems. The PP& PC problem based on the fuzzy environment becomes even more sophisticated as decision makers try to consider multi-objectives, Therefore, this study attempts to propose a novel scheme which is capable of dealing with these obstacles in PP& PC problem. Intuitionistic Fuzzy Optimization (1FO) by implementing the optimization problem in an Intuitionistic Fuzzy Set (IFS) environment and considered the degrees of rejection of objective(s) and of constraints as the complement of satisfaction degrees. The aim of the research is to propose a new method capable of dealing with these obstacles in the PP & PC problem. It takes into account uncertainty and makes trade-offs between multiple conflicting goals simultaneously. To verify the validity of the proposed method, a case study of the fuzzy multi-objective model of the PP&PC is used. This research takes into account uncertainty and makes a comparison between multiple conflicting goals at the same time. Therefore, this study attempts to propose a new scheme which is the modified Angelov’s approach

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