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Formulation of fuzzy linear programming problems as four-objective constrained optimization problems

APPLIED MATHEMATICS AND COMPUTATION 2003年第2-3期139卷 383-399页

作者： Zhang, GQ Wu, YH Remias, M Lu, J Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia Univ Technol Sydney Dept Software Engn Broadway NSW Australia

This paper concerns the solution of fuzzy linear programming (FLP) problems which involve fuzzy numbers in coefficients of objective functions. Firstly, a number of concepts of optimal solutions to FLP problems are introduced and investigated. Then, a number of theorems are developed so as to convert the FLP to a multi-objective optimization problem with four-objective functions. Finally, two illustrative examples are given to demonstrate the solution procedure. It also shows that our method of solution includes an existing method as a special case, (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： optimization fuzzy number linear programming multi-objective linear programming

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An exact algorithm for biobjective mixed integer linear programming problems

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COMPUTERS & OPERATIONS RESEARCH 2016年 72卷 204-213页

作者： Soylu, Banu Yildiz, Gazi Bilal Erciyes Univ Dept Ind Engn TR-38039 Kayseri Turkey

In this study, we develop a new criterion space search algorithm to find the Pareto frontier of biobjective mixed-integer linear programming problems. Our algorithm starts with the solution of an individual objective function and then sequentially finds all Pareto line segments and points, which are the elements of the Pareto frontier, of biobjective mixed-integer linear programming problems. At each iteration of the algorithm, one line segment (or one isolated point) of the Pareto frontier is detected. If there is no new Pareto line segment available, the algorithm ends. We provide numerical examples and present performance results of the algorithm over several test problems. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： multi-objective linear programming Biobjective mixed-integer linear programming epsilon-constraint methodology Tabu constraint Hamming distance

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Application of analytic hierarchy process in multi-objective mixed integer programming for airlift capacity planning

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2006年第1期23卷 61-76页

作者： Stannard, B Zahir, S Rosenbloom, ES Univ Lethbridge Fac Management Lethbridge AB T1K 3M4 Canada Univ Manitoba IH Asper Sch Business Winnipeg MB R3T 2N2 Canada

The analytic hierarchy process is combined with multi-objective mixed integer programming to determine the optimal allocation of a limited number of aircraft among a group of airlift users with varying levels of priority and length of usage. Canadian Forces airlift planners typically encounter such a capacity planning problem. The solution to this problem requires the constrained assignment of n variable length missions (tasks) integrating hundreds of airlift requests from several users with many priorities to m airframes (parallel machines).

关键词： decision model AHP scheduling sequencing capacity planning multi-objective linear programming mixed integer programming

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Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives

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PRODUCTION PLANNING & CONTROL 2007年第7期18卷 548-560页

作者： Liang, T.-F. Hsiuping Inst Technol Dept Ind Engn & Management Dali City 412 Taichung Taiwan

Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.

关键词： possibilistic linear programming aggregate production planning fuzzy set theory multi-objective linear programming

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A fuzzy programming approach to energy resource allocation

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 1999年第4期23卷 303-317页

作者： Chedid, R Mezher, T Jarrouche, C Amer Univ Beirut Fac Engn & Architecture Beirut Lebanon

This paper presents a fuzzy multi-objective linear programming approach to serve the energy allocation problem. For this, nine energy resources and six household end uses are considered. An optimal solution will be extracted, and an explicit interactive sensitivity analysis will be dealt with. As the results obtained depend on the fuzzy nature of the objective functions and on the conflicting nature of some of the objectives among themselves, the proposed method can be regarded as a decision support tool for the decision makers who can be guided by its results to arrive at an appropriate solution interactively. It will be shown that optimization using fuzzy logic can provide the decision-makers with more flexibility that would assist them in the allocation of various resources to meet the various end-uses by studying the effects of several factors such as price variations, membership function shapes and membership function reference values. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： multi-objective linear programming fuzzy logic energy balance decision analysis

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A goal programming approach to lean production system implementation

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2023年第1期74卷 403-416页

作者： Karakutuk, S. Serhat Ornek, M. Arslan Yasar Univ Grad Sch Izmir Turkey Yasar Univ Dept Ind Engn Izmir Turkey

Companies use different production policies to ensure customer demands are satisfied in time. To track the performance of production policies some important Key Performance Indicators related to production control and management are On-Time Delivery (OTD), machine or line productivity (OEE - Overall Equipment Efficiency), optimization of inventory levels between workstations (WIP), customer satisfaction i.e. prioritization of customer orders according to requirements of the customer, and backlog minimization. In this study, a real-life production management problem is described, modelled, and solved to improve customer delivery rate and, to plan manufacturing orders using lean production tools. Currently, the Make-to-Stock policy is used for semi-finished materials. The problems encountered are low customer service level, high level of WIP between operations and efficiency losses. Therefore, the goal of this study is to increase efficiency (OTD, OEE, and customer satisfaction) by minimizing setup time, decreasing WIP by minimizing earliness, backlog quantity level and improving service level by minimizing lateness of orders. Since these goals contradict each other, we propose a multi-objective mathematical formulation with a setup carryover strategy. Then we formulate a Goal programming (GP) model and solve it by using different GP variants and the normalization method. Finally, we discuss numerical results and provide our final remarks and conclusions.

关键词： Goal programming multi-objective linear programming push pull scheduling lean production planning

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Possibility linear programming with trapezoidal fuzzy numbers

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APPLIED MATHEMATICAL MODELLING 2014年第5-6期38卷 1660-1672页

作者： Wan, Shu-Ping Dong, Jiu-Ying Jiangxi Univ Finance & Econ Coll Informat Technol Nanchang 330013 Jiangxi Peoples R China Jiangxi Univ Finance & Econ Jiangxi Key Lab Data & Knowledge Engn Nanchang 330013 Jiangxi Peoples R China Jiangxi Univ Finance & Econ Coll Stat Nanchang 330013 Jiangxi Peoples R China

Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Fuzzy linear programming Trapezoidal fuzzy number Triangular fuzzy number multi-objective linear programming

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multiple objective branch and bound for mixed 0-1 linear programming: Corrections and improvements for the biobjective case

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COMPUTERS & OPERATIONS RESEARCH 2013年第1期40卷 498-509页

作者： Vincent, Thomas Seipp, Florian Ruzika, Stefan Przybylski, Anthony Gandibleux, Xavier Univ Nantes CNRS UMR 6241 LINA F-44322 Nantes 03 France Univ Kaiserslautern Dept Math AG Optimizat D-67663 Kaiserslautern Germany

This work addresses the correction and improvement of Mavrotas and Diakoulaki's branch and bound algorithm for mixed 0-1 multiple objective linear programs. We first elaborate the issues encountered by the original algorithm and then propose a corrected version for the biobjective case using an exact representation of the nondominated set associated with an appropriate update procedure. Then we introduce several improvements using better bound sets and branching strategies and finally present some experiments to study the effectiveness of our propositions. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： multi-objective mixed integer programming Nondominated set Dominance filtering multi-objective linear programming Branch and bound

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Optimizing the environmental performance of integrated waste management scenarios by means of linear programming: a case study

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JOURNAL OF CLEANER PRODUCTION 2016年第Part4期112卷 3086-3096页

作者： Tascione, Valentino Mosca, Raffaele Raggi, Andrea Univ G DAnnunzio DEc Dept Econ Studies Pescara Italy

When municipal waste scenarios are compared by using Life Cycle Assessment, the comparison is usually carried out among a limited number of alternative scenarios identified in advance. Therefore, however accurate and broad the scenario definition may be, the scenario actually generating the lowest environmental impacts might just not be included among the alternatives proposed and analysed. To overcome this limitation, this paper proposes linear programming models developed to identify, among all the potential scenarios, the waste management scenario that minimises one particular environmental impact or a set of impacts at the same time, using environmental data from Life Cycle Assessment. Besides describing the proposed models, a concise overview of solution methods for multi-objective linear programming is provided. These models were tested in a case study and the results obtained are here presented and analysed. As a case-study, a suitable waste management system in the Abruzzo Region, Italy, was identified. In addition, a further hypothetical waste management context, also including an incinerator plant, was considered. Moreover, a sensitivity analysis was carried out to identify how changing distances to plants may affect optimal scenarios. As a result, different best-performing scenarios for the analysed waste management system were obtained, one for each single impact category considered, and one for each solution method adopted. Furthermore, the analysis of the hypothetical context shows how the introduction of an additional treatment plant could affect the system. Both distances and the solution methods used affect the results. The models developed could be used in decision-making processes to identify the best-performing scenario of a waste management system from the environmental point of view. The models are easy to apply and flexible, since they can be modelled according to the context to be analysed by introducing new factors. (C) 2015 Elsevier Ltd. Al

关键词： Life cycle assessment linear programming multi-objective linear programming Scenario optimization Waste management

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Applying fuzzy goal programming to project management decisions with multiple goals in uncertain environments

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EXPERT SYSTEMS WITH APPLICATIONS 2010年第12期37卷 8499-8507页

作者： Liang, Tien-Fu Hsiuping Inst Technol Dept Ind Engn & Management Dali City 412 Taichung Taiwan

In real-life situations, the project manager must handle multiple conflicting goals and these conflicting goals are normally fuzzy owing to information is incomplete and unavailable. This study develops a two-phase fuzzy goal programming (FGP) method for solving the project management (PM) decision problems with multiple goals in uncertain environments. The original multi-objective linear programming (MOLP) model designed here attempts to simultaneously minimize total project costs, total completion time and total crashing costs with reference to direct costs, indirect and contractual penalty costs, duration of activities and the constraint of available budget. An industrial case is implemented to demonstrate the feasibility of applying the proposed two-phase FGP method to practical PM decisions. The contribution of this study lies in presenting a fuzzy mathematical programming methodology to fuzzy multi-objective PM decisions, and provides a systematic decision-making framework that facilitates the decision maker to interactively adjust the search direction until the preferred efficient solution is obtained. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Project management multi-objective linear programming Fuzzy sets Fuzzy goal programming

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