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Goal programming in the context of the assignment problem and a computationally effective solution method

APPLIED MATHEMATICS AND COMPUTATION 2008年第1期200卷 34-40页

作者： Jahanshahloo, G. R. Afzalinejad, M. Univ Tafresh Fac Math Tafresh *** Iran Teacher Training Univ Fac Math Sci & Comp Engn Tehran *** Iran

This paper develops the goal programming technique to solve the multiple objective assignment problem. The required model is formulated and an appropriate solution method is presented. The proposed method, which is a decomposition method, exploits the total unimodularity feature of the assignment problem and effectively reduces the computational efforts. Some issues related to the efficiency of a GP solution are stated and some specialized techniques for detecting and restoring efficiency are proposed. (C) 2007 Elsevier Inc. All rights reserved.

关键词： goal programming assignment problem multi-objective programming Pareto efficiency Dantzig-Wolfe reformulation

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Compromise programming with Tchebycheff norm for discrete stochastic orders

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ANNALS OF OPERATIONS RESEARCH 2013年第1期211卷 433-446页

作者： Sitarz, Sebastian Univ Silesia Inst Math PL-40007 Katowice Poland

This paper presents a method of decision making with returns in the form of discrete random variables. The proposed method is based on two approaches: stochastic orders and compromise programming used in multi-objective programming. Stochastic orders are represented by stochastic dominance and inverse stochastic dominance. Compromise programming uses the augmented Tchebycheff norm. This norm, in special cases, takes form of the Kantorovich and Kolmogorov probability metrics. Moreover, in the paper we show applications of the presented methodology in the following problems: projects selections, decision tree and choosing a lottery.

关键词： multi-objective programming Compromise programming Tchebycheff norm Stochastic dominance

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A practical weight sensitivity algorithm for goal and multiple objective programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第1期213卷 238-245页

作者： Jones, Dylan Univ Portsmouth Dept Math Logist & Management Math Grp Portsmouth PO1 3HF Hants England

This paper presents a weight sensitivity algorithm that can be used to investigate a portion of weight space of interest to the decision maker in a goal or multiple objective programme. The preferential information required from the decision maker is an initial estimate of their starting solution, with an equal weights solution being used as a default if this is not available, and preference information that will define the portion of weight space on which the sensitivity analysis is to be conducted. The different types of preferential information and how they are incorporated by the algorithm are discussed. The output of the algorithm is a set of distinct solutions that characterise the portion of weight space searched. The possible different output requirements of decision makers are detailed in the context of the algorithm. The methodology is demonstrated on two examples, one hypothetical and the other relating to predicting cinema-going behaviour. Conclusions and avenues for future research are given. (C) 2011 Elsevier B.V. All rights reserved.

关键词： multi-objective programming Goal programming Preferential weight choice multiple criteria decision making

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A mathematical programming framework for energy planning in services' sector buildings under uncertainty in load demand: The case of a hospital in Athens

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ENERGY POLICY 2008年第7期36卷 2415-2429页

作者： Mavrotas, George Diakoulaki, Danae Florios, Kostas Georgiou, Paraskevas Natl Tech Univ Athens Sch Chem Engn Lab Ind & Energy Econ Athens 15780 Greece

The aim of this paper is to provide an integrated modeling and optimization framework for energy planning in large consumers of the services' sector based on mathematical programming. The power demand is vaguely known and the underlying uncertainty is modeled using elements from fuzzy set theory. The defined fuzzy programming model is subsequently transformed to an equivalent multi-objective problem, where the minimization of cost and the maximization of demand satisfaction are the objective functions. The Pareto optimal solutions of this problem are obtained using a novel version of the e-constraint method and represent the possibly optimal solutions of the original problem under uncertainty. In the present case, in order to select the most preferred Pareto optimal solution, the minimax regret criterion is properly used to indicate the preferred configuration of the system (i.e. the size of the installed units) given the load uncertainty. Furthermore, the paper proposes a model reduction technique that can be used in similar cases and further examines its effect in the final results. The above methodology is applied to the energy rehabilitation of a hospital in the Athens area. The technologies under consideration include a combined heat and power unit for providing power and heat, an absorption unit and/or a compression unit for providing cooling load. The obtained results demonstrate that, increasing the degree of demand satisfaction, the total annual cost increases almost linearly. Although data compression allows obtaining realistic results, the size of the proposed units might be slightly changed. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： multi-objective programming energy planning minimax regret

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Maximizing conservation and in-kind cost share: Applying Goal programming to forest protection

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JOURNAL OF FOREST ECONOMICS 2012年第3期18卷 207-217页

作者： Fooks, Jacob R. Messer, Kent D. Univ Delaware Dept Appl Econ & Stat Newark DE 19716 USA

This research evaluates the potential gains in benefits from using Goal programming to preserve forestland. Two- and three-dimensional Goal programming models are developed and applied to data from applicants to the U.S. Forest Service's Forest Legacy Program, the largest forest protection program in the United States. Results suggest that not only do these model yield substantial increases in benefits, but by being able to account for both environmental benefits and in-kind partner cost share, Goal programming may be flexible enough to facilitate adoption by program managers needing to account for both ecological and political factors. (C) 2012 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea. Published by Elsevier GmbH. All rights reserved.

关键词： Goal programming multi-objective programming Conservation optimization Forest conservation Environmental services In-kind cost sharing Matching grants

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A reduction dynamic programming algorithm for the bi-objective integer knapsack problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2013年第2期231卷 299-313页

作者： Rong, Aiying Figueira, Jose Rui ISEG Tech Univ Lisbon Cemapre Ctr Appl Math & Econ P-1200781 Lisbon Portugal Univ Tecn Lisboa CEG IST Ctr Management Studies Inst Super Tecn P-1049001 Lisbon Portugal

This paper presents a backward state reduction dynamic programming algorithm for generating the exact Pareto frontier for the hi-objective integer knapsack problem. The algorithm is developed addressing a reduced problem built after applying variable fixing techniques based on the core concept. First, an approximate core is obtained by eliminating dominated items. Second, the items included in the approximate core are subject to the reduction of the upper bounds by applying a set of weighted-sum functions associated with the efficient extreme solutions of the linear relaxation of the multi-objective integer knapsack problem. Third, the items are classified according to the values of their upper bounds;items with zero upper bounds can be eliminated. Finally, the remaining items are used to form a mixed network with different upper bounds. The numerical results obtained from different types of bi-objective instances show the effectiveness of the mixed network and associated dynamic programming algorithm. (C) 2013 Elsevier B.V. All rights reserved.

关键词： multi-objective programming Integer knapsack problem Dynamic programming Dominance relation Core concept State reduction

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Resource allocation in the North Sea demersal fisheries: A goal programming approach

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ANNALS OF OPERATIONS RESEARCH 2000年第P1期94卷 321-342页

作者： Mardle, S Pascoe, S Tamiz, M Jones, D Univ Portsmouth CEMARE Portsmouth PO4 8JF Hants England Univ Portsmouth Sch Comp & Math Studies Portsmouth PO1 2EG Hants England

The management of a fishery is a complex task generally involving multiple, often conflicting, objectives. These objectives typically include economic, biological and social goals such as improving the income of fishers, reducing the catch of depleted species and maintaining employment. multi-criteria decision making (MCDM) techniques appear well-suited to such a management problem, allowing compromises between conflicting objectives to be analysed in a structured framework. In comparison to other fields, such as water resource planning, forestry and agriculture, there have been few applications of MCDM to fisheries. In this paper, a goal programming model of the North Sea demersal fishery is presented. The model is used to demonstrate the potential applicability of this type of approach to the analysis and development of fisheries management plans with multiple objectives. Alternative scenarios are considered for the problem, and trade-offs between given objectives are also highlighted and discussed.

关键词： goal programming multi-objective programming fisheries North Sea

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Sustainable Management and Environmental Protection for Basin Water Allocation: Differential Game-based multiobjective programming

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WATER RESOURCES MANAGEMENT 2023年第1期37卷 1-20页

作者： Di, Danyang Shi, Qi Wu, Zening Wang, Huiliang Zhengzhou Univ Sch Water Conservancy Engn Zhengzhou Peoples R China

It is important to manage water resources via emergy theory and its implementation mechanism for water dispatching while considering both economic development and environmental needs. The contribution of this paper is to propose a multi-objective dynamic differential game that can determine the optimal tax rate (OTR), optimal trading quantity of water (OTQW) in each province, and optimal bargain price (OBP) to balance resource consumption, economic development and environmental protection. Considering the sustainability of the ecological environment, the quantification of negative sewage value and net carbon emission constraints are introduced into the water allocation. To maximize the target revenue functions, minimize the net carbon emission constraints and obtain sustainable equilibrium solutions in this triple-level game, the costate function, Hamiltonian, and Lagrangian multiplier method are introduced. Then, a water dispatching structure is constructed for error correction between the predicted and actual runoff of the YRB. Taking the Yellow River Basin as an example, the validity of the proposed framework and solution method were verified under different hydrological years, with 6.5% similar to 9.1% higher economic benefits than other schemes and 4.3% similar to 5.9% lower net carbon emissions than other schemes. Compared to previous studies, this scheme can better meet the requirements of sustainable development and environmental protection.

关键词： Sustainability Coordinated development Water allocation multi-objective programming

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Goal programming technique for solving fully interval-valued intuitionistic fuzzy multiple objective transportation problems

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SOFT COMPUTING 2020年第18期24卷 13955-13977页

作者： Malik, Manisha Gupta, S. K. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

In transportation problems, the cost depends on various irresistible factors like climatic conditions, fuel expenses, etc. Consequently, the transportation problems with crisp parameters fail to handle such situations. However, the construction of the problems under an imprecise environment can significantly tackle these circumstances. The intuitionistic fuzzy number associated with a point is framed by two parameters, namely membership and non-membership degrees. The membership degree determines its acceptance level, while the non-membership measures its non-belongingness (rejection level). However, a person, because of some hesitation, instead of giving a fixed real number to the acceptance and rejection levels, may assign them intervals. This new construction not only generalizes the concept of intuitionistic fuzzy theory but also gives wider scope with more flexibility. In the present article, a balanced transportation problem having all the parameters and variables as interval-valued intuitionistic fuzzy numbers is formulated. Then, a solution methodology based on goal programming approach is proposed. This algorithm not only cares to maximize the acceptance level of the objective functions but simultaneously minimizes the deviational variables attached with each goal. To tackle the interval-valued intuitionistic fuzzy constraints corresponding to each objective function, three membership and non-membership functions, linear, exponential and hyperbolic, are used. Further, a numerical example is solved to demonstrate the computational steps of the algorithm, and a comparison is drawn amidst linear, exponential and hyperbolic membership functions.

关键词： multi-objective programming Interval-valued triangular intuitionistic fuzzy numbers Fuzzy goal programming Expected value Membership functions

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Computation of some stochastic linear programming problems with Cauchy and extreme value distributions

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2005年第6期82卷 685-698页

作者： Sahoo, NP Biswal, MP Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

Stochastic programming is concerned with optimization problems in which some or all parameters are treated as random variables in order to capture the uncertainty which is almost always an inherent feature of the system being modelled. It is a methodology for allocating today's resources to meet tomorrow's unknown demands. A general approach to deal with uncertainty is to assign a probability distribution to the unknown parameters. The basic idea used in stochastic optimization is to convert the probabilistic model to an equivalent deterministic model. The resulting model is then solved by standard linear or non-linear programming methods. In this paper two probability distributions, the Cauchy distribution and the extreme value distribution, are introduced for stochastic programming. Two different approaches are applied to transform the probabilistic multi-objective linear programming problem into deterministic models. The computational procedures of the models are discussed.

关键词： stochastic linear programming multi-objective programming goal programming Cauchy distribution extreme value distribution computation

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