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A multi-objective programming approach to 1.5-dimensional assortment problem

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第1期179卷 64-79页

作者： Gasimov, Rafail N. Sipahioglu, Aydin Sarac, Tugba Eskisehir Osmangazi Univ Dept Ind Engn TR-26030 Bademlik Eskisehir Turkey

In this paper we study a 1.5-dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations. We propose a new multi-objective mixed integer linear programming (MILP) model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders. An equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes, have also been considered. A new method called the conic scalarization is proposed for scalarizing non-convex multi-objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches. (c) 2006 Elsevier B.V. All rights reserved.

关键词： cutting 1.5-dimensional assortment problem multi-objective programming weighted sum scalarization conic scalarization mixed integer linear programming

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multi-objective Dispatching Model and Algorithm of Railway Emergency Materials

Multi-objective Dispatching Model and Algorithm of Railway E...

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2012 IEEE 3rd International Conference on Emergency Management and ManagementSciences(ICEMMS 2012)

作者： Yanchun Zhang School of Civil Engineering, Central South University, Hunan, Changsha, 410004, China Mengjun Wang School of Civil Engineering, Central South University, Hunan, Changsha, 410004, China

In order to solve the problem of railway emergency materials dispatching optimization considering the difference of the emergency time limit of the materials, the uniqueness of this problem is analyzed and a multi-objective dispatching model is established with multi-objective programming method. On base of satisfying the requirement of emergency time limit of different materials, the model achieves the objectives of minimum number of selected depots and minimum cost of dispatching. Then the solution procedure and algorithm of the model is designed and an example is set to verify the feasibility of this algorithm. Analytic results indicate that the model can ensure utilizing and dispatching the emergency materials efficiently and methodically.

关键词： railway transportation economics emergency materials multi-objective programming dispatching.

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A fuzzy multi-objective programming for optimization of fire station locations through genetic algorithms

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期181卷 903-915页

作者： Yang, Lili Jones, Bryan F. Yang, Shuang-Hua Univ Loughborough Sch Business Loughborough LE11 3TU Leics England Univ Derby Appl Comp Dept Derby DE22 1GB England Univ Loughborough Dept Comp Sci Loughborough LE11 3TU Leics England

Location of fire stations is an important factor in its fire protection capability. This paper aims to determine the optimal location of fire station facilities. The proposed method is the combination of a fuzzy multi-objective programming and a genetic algorithm. The original fuzzy multiple objectives are appropriately converted to a single unified 'min-max' goal, which makes it easy to apply a genetic algorithm for the problem solving. Compared with the existing methods of fire station location our approach has three distinguish features: (1) considering fuzzy nature of a decision maker (DM) in the location optimization model;(2) fully considering the demands for the facilities from the areas with various fire risk categories;(3) being more understandable and practical to DM. The case study was based on the data collected from the Derbyshire fire and rescue service and used to illustrate the application of the method for the optimization of fire station locations. (c) 2006 Elsevier B.V. All rights reserved.

关键词： location fire stations multi-objective programming genetic algorithm fuzzy programming

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programming Problems with a Large Number of objective Functions

Programming Problems with a Large Number of Objective Functi...

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International Conference on Numerical Methods and Applications

作者： Resteanu, Cornel Trandafir, Romica Natl Inst Res & Dev Informat 8-10 Averescu Ave Bucharest 011455 1 Romania Tech Univ Civil Engn Bucharest 020396 Romania

ISBN: (纸本)9783642184659

The paper treats the multi-objective programming problem with a large composite set of (linear and nonlinear) objective functions, the domain of feasible solutions being defined by a set of linear equalities/inequalities representing a large scale problem. One constructs a preferred solution i.e. a non-dominated solution chosen via extending the decision-making framework. A feasible approach, for this class of problems, is to use a solver for the Linear programming problems and a solver for multiple Attribute Decision Making problems in combination with Parallel and Distributed Computing techniques based on a GRID configuration.

关键词： multi-objective programming Large Scale Problems multiple Attribute Decision Making Parallel and Distributed Computing GRID Nets

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objective programming Approach to Food Supply-chain Theory

Objective Programming Approach to Food Supply-chain Theory

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International Conference on Environmental Biotechnology and Materials Engineering

作者： Wang-Qiang Zhang-Yu Harbin Univ Commerce Sch Management Harbin Peoples R China Harbin Univ Commerce Sch Basic Sci Harbin Peoples R China

ISBN: (纸本)9783037850220

Contemporary food supply chains are generating externalities with high economic and social costs, notably in public health terms through the rise in diet-related non-communicable disease. A decision making model of multi-product multi-stage food supply-chain consisted of single manufacturer and single supplier is proposed in this article. The model is proved to be superior and efficient through application example. Reasonable decisions are suggested by analyzing the solution of dual problem. The decisions could help members of food supply-chain get more profits.

关键词： food supply-chain management multi-objective programming dual problem

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An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期201卷 390-398页

作者： Charles, V. Udhayakumar, A. Uthariaraj, V. Rhymend Pontificia Univ Catolica Peru CTR Catolica Santiago De Surco Peru Hindustan Coll Engn Dept Comp Applicat Madras 603103 Tamil Nadu India Anna Univ Ramanujan Comp Ctr Madras 600025 Tamil Nadu India

Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundancy in constraints and variables are usually studied in a class of mathematical programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective function(s) and redundant constraint(s) simultaneously in multi-objective nonlinear stochastic fractional programming problems is provided. A solution procedure is also illustrated with numerical examples. The proposed algorithm reduces the number of nonlinear fractional objective functions and constraints in cases where redundancy exists. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Stochastic programming Fractional programming multi-objective programming Redundancy

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Using the idea of expanded core for the exact solution of bi-objective multi-dimensional knapsack problems

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JOURNAL OF GLOBAL OPTIMIZATION 2011年第4期49卷 589-606页

作者： Mavrotas, George Figueira, Jose Rui Antoniadis, Alexandros Natl Tech Univ Athens Athens 15780 Greece Inst Super Tecn Dept Engn & Gestao P-2780990 Porto Salvo Portugal

We propose a methodology for obtaining the exact Pareto set of Bi-objective multi-Dimensional Knapsack Problems, exploiting the concept of core expansion. The core concept is effectively used in single objective multi-dimensional knapsack problems and it is based on the "divide and conquer" principle. Namely, instead of solving one problem with n variables we solve several sub-problems with a fraction of n variables (core variables). In the multi-objective case, the general idea is that we start from an approximation of the Pareto set (produced with the multi-Criteria Branch and Bound algorithm, using also the core concept) and we enrich this approximation iteratively. Every time an approximation is generated, we solve a series of appropriate single objective Integer programming (IP) problems exploring the criterion space for possibly undiscovered, new Pareto Optimal Solutions (POS). If one or more new POS are found, we appropriately expand the already found cores and solve the new core problems. This process is repeated until no new POS are found from the IP problems. The paper includes an educational example and some experiments.

关键词： Knapsack problem multi-objective programming Core Exact algorithm

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An Electric Energy Balancing Model in a Medium Enterprise Grid

An Electric Energy Balancing Model in a Medium Enterprise Gr...

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Asia-Pacific Power and Energy Engineering Conference (APPEEC)

作者： Wang, Zhaojie Wang, Fei Gao, Feng Zhai, Qiaozhu Zhou, Dianmin Xi An Jiao Tong Univ SKLMS MOE KLINNS Syst Engn Inst Xian Peoples R China Baoshan Iron & Steel Co Ltd Baosteel Branch Energy Dept Shanghai Peoples R China

ISBN: (纸本)9781424462551

In the smart grid environment, appropriate power energy exchange strategies will be necessary for energy intensive industries (EIIs) with industrial power plants. This paper presents a systematic approach that can cope with the integration of industry consumers and an energy exchange strategy aiming at achieving balance between power production and consumption in EIIs. A basic balance model using Linear programming (LP) is built and the generation levels of thermal units are obtained. The solution is further improved to provide a more smooth power output curve. The ramping constraints of thermal units are addressed to ensure the result obtained is energy realizable. Penalty terms are also introduced in the objective function to reduce the level of power energy exchange between EII and the grid. Finally, numerical tests are performed and the simulation results for a real system suggest that the method presented is effective.

关键词： industry demand side energy balance rolling optimization linear programming multi-objective programming

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A Linear programming Priority Method for a Fuzzy Transportation Problem with Non-linear Constraints - The Case of a General Contractor Company

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FUZZY INFORMATION AND ENGINEERING 2011年第2期3卷 193-208页

作者： Barough, Hossein Abdollahnejad Payame Noor Univ Dept Ind Engn Tehran Iran

Demand and supply pattern for most products varies during their life cycle in the markets. In this paper, the author presents a transportation problem with non-linear constraints in which supply and demand are symmetric trapezoidal fuzzy value. In order to reflect a more realistic pattern, the unit of transportation cost is assumed to be stochastic. Then, the non-linear constraints are linearized by adding auxiliary constraints. Finally, the optimal solution of the problem is found by solving the linear programming problem with fuzzy and crisp constraints and by applying fuzzy programming technique. A new method proposed to solve this problem, and is illustrated through numerical examples. multi-objective goal programming methodology is applied to solve this problem. The results of this research were developed and used as one of the Decision Support System models in the Logistics Department of Kayson Co.

关键词： Fuzzy transportation Non-linear programming multi-objective programming Fuzzy linear programming Stochastic programming

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Alternative targets for data envelopment analysis through multi-objective linear programming: Rio de Janeiro Odontological Public Health System Case Study

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2007年第7期58卷 865-873页

作者： Frota Neto, J. Quariguasi Angulo-Meza, L. Erasmus Univ Rotterdam Sch Management NL-3000 DR Rotterdam Netherlands Univ Fed Fluminense Rio De Janeiro Brazil

In the last 10 years much has been written about the drawbacks of radial projection. During this time, many authors proposed methods to explore, interactively or not, the efficient frontier via non-radial projections. This paper compares three families of data envelopment analysis (DEA) models: the traditional radial, the preference structure and the multi-objective models. We use the efficiency analysis of Rio de Janeiro Odontological Public Health System as a background for comparing the three methods through a real case with one integer and one exogenous variable. The objectives of the study case are ( i) to compare the applicability of the three approaches for efficiency analysis with exogenous and integer variables, (ii) to present the main advantages and drawbacks for each approach, (iii) to prove the impossibility to project in some regions and its implications, (iv) to present the approximate CPU time for the models, when this time is not negligible. We find that the multi-objective approach, although mathematically equivalent to its preference structure peer, allows projections that are not present in the latter. Furthermore, we find that, for our case study, the traditional radial projection model provides useless targets, as expected. Furthermore, for some parts of the frontier, none of the models provide suitable targets. Other interesting result is that the CPU-time for the multi-objective formulation, although its endogenous high complexity, is acceptable for DEA applications, due to its compact nature.

关键词： data envelopment analysis multi-objective programming optimization

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