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Some Recent Results in parametric Semi-Infinite programming

Optimization 1995年第4期32卷 359-372页

作者： Hettich, R. Universitaet Trier Trier 54286 Germany

In this tutorial paper we present some recent developments in parametric semi-infinite programming. We mainly focus our attention to two problems: The determination of one-sided derivatives of the value-function with a special application to the problem of finding zeros of that function and, secondly, the problem of following a path of solutions. For the latter, a continuation method is presented which can be shown to be applicable to an open and dense class of problems. © 1995, Taylor & Francis Group, LLC. All rights reserved.

关键词： Derivatives of value function parametric programming Path-following methods Semi-infinite programming

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STABILITY IN DISTRIBUTION PROBLEMS OF NONLINEAR STOCHASTIC-programming

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 1991年第2期8卷 128-134页

作者： WANG, JD NANJING UNIV DEPT MATHNANJINGPEOPLES R CHINA

In this paper concerned is the stability property of the optimum of nonlinear distribution problems with respect to the random vector. We give conditions, under which the optimum of the problem with approximate random vectors will converge to the optimum of the original problem in distribution sense, L1-sense or in the sense of mean-convergence respectively. Based upon this stability an approximation method is suggested.

关键词： STABILITY DISTRIBUTION PROBLEM NONLINEAR STOCHASTIC programming parametric programming

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Generalized linear multiplicative and fractional programming

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Annals of Operations Research 1990年第1期25卷 147-161页

作者： Konno, Hiroshi Kuno, Takahito Institute of Human and Social Sciences Tokyo Institute of Technology Tokyo 152 2-12-1 Oh-Okayama Meguro-ku Japan Department of Social Engineering Tokyo Institute of Technology Tokyo 152 2-12-1 Oh-Okayama Meguro-ku Japan

This paper addresses itself to the algorithm for minimizing the sum of a convex function and a product of two linear functions over a polytope. It is shown that this nonconvex minimization problem can be solved by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in higher dimension and apply a parametric programming (path following) approach. Also it is shown that the same idea can be applied to a generalized linear fractional programming problem whose objective function is the sum of a convex function and a linear fractional function. © 1990 J.C. Baltzer A.G. Scientific Publishing Company.

关键词： generalized linear fractional function generalized linear multiplicative function lobal minimization Nonconvex minimization parametric programming

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A bilevel programming framework for enterprise-wide process networks under uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2004年第6-7期28卷 1121-1129页

作者： Ryu, JH Dua, V Pistikopoulos, EN Univ London Imperial Coll Sci & Technol Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England

Enterprise-wide supply chain planning problems naturally exhibit a multi-level decision network structure, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a corresponding plant-wide planning/network problem. Such a multi-level decision network structure can be mathematically represented by using multi-level programming principles. In this paper, we specifically address bilevel decision-making problems under uncertainty in the context of enterprise-wide supply chain optimization with one level corresponding to a plant planning problem, while the other to a distribution network problem. We first describe how such problems can be modelled as bilevel programming problems and then we present an effective solution strategy based on parametric programming techniques. An attractive feature of the proposed strategy is the fact that it transforms the bilevel problem into a family of single parametric optimization problems, which can be solved to global optimality. A numerical example is presented to illustrate the proposed framework. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： supply chain planning bilevel programming parametric programming uncertainty

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Linear programming and Resource Allocation Modeling 1

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丛书名： []

2018年

作者： Michael J. Panik

ISBN: (数字)9781119509455

ISBN: (纸本)9781119509448

Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal Useful as a main resource or as a supplement in an economics or management science course, this comprehensive book addresses the deficiencies of other texts when it comes to covering linear programming theory--especially where data envelopment analysis (DEA) is concerned--and provides the foundation for the development of DEA. Linear programming and Resource Allocation Modeling begins by introducing primal and dual problems via an optimum product mix problem, and reviews the rudiments of vector and matrix operations. It then goes on to cover: the canonical and standard forms of a linear programming problem; the computational aspects of linear programming; variations of the standard simplex theme; duality theory; single- and multiple- process production functions; sensitivity analysis of the optimal solution; structural changes; and parametric programming. The primal and dual problems are then reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. The book also covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming, and data envelopment analysis (DEA). This book: Appeals to those wishing to solve linear optimization problems in areas such as economics, business administration and management, agriculture and energy, strategic planning, public decision making, and health care Fills the need for a linear programming applications component in a management science or economics course Provides a complete treatment of linear programming as applied to activity selection and usage Contains many detailed example problems as well as textual and graphical explanations Linear programming and Resourc

关键词： linear programming linear programming applications DEA modeling linear programming fundamentals network flows linear models mathematical programming economics linear programming for economics applied mathematics statistics applied statistics data envelopment analysis tools for productivity comparisons solving resource allocation problems parametric programming DEA for finance DEA for business DEA for strategic planning DEA for decision making guide to DEA guide to linear programming linear programming for business linear programming for finance linear programming for decision making linear programming and management computer programming Michael J. Panik Linear programming and Resource Allocation Modeling

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A bilevel programming framework for enterprise-wide process networks under uncertainty

A bilevel programming framework for enterprise-wide process ...

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International Conference on Foundations of Computer-Aided Process Operations

作者： Ryu, JH Dua, V Pistikopoulos, EN Univ London Imperial Coll Sci & Technol Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England

关键词： supply chain planning bilevel programming parametric programming uncertainty

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Multiparametric linear fractional functionals programming

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Trabajos de Investigacion Operativa 1989年第1期4卷 3-10页

作者： Chada, S.S. Universidad de Wisconsin Eau Claire Eau-Claire 54701 Wisconsin United States

In this paper a multiparametric linear fractional functionals program, with parameters appearing only in the objective function, is generated. The optimum solution of this parametric program is supposed to satisfy the constraints as equations only. It is also shown that the set of parameters forms a convex polyhedron. © 1989 SEIO.

关键词： AMS Classification: 90C31 (parametric programming) linear fractional programming optimization parametric programming

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Pivot rules for linear programming: A survey on recent theoretical developments

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Annals of Operations Research 1993年第1期46-47卷 203-233页

作者： Terlaky, Tamás Zhang, Shuzhong Faculty of Technical Mathematics and Computer Science Delft University of Technology Delft 2600 GA P.O. Box 5031 Netherlands Department of Econometrics University of Groningen Groningen 9700 AV P.O. Box 800 Netherlands

The purpose of this paper is to discuss the various pivot rules of the simplex method and its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland. We are mainly concerned with finiteness properties of simplex type pivot rules. Well known classical results concerning the simplex method are not considered in this survey, but the connection between the new pivot methods and the classical ones, if there is any, is discussed. In this paper we discuss three classes of recently developed pivot rules for linear programming. The first and largest class is the class of essentially combinatorial pivot rules including minimal index type rules and recursive rules. These rules only use labeling and signs of the variables. The second class contains those pivot rules which can actually be considered as variants or generalizations or specializations of Lemke's method, and so they are closely related to parametric programming. The last class has the common feature that the rules all have close connections to certain interior point methods. Finally, we mention some open problems for future research. © 1993 J.C. Baltzer AG, Science Publishers.

关键词： cycling Linear programming minimal index rule parametric programming pivot rules recursion simplex method

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Two Approaches to Inner Estimations of the Optimal Solution Set in Interval Linear programming 20

Two Approaches to Inner Estimations of the Optimal Solution ...

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4th International Conference on Intelligent Systems, Metaheuristics and Swarm Intelligence (ISMSI) / India International Congress on Computational Intelligence (IICCI)

作者： Hladik, Milan Charles Univ Prague Dept Appl Math Malostranske Nam 25 Prague 11800 Czech Republic

ISBN: (纸本)9781450377614

We consider a linear programming problem with uncertain input coefficients. The only information we have are lower and upper bounds for the uncertain values. This gives rise to the so called interval linear programming. The challenging problem here is to characterize and determine the set of all possible optimal solutions. Most of the scholars were focus on computing outer bounds for the optimal solution. Herein, we will be interested with computing inner bounds. We propose a local search algorithm and a genetic algorithm. We compare both methods numerically on random data to ascertain what is their real time complexity and quality of inner estimations.

关键词： Linear programming Interval computation parametric programming Genetic algorithm Heuristic

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A fuzzy bi-criteria transportation problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2011年第4期61卷 947-957页

作者： Keshavarz, Esmaile Khorram, Esmaile Amirkabir Univ Technol Fac Math & Comp Sci Tehran 15914 Iran Islamic Azad Univ Sirjan Branch Dept Math Sirjan Iran

In this paper, a fuzzy bi-criteria transportation problem is studied. Here, the model concentrates on two criteria: total delivery time and total profit of transportation. The delivery times on links are fuzzy intervals with increasing linear membership functions, whereas the total delivery time on the network is a fuzzy interval with a decreasing linear membership function. On the other hand, the transporting profits on links are fuzzy intervals with decreasing linear membership functions and the total profit of transportation is a fuzzy number with an increasing linear membership function. Supplies and demands are deterministic numbers. A nonlinear programming model considers the problem using the max-min criterion suggested by Bellman and Zadeh. We show that the problem can be simplified into two bi-level programming problems, which are solved very conveniently. A proposed efficient algorithm based on parametric linear programming solves the bi-level problems. To explain the algorithm two illustrative examples are provided, systematically. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Fuzzy interval Membership function Bi-criteria transportation Fuzzy transportation Bi-level programming parametric programming

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