Author: Suvrajeet Sen
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description

Author: Dinakar Gade
Publisher:
ISBN:
Category :
Languages : en
Pages : 137

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Book Description
Abstract: In this dissertation, we develop methodologies to solve difficult classes of discrete optimization problems under uncertainty by using techniques from integer programming. First, we consider a class of two-stage stochastic integer programs with binary variables in the first stage, general integer variables in the second stage and random data with finitely many outcomes. We develop an L-shaped decomposition algorithm that iteratively tightens the linear relaxation of the scenario subproblems using Gomory cuts and maintains convex first stage approximations. We show that the algorithm is not only finitely convergent, but also computationally amenable allowing several alternative implementations. We develop a computer implementation of this algorithm and report computational results on the stochastic server location problem instances. With the goal of extending our methods to solve stochastic mixed integer programs, we develop extensions to the cutting plane tree algorithm by integrating Gomory cuts with disjunctive cuts. We report computational results with the Gomory-enhanced simple disjunctive cuts using benchmark test instances. Second, we introduce the concept of service levels into deterministic lot sizing problems and develop a polynomial time algorithm for a single item lot sizing problem with a ready rate service level constraint. Based on the algorithm, we develop compact extended reformulations for this problem and a relaxation. We show that although the extended reformulations are large, they outperform standard formulations of the problem while guaranteeing optimal solutions when they are used to solve capacitated multi-item instances.

Author: L. Stougie
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 110

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Book Description

Author: Alexander Shapiro
Publisher: SIAM
ISBN: 0898718759
Category : Mathematics
Languages : en
Pages : 447

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Book Description
Optimization problems involving stochastic models occur in almost all areas of science and engineering, such as telecommunications, medicine, and finance. Their existence compels a need for rigorous ways of formulating, analyzing, and solving such problems. This book focuses on optimization problems involving uncertain parameters and covers the theoretical foundations and recent advances in areas where stochastic models are available. Readers will find coverage of the basic concepts of modeling these problems, including recourse actions and the nonanticipativity principle. The book also includes the theory of two-stage and multistage stochastic programming problems; the current state of the theory on chance (probabilistic) constraints, including the structure of the problems, optimality theory, and duality; and statistical inference in and risk-averse approaches to stochastic programming.

Author: Lewis Ntaimo
Publisher: Springer Nature
ISBN: 3031524640
Category :
Languages : en
Pages : 518

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Book Description

Author: Karen Aardal
Publisher: Springer Nature
ISBN: 3031069013
Category : Computers
Languages : en
Pages : 469

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Book Description
This book constitutes the refereed proceedings of the 23rd International Conference on Integer Programming and Combinatorial Optimization, IPCO 2022, held in Eindhoven, The Netherlands, in June 2022. The 33 full papers presented were carefully reviewed and selected from 93 submissions addressing key techniques of document analysis. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting the latest results of theory and practice of the various aspects of discrete optimization.

Author: Vassilios S. Vassiliadis
Publisher: Cambridge University Press
ISBN: 1108916120
Category : Technology & Engineering
Languages : en
Pages : 353

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Book Description
Discover the subject of optimization in a new light with this modern and unique treatment. Includes a thorough exposition of applications and algorithms in sufficient detail for practical use, while providing you with all the necessary background in a self-contained manner. Features a deeper consideration of optimal control, global optimization, optimization under uncertainty, multiobjective optimization, mixed-integer programming and model predictive control. Presents a complete coverage of formulations and instances in modelling where optimization can be applied for quantitative decision-making. As a thorough grounding to the subject, covering everything from basic to advanced concepts and addressing real-life problems faced by modern industry, this is a perfect tool for advanced undergraduate and graduate courses in chemical and biochemical engineering.

Author: Alexander Schrijver
Publisher: John Wiley & Sons
ISBN: 9780471982326
Category : Mathematics
Languages : en
Pages : 488

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Book Description
Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.

Author: Julia L. Higle
Publisher: Springer Science & Business Media
ISBN: 1461541158
Category : Mathematics
Languages : en
Pages : 237

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Book Description
Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models. There are several arenas model is appropriate, and such models have found applications in air line yield management, capacity planning, electric power generation planning, financial planning, logistics, telecommunications network planning, and many more. In some of these applications, modelers represent uncertainty in terms of only a few seenarios and formulate a large scale linear program which is then solved using LP software. However, there are many applications, such as the telecommunications planning problem discussed in this book, where a handful of seenarios do not capture variability well enough to provide a reasonable model of the actual decision-making problem. Problems of this type easily exceed the capabilities of LP software by several orders of magnitude. Their solution requires the use of algorithmic methods that exploit the structure of the SLP model in a manner that will accommodate large scale applications.

Author: Shmuel Onn
Publisher: European Mathematical Society
ISBN: 9783037190937
Category : Combinatorial optimization
Languages : en
Pages : 0

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Book Description
This monograph develops an algorithmic theory of nonlinear discrete optimization. It introduces a simple and useful setup, which enables the polynomial time solution of broad fundamental classes of nonlinear combinatorial optimization and integer programming problems in variable dimension. An important part of this theory is enhanced by recent developments in the algebra of Graver bases. The power of the theory is demonstrated by deriving the first polynomial time algorithms in a variety of application areas within operations research and statistics, including vector partitioning, matroid optimization, experimental design, multicommodity flows, multi-index transportation and privacy in statistical databases. This monograph is intended for graduate students and researchers. It is accessible to anyone with standard undergraduate knowledge and mathematical maturity.