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Integer Programming
A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems.The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared.The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers.The result has been a speed-up of several orders of magnitude.The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition.The revised second edition: Contains new developments on column generationOffers a new chapter on Benders’ algorithmIncludes expanded information on preprocessing, heuristics, and branch-and-cutPresents several basic and extended formulations, for example for fixed costnetwork flowsAlso touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field.
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The Encyclopedia of Integer Sequences
This encyclopedia contains more than 5000 integer sequences, over half of which have never before been catalogued. Because the sequences are presented in the most natural form, and arranged for easy reference, this book is easier to use than the authors earlier classic A Handbook of Integer Sequences. The Encyclopedia gives the name, mathematical description, and citations to literature for each sequence. Following sequences of particular interest, thereare essays on their origins, uses, and connections to related sequences (all cross-referenced). A valuable new feature to this text is the inclusion of a number of interesting diagrams and illustrations related to selected sequences. The initial chapters are both amusing and enlightening. They serve as a delightful introduction to the subject and a short course on how to identify and work with integer sequences. This encyclopedia brings Sloanes ground-breaking Handbook up to date, more than doubling its size, and linking both the old and the new material to an extensive bibliography (over 25 pages long), of current and classic references. An index to all the sequences in the book is also available separately on disk in Macintosh and IBM formats.
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Scheduling in Supply Chains Using Mixed Integer Programming
A unified, systematic approach to applying mixed integer programming solutions to integrated scheduling in customer-driven supply chains Supply chain management is a rapidly developing field, and the recent improvements in modeling, preprocessing, solution algorithms, and mixed integer programming (MIP) software have made it possible to solve large-scale MIP models of scheduling problems, especially integrated scheduling in supply chains.Featuring a unified and systematic presentation, Scheduling in Supply Chains Using Mixed Integer Programming provides state-of-the-art MIP modeling and solutions approaches, equipping readers with the knowledge and tools to model and solve real-world supply chain scheduling problems in make-to-order manufacturing. Drawing upon the author's own research, the book explores MIP approaches and examples-which are modeled on actual supply chain scheduling problems in high-tech industries-in three comprehensive sections: Short-Term Scheduling in Supply Chains presents various MIP models and provides heuristic algorithms for scheduling flexible flow shops and surface mount technology lines, balancing and scheduling of Flexible Assembly Lines, and loading and scheduling of Flexible Assembly SystemsMedium-Term Scheduling in Supply Chains outlines MIP models and MIP-based heuristic algorithms for supplier selection and order allocation, customer order acceptance and due date setting, material supply scheduling, and medium-term scheduling and rescheduling of customer orders in a make-to-order discrete manufacturing environmentCoordinated Scheduling in Supply Chains explores coordinated scheduling of manufacturing and supply of parts as well as the assembly of products in supply chains with a single producer and single or multiple suppliers; MIP models for a single- or multiple-objective decision making are also provided Two main decision-making approaches are discussed and compared throughout.The integrated (simultaneous) approach, in which all required decisions are made simultaneously using complex, monolithic MIP models; and the hierarchical (sequential) approach, in which the required decisions are made successively using hierarchies of simpler and smaller-sized MIP models.Throughout the book, the author provides insight on the presented modeling tools using AMPL® modeling language and CPLEX solver. Scheduling in Supply Chains Using Mixed Integer Programming is a comprehensive resource for practitioners and researchers working in supply chain planning, scheduling, and management.The book is also appropriate for graduate- and PhD-level courses on supply chains for students majoring in management science, industrial engineering, operations research, applied mathematics, and computer science.
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Linear and Integer Optimization : Theory and Practice, Third Edition
Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts.The first covers the theory of linear and integer optimization, including both basic and advanced topics.Dantzig’s simplex algorithm, duality, sensitivity analysis, integer optimization models, and network models are introduced.More advanced topics also are presented including interior point algorithms, the branch-and-bound algorithm, cutting planes, complexity, standard combinatorial optimization models, the assignment problem, minimum cost flow, and the maximum flow/minimum cut theorem. The second part applies theory through real-world case studies.The authors discuss advanced techniques such as column generation, multiobjective optimization, dynamic optimization, machine learning (support vector machines), combinatorial optimization, approximation algorithms, and game theory. Besides the fresh new layout and completely redesigned figures, this new edition incorporates modern examples and applications of linear optimization.The book now includes computer code in the form of models in the GNU Mathematical Programming Language (GMPL).The models and corresponding data files are available for download and can be readily solved using the provided online solver. This new edition also contains appendices covering mathematical proofs, linear algebra, graph theory, convexity, and nonlinear optimization.All chapters contain extensive examples and exercises.This textbook is ideal for courses for advanced undergraduate and graduate students in various fields including mathematics, computer science, industrial engineering, operations research, and management science.
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Which kitchen appliances have a long lifespan, such as mixers, etc.?
Kitchen appliances that typically have a long lifespan include mixers, food processors, and high-quality blenders. These appliances are built to withstand frequent use and are often made with durable materials that can last for many years. Investing in well-known brands and models known for their longevity can also help ensure that these appliances have a longer lifespan. Regular maintenance and proper care, such as cleaning and storage, can also contribute to extending the lifespan of these kitchen appliances.
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Which kitchen appliances also have a long lifespan, such as mixers, etc.?
Kitchen appliances such as mixers, blenders, and food processors are known for their long lifespan. These appliances are designed to withstand heavy use and are built with durable materials, making them reliable for many years. Additionally, high-quality brands and models of these appliances are often built to last, making them a worthwhile investment for any kitchen. Regular maintenance and proper care can also help extend the lifespan of these appliances.
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What are integer exponents?
Integer exponents are a way of representing repeated multiplication of a number by itself. An integer exponent is a whole number that indicates how many times the base number should be multiplied by itself. For example, in the expression 2^3, the base number is 2 and the exponent is 3, indicating that 2 should be multiplied by itself 3 times. Integer exponents can be positive, negative, or zero, and they are used to simplify and solve mathematical expressions involving powers.
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What are Integer Cluster CPUs?
Integer Cluster CPUs are a type of central processing unit that consist of multiple cores grouped together in clusters. Each cluster is dedicated to handling integer-based calculations, which are common in tasks such as general computing, data processing, and artificial intelligence. By dividing the workload among multiple clusters, Integer Cluster CPUs can improve overall performance and efficiency for these types of tasks.
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Mathematical Programming Approaches for Multi-Vehicle Motion Planning : Linear, Nonlinear, and Mixed Integer Programming
Real world Multi-Vehicle Motion Planning (MVMP) problems require the optimization of suitable performance measures under an array of complex and challenging constraints involving kinematics, dynamics, collision avoidance, and communication connectivity.The general MVMP problem is thus formulated as a Mathematical Programming (Optimization) problem. This book presents a Mathematical Programming (MP) framework that captures the salient features of the general MVMP problem.To demonstrate the use of MP for the formulation and solution of MVMP problems, it examines in detail four representative works and summarizes several other related ones.Following this conceptual discussion, it provides a step-by-step demonstration of how to formulate, solve, and experimentally validate an MP problem that represents a MVMP.Finally, it discusses the advantages, technical challenges, and limitations of this framework. As solution algorithms and their implementations in solvers continue to develop, it is anticipated that MP solution techniques will be applied to an increasing number of MVMP problems.The framework, formulations, and experimental approach presented here may serve as a guide for future MVMP research.
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Integer Linear Programming in Computational and Systems Biology : An Entry-Level Text and Course
Integer linear programming (ILP) is a versatile modeling and optimization technique that is increasingly used in non-traditional ways in biology, with the potential to transform biological computation.However, few biologists know about it. This how-to and why-do text introduces ILP through the lens of computational and systems biology.It uses in-depth examples from genomics, phylogenetics, RNA, protein folding, network analysis, cancer, ecology, co-evolution, DNA sequencing, sequence analysis, pedigree and sibling inference, haplotyping, and more, to establish the power of ILP.This book aims to teach the logic of modeling and solving problems with ILP, and to teach the practical 'work flow' involved in using ILP in biology.Written for a wide audience, with no biological or computational prerequisites, this book is appropriate for entry-level and advanced courses aimed at biological and computational students, and as a source for specialists.Numerous exercises and accompanying software (in Python and Perl) demonstrate the concepts.
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Sian's Kitchen : Caribbean Comfort Cooking
Bring entertainment to the kitchen to please every crowd.Sian's Kitchen is a collection of comforting dishes with Caribbean flair. BBC Radio 1Xtra broadcaster, DJ, Channel 5/BET presenter and restaurateur Sian Anderson is an exciting new voice in the culinary scene.After founding her immensely popular restaurant Octaves, Sian is now celebrating her Black British identity with Jamaican and St Lucian heritage in a modern Caribbean cookbook. Among the 80 fresh and flavoursome recipes are interviews with Big Zuu, Julie Adenuga and Big Narstie, as Sian invites them to dinner to discuss their favourite food, plus there is a playlist for every chapter to help you set the mood. This is an invitation to enjoy a taste of what makes Caribbean culture in the UK so special – gathering around the table to share comforting, vibrant dishes.With chapters including 20-Minute Fixes, Comfort Classics and From the Islands, you’ll find plenty of inspiration with recipes such as:Caribbean Plantain & Black Bean Bowl Ackee Fried RiceJamaican Curry Snapper FishOxtail StewCurry ChickenJerk Lamb with all the extrasAnd keep the conversation flowing with:Jam TartsSprinkle CakeRum PunchSian's Kitchen is a crowd-pleasing, love letter of a cookbook containing everything Sian holds close to her heart: cooking, culture and entertainment.
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Their Majesties’ Mixers
Famed as much for their love of the drink as they are for their prosperous or tumultuous reigns, Britain’s monarchs have always indulged in their favourite choices of ales, liquors and spirits.Her Majesty Queen Elizabeth II and the members of the House of Windsor are no exception.Written by Royal expert and historian Thomas J Mace-Archer-Mills, the Chairman of British Monarchist Society, this meticulously researched and beautifully crafted book is a real in-depth celebration of the monarchy.Filled with fascinating historical facts, anecdotes and timelines, it is lavishly illustrated with photographs taken from his private collection that have never been seen before. With contributions by such political greats as Sir David Amess MP and Andrew Rosindell MP, this celebratory book contains over 300 pages of glorious colour and is a fascinating and amusing celebration of the lesser known facts which blend spirits with the monarchy.Filled with refreshing drink recipes, Royal canape recipes by Sandhurst's Former Executive Chef Robert Kennedy, fun facts, quotes and timelines, this inclusive celebration of the monarchy and its colourful members encompass the latest Royal weddings, births, anniversaries and international milestones that you can continue to be a part of.Their Majesties’ Mixers is sure to delight and appeal to those who enjoy a good tipple, great food, decadent Royalty and the one-thousand-year history of the British Isles.
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What are integer solution triples?
Integer solution triples are sets of three integers (a, b, c) that satisfy a given equation or inequality. These triples are solutions to equations or inequalities where all three variables are integers. For example, in the equation a^2 + b^2 = c^2, the set of integers (3, 4, 5) is an integer solution triple because it satisfies the equation. Integer solution triples are often used in number theory and geometry to find relationships between integers and to solve problems involving integer solutions.
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What is an integer division?
Integer division is a mathematical operation that divides one integer by another and produces an integer result. In integer division, any fractional part of the result is discarded, and only the whole number part is kept. For example, when dividing 7 by 3 using integer division, the result would be 2, as the fractional part (0.333) is discarded. Integer division is often denoted by the // operator in programming languages.
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How are integer variables declared?
Integer variables are declared by specifying the data type "int" followed by the variable name. For example, to declare an integer variable named "num", the syntax would be "int num;". This tells the compiler to allocate memory for an integer variable named "num" that can store whole numbers within a certain range. Integer variables can also be initialized at the time of declaration by assigning a value, such as "int num = 5;".
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Why doesn't Eclipse import the Integer?
Eclipse does not import the `Integer` class by default because it is part of the `java.lang` package, which is automatically imported in every Java class. Therefore, there is no need to explicitly import the `Integer` class in Eclipse. This is done to reduce clutter and make the code more readable. If you are encountering issues with using the `Integer` class in Eclipse, it may be due to a different problem such as a typo or incorrect usage of the class.
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