Introduction to Mathematical Models in Operations Planning


Book Description

Discover the intricate nature of a company's production function and the comprehensive principles of planning operations in this book. Through practical applications and enriched by numerical examples, readers gain essential knowledge of elementary mathematical methods in operations planning. The inclusion of the powerful R programming language, accompanied by code scripts and real-world examples, enhances the learning experience. Blending theory with practice, this resource equips readers with the tools necessary to optimize production systems, make informed decisions, and gain a competitive edge in today's dynamic business landscape.




Introduction to Mathematical Models in Operations Planning


Book Description

"The book "Introduction to Mathematical Models in Operations Planning" is contemporary and agile. It gives readers a concise overview of the subject as well as clear and practical examples, making it a reference resource for both professionals and students. The book also includes a section on the R computer programming language, making it more useful to readers"--




An Introduction to Mathematical Modeling


Book Description

Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.




An Introduction to the Mathematics of Planning and Scheduling


Book Description

This book introduces readers to the many variables and constraints involved in planning and scheduling complex systems, such as airline flights and university courses. Students will become acquainted with the necessity for scheduling activities under conditions of limited resources in industrial and service environments, and become familiar with methods of problem solving. Written by an expert author with decades of teaching and industry experience, the book provides a comprehensive explanation of the mathematical foundations to solving complex requirements, helping students to understand underlying models, to navigate software applications more easily, and to apply sophisticated solutions to project management. This is emphasized by real-world examples, which follow the components of the manufacturing process from inventory to production to delivery. Undergraduate and graduate students of industrial engineering, systems engineering, and operations management will find this book useful in understanding optimization with respect to planning and scheduling.




A Primer on Mathematical Modelling


Book Description

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.




Mathematical Methods and Models in Economic Planning, Management and Budgeting


Book Description

This book describes a system of mathematical models and methods that can be used to analyze real economic and managerial decisions and to improve their effectiveness. Application areas include: management of development and operation budgets, assessment and management of economic systems using an energy entropy approach, equation of exchange rates and forecasting foreign exchange operations, evaluation of innovative projects, monitoring of governmental programs, risk management of investment processes, decisions on the allocation of resources, and identification of competitive industrial clusters. The proposed methods and models were tested on the example of Kazakhstan’s economy, but the generated solutions will be useful for applications at other levels and in other countries. Regarding your book "Mathematical Methods and Models in Economics", I am impressed because now it is time when "econometrics" is becoming more appreciated by economists and by schools that are the hosts or employers of modern economists. ... Your presented results really impressed me. John F. Nash, Jr., Princeton University, Nobel Memorial Prize in Economic Sciences The book is within my scope of interest because of its novelty and practicality. First, there is a need for realistic modeling of complex systems, both natural and artificial that conclude computer and economic systems. There has been an ongoing effort in developing models dealing with complexity and incomplete knowledge. Consequently, it is clear to recognize the contribution of Mutanov to encapsulate economic modeling with emphasis on budgeting and innovation. Secondly, the method proposed by Mutanov has been verified by applying to the case of the Republic of Kazakhstan, with her vibrant emerging economy. Thirdly, Chapter 5 of the book is of particular interest for the computer technology community because it deals with innovation. In summary, the book of Mutanov should become one of the outstanding recognized pragmatic guides for dealing with innovative systems. Andrzej Rucinski, University of New Hampshire This book is unique in its theoretical findings and practical applicability. The book is an illuminating study based on an applied mathematical model which uses methods such as linear programming and input-output analysis. Moreover, this work demonstrates the author’s great insight and academic brilliance in the fields of finance, technological innovations and marketing vis-à-vis the market economy. From both theoretical and practical standpoint, this work is indeed a great achievement. Yeon Cheon Oh, President of Seoul National University




Introduction to Mathematical Models in Market and Opinion Research


Book Description

In the introduction to his book Dr. Harder has very clearly described its purpose and organization. I only want to add for the English-speaking reader a few words on the place the present text is likely to have in the cur rent literature. At first Dr. Harder's undertaking might come as a surprise. Only a few years ago, Zeisel's Say it with Figures gave the market research practi tioner some ideas of how simple figures and tables could be successfully employed; Langhoff's publication for the American Marketing Associa tion presented some pertinent mathematical models in the most elemen tary form; why should a German author believe he can already introduce us to serious mathematical procedures for use in product management and advertising? After reading the book, incredulity turns into pleasure because of the skill with which the author has pursued his task. As a matter of fact, the book can serve two audiences who at first glance might appear to have quite opposing interests. For the mathematically trained market re searcher, the book has the marked advantage of combining a variety of ap proaches not ordinarily mixed in one volume. If the market researcher be gan as an economist he is already familiar with difference equations and time series analysis; if he moved in from psychology, he is already ac quainted with factor analysis. But as he reads this book, he finds the two worlds well integrated.




Production Planning by Mixed Integer Programming


Book Description

This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations. Review by Jakub Marecek (Computer Journal) The emphasis put on mixed integer rounding and mixing sets, heuristics in-built in general purpose integer programming solvers, as well as on decompositions and heuristics using integer programming should be praised... There is no doubt that this volume offers the present best introduction to integer programming formulations of lotsizing problems, encountered in production planning. (2007)




Mathematical Modeling


Book Description

Mathematical Modeling, Third Edition is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems. Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines. Increased support for instructors, including MATLAB material New sections on time series analysis and diffusion models Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems




Mathematical Models for Planning Support


Book Description

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator.