Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimize their use of planes and staff. NASA has been using them for years to optimize their use of limited resources. Oil companies use them to optimize their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In my study, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for ist optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the product-mix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this study is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit, which still touches the feasible region. The most critical part is the sensitivity analysis, using Excel Solver, and Parametric Analysis, using computer software, which allows us to study the effect on optimal solution due to discrete and continuous change in parameters of the LP model including to identify bottlenecks. We have examined other options like product outsourcing, one-time cost, cross training of one operator, manufacturing of hypothetical third product on under-utilized machines and optimal sequencing of jobs on machines.

Master's Thesis from the year 2013 in the subject Engineering - Industrial Engineering and Management, grade: Good, LMU Munich (Dr. B R Ambedkar National Institute of Technology, Jalandhar), course: Industrial Engg., language: English, abstract: Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimize their use of planes and staff. NASA has been using them for many years to optimize their use of limited resources. Oil companies use them to optimize their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In my study, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for its optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the product-mix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this paper is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit which still touches the feasible region. The most critical part is the sensitivity analysis using Excel Solver and Parametric Analysis using computer software which allows us to study the effect on optimal solution due to discrete and continuous change in parameters of the LP model including to identify bottlenecks. We have examined other options like product outsourcing, one-time cost, cross training of one operator, manufacturing of hypothetical third product on under-utilized machines and optimal sequencing of jobs on machines.

Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.

This textbook is designed for students and industry practitioners for a first course in optimization integrating MATLAB® software.

For first courses in operations research, operations management Optimization in Operations Research, Second Edition covers a broad range of optimization techniques, including linear programming, network flows, integer/combinational optimization, and nonlinear programming. This dynamic text emphasizes the importance of modeling and problem formulation andhow to apply algorithms to real-world problems to arrive at optimal solutions. Use a program that presents a better teaching and learning experience-for you and your students. Prepare students for real-world problems: Students learn how to apply algorithms to problems that get them ready for their field. Use strong pedagogy tools to teach: Key concepts are easy to follow with the text's clear and continually reinforced learning path. Enjoy the text's flexibility: The text features varying amounts of coverage, so that instructors can choose how in-depth they want to go into different topics.

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.