Strategic Allocation Of Resources Using Linear Programming Model With Parametric Analysis In Matlab And Excel Solver

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

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 Resource Allocation Modeling is an excellent resource for professionals looking to solve linear optimization problems, and advanced undergraduate to beginning graduate level management science or economics students.

Linear programming is one of the most extensively used techniques in the toolbox of quantitative methods of optimization. One of the reasons of the popularity of linear programming is that it allows to model a large variety of situations with a simple framework. Furthermore, a linear program is relatively easy to solve. The simplex method allows to solve most linear programs efficiently, and the Karmarkar interior-point method allows a more efficient solving of some kinds of linear programming. The power of linear programming is greatly enhanced when came the opportunity of solving integer and mixed integer linear programming. In these models all or some of the decision variables are integers, respectively. In this book we provide a brief introduction to linear programming, together with a set of exercises that introduce some applications of linear programming. We will also provide an introduction to solve linear programming in R. For each problem a possible solution through linear programming is introduced, together with the code to solve it in R and its numerical solution.

The field of operations research provides a scientific approach to managerial decision making. In a contemporary, hypercompetitive ever-changing business world, a manager needs quantitative and factual ways of solving problems related to optimal allocation of resources, profit/loss, maximization/minimization etc. In this endeavor, the subject of doing research on how to manage and make operations efficient is termed as Operations Research. The reference text provides conceptual and analytical knowledge for various operations research techniques. Readers, especially students of this subject, are skeptic in dealing with the subject because of its emphasis on mathematics. However, this book has tried to remove such doubts by focusing on the application part of OR techniques with minimal usage of mathematics. The attempt was to make students comfortable with some complicated topics of the subject. It covers important concepts including sensitivity analysis, duality theory, transportation solution method, Hungarian algorithm, program evaluation and review technique and periodic review system. Aimed at senior undergraduate and graduate students in the fields of mechanical engineering, civil engineering, industrial engineering and production engineering, this book: • Discusses extensive use of Microsoft Excel spreadsheets and formulas in solving operations research problems • Provides case studies and unsolved exercises at the end of each chapter • Covers industrial applications of various operations research techniques in a comprehensive manner • Discusses creating spreadsheets and using different Excel formulas in an easy-to-understand manner • Covers problem-solving procedures for techniques including linear programming, transportation model and game theory

An accessible introduction to optimization analysis using spreadsheets Updated and revised, Optimization Modeling with Spreadsheets, Third Edition emphasizes model building skills in optimization analysis. By emphasizing both spreadsheet modeling and optimization tools in the freely available Microsoft® Office Excel® Solver, the book illustrates how to find solutions to real-world optimization problems without needing additional specialized software. The Third Edition includes many practical applications of optimization models as well as a systematic framework that illuminates the common structures found in many successful models. With focused coverage on linear programming, nonlinear programming, integer programming, and heuristic programming, Optimization Modeling with Spreadsheets, Third Edition features: An emphasis on model building using Excel Solver as well as appendices with additional instructions on more advanced packages such as Analytic Solver Platform and OpenSolver Additional space devoted to formulation principles and model building as opposed to algorithms New end-of-chapter homework exercises specifically for novice model builders Presentation of the Sensitivity Toolkit for sensitivity analysis with Excel Solver Classification of problem types to help readers see the broader possibilities for application Specific chapters devoted to network models and data envelopment analysis A companion website with interactive spreadsheets and supplementary homework exercises for additional practice Optimization Modeling with Spreadsheets, Third Edition is an excellent textbook for upper-undergraduate and graduate-level courses that include deterministic models, optimization, spreadsheet modeling, quantitative methods, engineering management, engineering modeling, operations research, and management science. The book is an ideal reference for readers wishing to advance their knowledge of Excel and modeling and is also a useful guide for MBA students and modeling practitioners in business and non-profit sectors interested in spreadsheet optimization.

Optimization Toolbox provides functions for finding parameters that minimize or maximize objectives while satisfying constraints. The toolbox includes solvers for linear programming (LP), mixed-integer linear programming (MILP), quadratic programming (QP), nonlinear programming (NLP), constrained linear least squares, nonlinear least squares, and nonlinear equations. You can define your optimization problem with functions and matrices or by specifying variable expressions that reflect the underlying mathematics. You can use the toolbox solvers to fin optimal solutions to continuous and discrete problems, perform trade of analyses, and incorporate optimization methods into algorithms and applications. The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. It can be used to fin optimal solutions in applications such as portfolio optimization, resource allocation, and production planning and scheduling.You can use the toolbox solvers to find optimal solutions to continuous and discrete problems, perform tradeoff analyses, and incorporate optimization methods into algorithms and applications. The toolbox lets you perform design optimization tasks, including parameter estimation, component selection, and parameter tuning. It can be used to find optimal solutions in applications such as portfolio optimization, resource allocation, and production planning and scheduling.Quadratic programming is the problem of finding a vector x that minimizes a quadratic function, possibly subject to linear constraints.Least squares, in general, is the problem of finding a vector x that is a local minimizer to a function that is a sum of squares, possibly subject to some constraints. There are several Optimization Toolbox solvers available for various types of F(x) and various types of constraints.Given a set of n nonlinear functions Fi(x), where n is the number of components of the vector x, the goal of equation solving is to find a vector x that makes all Fi(x) = 0. fsolve attempts to solve systems of equations by minimizing the sum of squares of the components. If the sum of squares is zero, the system of equation is solved.Matlab also support Big Data for Optimization across parallel computing. Parallel computing is the technique of using multiple processors on a single problem. The reason to use parallel computing is to speed computations for Big Data. The following Optimization Toolbox solvers can automatically distribute the numerical estimation of gradients of objective functions and nonlinear constraint functions to multiple processors: fmincon, fminunc, fgoalattain, fminimax, fsolve, lsqcurvefit and lsqnonlin.

Economic policy and operations research; Methods of linear programming: extension and applications; Nonlinear and dynamic programming; Sensitivity analysis in programming; Probabilistic programming methods; Models of firm behavior and other applications; Models of resource allocation and planning in educational institutions and systems; Models of decomposition or decentralization in firm behavior and economic policy; Operations research and complex social systems.