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.
Inhaltsverzeichnis (Table of Contents)
- CHAPTER 1 INTRODUCTION
- 1.1 HISTORY
- 1.2 PRINCIPLES OF MATHEMATICAL PROGRAMMING
- 1.3 LINEAR PROGRAMMING
- 1.3.1 Limitations of LP model
- 1.4 MOTIVATION
- 1.4.1 Examples of successful LP applications
- 1.5 CHARACTERSTICS OF LINEAR PROGRAMMING
- 1.6 SOLVING LP PROBLEMS
- 1.7 BASIC STEPS FOR SOLVING A LP MODEL
- 1.7.1 Recognize the problem
- 1.7.2 Define the problem
- 1.7.3 Define the decision variables
- 1.7.4 Collect the necessary parametric data
- 1.7.5 Formulate a model
- 1.7.6 Solve the model
- 1.7.7 Verify and validate the model
- 1.7.8 Analyze model output
- 1.7.9 Interpret model results
- 1.7.10 Recommend a course of action
- 1.8 FORMULATING LP PROBLEMS
- 1.9 OBJECTIVES OF THE PRESENT WORK
- 1.10 ORGANISATION OF THE DISSERTATION
- 1.11 SUMMARY
- CHAPTER 2 LITERATURE REVIEW
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This dissertation aims to solve a typical product-mix problem in a manufacturing system using linear programming and parametric analysis. The study utilizes MATLAB's `simpl` command to find the optimal product mix that maximizes profit. Sensitivity analysis, using Excel Solver and other software, is employed to assess the impact of parameter changes on the optimal solution and identify potential bottlenecks. Alternative strategies, such as outsourcing and cross-training, are also explored.
- Optimal resource allocation in manufacturing
- Linear programming model application and solution
- Parametric analysis and sensitivity analysis of the model
- Identification of bottlenecks and alternative strategies
- Profit maximization through product mix optimization
Zusammenfassung der Kapitel (Chapter Summaries)
CHAPTER 1 INTRODUCTION: This chapter introduces linear programming (LP) and its applications across various industries, from airlines to oil companies. It details the historical context of LP models and their foundational principles within mathematical programming. The chapter outlines the characteristics of LP problems, steps involved in solving them (problem recognition, variable definition, data collection, model formulation, solution, verification, analysis, interpretation, and recommendation), and methods for formulating LP problems. The chapter concludes by stating the objectives of the present work and outlining its organization. The overall aim is to establish a firm theoretical foundation for the subsequent chapters, highlighting the importance and versatility of LP models in real-world optimization problems.
CHAPTER 2 LITERATURE REVIEW: (Note: The provided text excerpt does not offer sufficient information to produce a 75-word summary for Chapter 2. A full text would be required.)
Schlüsselwörter (Keywords)
Linear programming, optimization, resource allocation, product mix, parametric analysis, sensitivity analysis, MATLAB, Excel Solver, manufacturing, profit maximization, bottleneck identification, decision making.
Frequently Asked Questions: Comprehensive Language Preview
What is the purpose of this document?
This document provides a comprehensive preview of a dissertation focused on solving a product-mix problem in a manufacturing system using linear programming and parametric analysis. It includes a table of contents, objectives and key themes, chapter summaries, and keywords.
What are the key themes explored in the dissertation?
The key themes include optimal resource allocation in manufacturing, application and solution of linear programming models, parametric and sensitivity analysis, bottleneck identification, alternative strategies (outsourcing, cross-training), and profit maximization through product mix optimization.
What methodologies are used in the dissertation?
The dissertation utilizes linear programming, parametric analysis, sensitivity analysis, MATLAB's `simpl` command, and Excel Solver to find and analyze the optimal product mix.
What problem does the dissertation address?
The dissertation addresses a typical product-mix problem in a manufacturing system, aiming to find the optimal product mix that maximizes profit.
What software is used in the analysis?
The analysis employs MATLAB (specifically the `simpl` command) and Excel Solver.
What are the chapter summaries provided?
Chapter 1 provides an introduction to linear programming, its history, principles, applications, and the steps involved in solving LP problems. It also outlines the dissertation's objectives and organization. Chapter 2 (a literature review) summary is not provided due to insufficient text.
What are the key words associated with this dissertation?
Linear programming, optimization, resource allocation, product mix, parametric analysis, sensitivity analysis, MATLAB, Excel Solver, manufacturing, profit maximization, bottleneck identification, decision making.
What is the overall objective of the dissertation?
The dissertation aims to solve a product-mix problem using linear programming and parametric analysis, maximizing profit while identifying potential bottlenecks and exploring alternative strategies.
What are some alternative strategies explored?
The dissertation explores alternative strategies such as outsourcing and cross-training to address potential bottlenecks and improve efficiency.
- Citar trabajo
- Dinesh Gupta (Autor), 2013, Strategic Allocation of Resources Using Linear Programming Model with Parametric Analysis, Múnich, GRIN Verlag, https://www.grin.com/document/271318
