Strategic Allocation of Resources Using Linear Programming Model with Parametric Analysis

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

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

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.)

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.