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

2.1 INTRODUCTION

2.2 DECISION MAKING IN POM

2.3 THE SIMPLEX METHOD

2.4 THE COMMAND linprog

2.5 USING EXCEL SOLVER OPTIMIZATION PROBLEM

2.5.1 Spreadsheet modeling & Excel Solver

2.6 PRODUCTION OUTSOURCING: A LP MODEL FOR THE TOC

2.7 GENERAL RESOURCE ALLOCATION MODEL

2.8 SUMMARY

CHAPTER 3 LINEAR PROGRAMMING MODEL

3.1 INTRODUCTION

3.2 THE PROBLEM STATEMENT

3.3 FORMULATION OF LP MODEL

3.4 SOLUTION USING MATLAB

3.5 THE COMMAND simlp

3.6 THE OPTIMAL SOLUTION USING MATLAB

3.7 SOLUTION USING EXCEL SOLVER

3.8 OPTIMAL SCHEDULING ON MACHINES

3.8.1 Assumptions in sequencing problem

3.8.2 Processing two jobs through four machines

3.9 SUMMARY

CHAPTER 4 INTERPRETING COMPUTER SOLUTIONS OF LP PROBLEM

4.1 INTRODUCTION

4.2 TERMS

4.2.1 Slack variables

4.2.2 Basic & non-basic variables

4.3 ANSWER REPORT ANALYSIS

4.4 SENSITIVITY ANALYSIS

4.4.1 Find the bottleneck

4.4.2 Find the range over which the unit profit may change

4.4.3 Find the marginal benefit of increasing the time availability

4.4.4 Find the range over which the time availability may change

4.5 PARAMETRIC ANALYSIS

4.6 SUMMARY

CHAPTER 5 RESULT & DISCUSSIONS

5.1 INTRODUCTION

5.2 SEARCH FOR THE OPTIMAL SOLUTION

5.3 BOTTLENECKS

5.4 RANGE OVER WHICH THE UNIT PROFIT MAY CHANGE

5.5 MARGINAL BENEFIT OF INCREASING THE TIME AVAILABILITY

5.6 RANGE OVER WHICH THE TIME AVAILABILITY MAY CHANGE

5.7 REDUCED COST FOR NON-BASIC VARIABLES

5.8 SLACK VALUES FOR CONSTRAINTS

5.9 RECOMMENDED COURSE OF ACTION

5.9.1 Product Outsourcing

5.9.2 One-time cost

5.9.3 Cross Training of one machine operator

5.9.4 Possibility of third product manufacturing

5.9.5 Optimal sequencing to process jobs on machines

5.10 SUMMARY

CHAPTER 6 CONCLUSIONS

6.1 INTRODUCTION

6.2 SUMMARY OF THE PRESENT WORK

6.3 SUMMARY OF CONTRIBUTION

6.4 SCOPE FOR FUTURE WORK

6.5 CONCLUDING REMARKS

Research Objectives and Core Topics

The primary objective of this dissertation is to explore the strategic application of linear programming (LP) for optimal resource allocation in a manufacturing product-mix environment. The research aims to formulate a mathematical model to maximize profit, solve it using MATLAB and Excel Solver, and conduct detailed sensitivity and parametric analyses to understand how dynamic changes in variables and resource constraints impact the optimal solution and organizational outcomes.

• Strategic resource allocation using linear programming models.
• Implementation of optimization solutions via MATLAB and Excel Solver.
• Sensitivity analysis to identify production bottlenecks and resource limits.
• Parametric analysis for continuous and discrete variable variation.
• Optimal job sequencing on multiple machines using Gantt charts.
• Practical decision-making scenarios including outsourcing and multi-product manufacturing.

Excerpt from the Book

Summary of Chapters

CHAPTER 1 INTRODUCTION: Provides an overview of the history, principles, and applications of linear programming as a decision-making tool in industrial operations.

CHAPTER 2 LITERATURE REVIEW: Reviews existing research and methodologies concerning POM, the Simplex method, and the integration of spreadsheet software in operations research.

CHAPTER 3 LINEAR PROGRAMMING MODEL: Details the formulation of a specific product-mix model, its numerical solution, and machine sequencing strategies.

CHAPTER 4 INTERPRETING COMPUTER SOLUTIONS OF LP PROBLEM: Explains how to interpret the output reports from computer solvers, including sensitivity analysis and slack variable usage.

CHAPTER 5 RESULT & DISCUSSIONS: Presents the findings of the optimized production mix, discusses the impacts of resource variations, and recommends practical courses of action.

CHAPTER 6 CONCLUSIONS: Summarizes the contributions of the research and outlines potential directions for future study using fuzzy algorithms.

Key Words

Linear Programming, Resource Allocation, Optimization, Product-Mix, MATLAB, Excel Solver, Sensitivity Analysis, Parametric Analysis, Operations Research, Bottlenecks, Manufacturing, Simplex Method, Decision Making, Production and Operations Management, Gantt Chart

Frequently Asked Questions

What is the fundamental focus of this dissertation?

This work fundamentally focuses on the strategic allocation of limited resources in a manufacturing environment using linear programming to maximize profit.

What are the primary thematic fields addressed?

The key themes include operations research, linear programming formulation, computer-based optimization, sensitivity analysis, and industrial resource scheduling.

What is the primary goal of the research?

The goal is to determine the optimal product-mix and resource allocation that maximizes profitability while identifying critical production bottlenecks.

Which scientific methods are utilized?

The study employs linear programming modeling, the Simplex method, graphical solution techniques, sensitivity analysis, and parametric analysis via MATLAB and Excel Solver.

What topics are covered in the main body?

The main body covers problem formulation, computational solutions, interpretation of solver reports, sensitivity and parametric modeling, and the optimal sequencing of tasks on machines.

Which keywords characterize this work?

Core keywords include Linear Programming, Optimization, MATLAB, Excel Solver, Sensitivity Analysis, and Product-Mix.

How is the sensitivity analysis performed?

Sensitivity analysis is conducted by utilizing Excel Solver reports to assess how discrete and continuous changes in input parameters affect the stability and optimality of the final production plan.

What conclusions are drawn regarding machine bottlenecks?

The study identifies specific machine workstations as bottlenecks when they operate at maximum capacity, demonstrating how LP highlights these limitations to inform management decisions.