1. © Yanbu University College YANBU UNIVERSITY COLLEGE Women’s Campus © Yanbu University College Introduction to Quantitative Analysis Chapter 1 Ms.Atiya Masood

2. © Yanbu University College Learning Objectives Students will be able to: 1. Describe the quantitative analysis (QA) approach. 2. Understand the application of QA in a real situation. 3. Describe the use of modeling in QA. 4. Discuss possible problems in using quantitative analysis. 5. Perform a break-even analysis.

3. © Yanbu University College Chapter Outline 1.1 Introduction 1.2 What Is Quantitative Analysis (QA)? 1.3 The QA Approach 1.4 How to Develop a QA Model

4. © Yanbu University College Introduction  Mathematical tools have been used for thousands of years.  QA can be applied to a wide variety of problems.  One must understand the specific applicability of the technique, its limitations, and its assumptions.

5. © Yanbu University College Examples of Quantitative Analyses  Taco Bell saved over $150 million using forecasting and scheduling QA models.  NBC increased revenues by over $200 million by using QA to develop better sales plans.  Continental Airlines saved over $40 million using QA models to quickly recover from weather and other disruptions.

6. © Yanbu University College Quantitative Analysis: A scientific approach to managerial decision making whereby raw data are processed and manipulated resulting in meaningful information. Raw Data Quantitative Analysis Meaningful Information Overview of Quantitative Analysis Qualitative Factors: Information that may be difficult to quantify but can affect the decision- making process such as the weather, state, and federal legislation.

7. © Yanbu University College The QA Approach: Fig 1.1 Define the problem Develop a model Acquire input data Develop a solution Test the solution Analyze the results Implement the results

8. © Yanbu University College Define the Problem Problem Definition: A clear and concise statement that gives direction and meaning to the subsequent QA steps and requires specific, measurable objectives. THIS MAY BE THE MOST DIFFICULT STEP! …because true problem causes must be identified and the relationship of the problem to other organizational processes must be considered.

9. © Yanbu University College Develop the Model Quantitative Analysis Model: A realistic, solvable, and understandable mathematical statement showing the relationship between variables. Models contain both controllable (decision variables) and uncontrollable variables and parameters. Typically, parameters are known quantities (salary of sales force) while variables are unknown (sales quantity).

10. © Yanbu University College Develop the Model Models generally contain variables (controllable and uncontrollable) and parameters Controllable variables are generally the decision variables and are generally unknown Parameters are known quantities that are a part of the problem

11. © Yanbu University College Acquire Data Model Data: Accurate input data that may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement, or statistical sampling.

12. © Yanbu University College Develop a Solution Model Solution:  The best model solution is found by manipulating the model variables until a practical and implemental solution is obtained.  Manipulation can be done by solving the equation(s), trying various approaches (trial and error), trying all possible variables (complete enumeration), and/or implementing an algorithm (repeating a series of steps).

13. © Yanbu University College Test the Solution Model Testing: The collection of data from a different source to validate the accuracy and completeness and sensibility of both the model and model input data ~ consistency of results is key! – New data can be collected to test the model – Results should be logical, consistent, and represent the real situation

14. © Yanbu University College Analyzing the Results Determine the implications of the solution – Implementing results often requires change in an organization – The impact of actions or changes needs to be studied and understood before implementation Sensitivity analysis Sensitivity analysis determines how much the results of the analysis will change if the model or input data changes  Sensitive models should be very thoroughly tested

15. © Yanbu University College Implement the Results Results Implementation: The incorporation of the solution into the company and the monitoring of the results.

16. © Yanbu University College How To Develop a Quantitative Analysis Model  Development is an important part of the quantitative analysis approach  Let’s look at a simple mathematical model of profit Profit = Revenue – Expenses Profit = Sx - f -Vx s: selling price per unit f: fixed cost V: variable cost X: number or quantity of units sold

17. © Yanbu University College Breakeven Example The company buys, sells, and repairs old clocks. Rebuilt springs sell for $10 per unit. Fixed cost of equipment to build springs is $1,000. Variable cost for spring material is $5 per unit. Calculate the profit when X is 1000?

18. © Yanbu University College Bagels R Us QA Model Example Profits = Revenue - Expenses Profits = $1X - $100 - $.5X Assume you are the new owner of Bagels R Us and you want to develop a mathematical model for your daily profits and breakeven point. Your fixed overhead is $100 per day and your variable costs are 0.50 per bagel (these are GREAT bagels). You charge $1 per bagel. (Price per Unit)  (Number Sold) - Fixed Cost - (Variable Cost/Unit)  (Number Sold)

19. © Yanbu University College Bagels R Us QA Model Breakeven Example Breakeven point occurs when Revenue = Expenses Revenue = Expenses Where, X= quantity of bagels sold F = fixed cost per day of operation V = variable cost/bagel So, $1X= $100 + $.5X Solve for X $1X-.5X= 100 => X= 200 Breakeven Quantity = F/(P-V)

20. © Yanbu University College Question The company buys, sells, and repairs old TV. Rebuilt Winter sell for $100 per unit. Fixed cost of equipment to build springs is $1,000. Variable cost for spring material is $50 per unit. A) develop a model of profit and BEP B) If X= 100, profits

21. © Yanbu University College Summary Quantitative analysis is a scientific approach to decision making The approach includes – Defining the problem – Acquiring input data – Developing a solution – Testing the solution – Analyzing the results – Implementing the results

22. © Yanbu University College Question time Accuracy of the output is determined by the accuracy of the __________ and the __________. model, input data result data, software used test graph judgment, intuition

23. © Yanbu University College Question time __________ determines how the solutions will change with a different model or different input data Testing Variation analysis Sensitivity analysis

24. © Yanbu University College Question time Quantitative analysis uses a(n) __________ approach to decision making. qualitative Scientific common sense judgmental

25. © Yanbu University College 25 THE END Q & A