Materi 2 (Chapter 2) ntroduction to Quantitative Analysis

Learning Objectives Students will be able to: Describe the quantitative analysis (QA) approach. Understand the application of QA in a real situation. Describe the use of modeling in QA. Use computers and spreadsheet models to perform QA. Discuss possible problems in using quantitative analysis. Perform a break-even analysis.

Chapter Outline 2.1 Introduction 2.2 What Is Quantitative Analysis (QA)? 2.3 The QA Approach 2.4 How to Develop a QA Model 2.5 The Role of Computers and Spreadsheet Models in the QA Approach 2.6 Possible Problems in the QA Approach 2.7 Implementation - Not Just the Final Step

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.

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.

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

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

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.

Develop the Model Quantitative Analysis Model: A realistic, solvable, and understandable mathematical statement showing the relationship between variables. revenues y = mx + b sales 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).

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. Garbage In Garbage Out =

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).

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!

Analyze the Results Results Analysis: Understanding actions implied by the solution and their implications, as well as conducting a sensitivity analysis (a change to input values or the model) to evaluate the impact of a change in model parameters. Sensitivity analyses allow the “what- ifs” to be answered.

Implement the Results Results Implementation: The incorporation of the solution into the company and the monitoring of the results.

Modeling in the Real World Real World Models can be: Complex, expensive, and difficult to sell. BUT… Real world models are used in the real world by real organizations to solve real problems!

Possible Pitfalls in Using Models Prior to developing and implementing models, managers should be aware of the potential pitfalls. Define the Problem Conflicting viewpoints Departmental impacts Assumptions Develop a Model Fitting the model Understanding the model Acquire Input Data Availability of data Validity of data

Possible Pitfalls (Continued) Develop a Solution Complex mathematics Solutions become quickly outdated Test the Solution Identifying appropriate test procedures Analyze the Results Holding all other conditions constant Identifying cause and effect Implement the Solution Selling the solution to others

Bagels R Us QA Model Example 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. Profits = Revenue - Expenses (Price per Unit)  (Number Sold) Fixed Cost - (Variable Cost/Unit)  (Number Sold) Profits = $1Q - $100 - $.5Q

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

Conclusions Models can help managers: Gain deeper insight into the nature of business relationships. Find better ways to assess values in such relationships; and See a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions.

Conclusions (continued) Models: Are less expensive and disruptive than experimenting with real world systems, but may be expensive to develop and test. Allow “What if” questions to be asked. Are built for management problems and encourage input, but may be misunderstood due to the mathematical complexity. Enforce consistency in approach. Require specific constraints and goals, but tend to downplay qualitative information. Help communicate problem solutions to others, but may oversimplify assumptions and variables.

Models: The Up Side Models: accurately represent reality. help a decision maker understand the problem. save time and money in problem solving and decision making. help communicate problems and solutions to others. provide the only way to solve large or complex problems in a timely fashion.

Models: The Down Side Models: may be expensive and time-consuming to develop and test. are often misused and misunderstood (and feared) because of their mathematical complexity. tend to downplay the role and value of nonquantifiable information. often have assumptions that oversimplify the variables of the real world.

QM for Windows

QM for Windows

Excel QM

Excel QM’s Main Menu of Models

Excel QM’s Main Menu of Models continued The highlighted area shows forecasting models The End