Quantitative Analysis Notes

Introduction to Quantitative Analysis

Learning Objectives

  • Describe the quantitative analysis approach.

  • Understand the application of quantitative analysis in a real situation.

  • Describe the use of modeling in quantitative analysis.

  • Use computers and spreadsheet models to perform quantitative analysis.

  • Discuss possible problems in using quantitative analysis.

  • Perform a break-even analysis.

Chapter Outline

  • Introduction

  • What Is Quantitative Analysis?

  • The Quantitative Analysis Approach

  • How to Develop a Quantitative Analysis Model

  • The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach

  • Possible Problems in the Quantitative Analysis Approach

  • Implementation — Not Just the Final Step

Introduction

  • Mathematical tools have been used for thousands of years.

  • Quantitative analysis can be applied to a wide variety of problems.

  • It’s not enough to just know the mathematics of a technique; 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 quantitative analysis models in the mid-1990s.

  • NBC television increased revenues by over 200 million between 1996 and 2000 by using quantitative analysis to develop better sales plans.

  • Continental Airlines saved over 40 million in 2001 using quantitative analysis models to quickly recover from weather delays and other disruptions.

What is Quantitative Analysis?

  • Quantitative analysis is a scientific approach to managerial decision making in which raw data are processed and manipulated to produce meaningful information.

  • Raw Data --> Quantitative Analysis --> Meaningful Information

Quantitative vs. Qualitative Factors

  • Quantitative factors: Data that can be accurately calculated.

    • Examples: Investment alternatives, interest rates, inventory levels, demand, labor cost.

  • Qualitative factors: More difficult to quantify but affect the decision process.

    • Examples: Weather, state and federal legislation, technological breakthroughs.

The Quantitative Analysis Approach

  • The general steps are:

    • Defining the Problem

    • Developing a Model

    • Acquiring Input Data

    • Developing a Solution

    • Testing the Solution

    • Analyzing the Results

    • Implementing the Results

Defining the Problem

  • Develop a clear and concise statement that gives direction and meaning to subsequent steps.

  • This may be the most important and difficult step.

  • It is essential to go beyond symptoms and identify true causes.

  • It may be necessary to concentrate on only a few of the problems

  • selecting the right problems is very important

  • Specific and measurable objectives may have to be developed.

Developing a Model

  • Quantitative analysis models are realistic, solvable, and understandable mathematical representations of a situation.

  • Types of Models:

    • Schematic models

    • Scale models

  • Models generally contain variables (controllable and uncontrollable) and parameters.

    • Controllable variables: Decision variables and are generally unknown (e.g., how many items should be ordered for inventory?).

    • Parameters: Known quantities that are a part of the model (e.g., What is the holding cost of the inventory?).

Acquiring Input Data

  • Input data must be accurate – GIGO (Garbage In, Garbage Out) rule.

  • Data may come from various sources such as company reports, documents, interviews, on-site direct measurement, or statistical sampling.

Developing a Solution

  • The best (optimal) solution to a problem is found by manipulating the model variables until a solution is found that is practical and can be implemented.

  • Common techniques:

    • Solving equations.

    • Trial and error – trying various approaches and picking the best result.

    • Complete enumeration – trying all possible values.

    • Using an algorithm – a series of repeating steps to reach a solution.

Testing the Solution

  • Both input data and the model should be tested for accuracy before analysis and implementation.

  • New data can be collected to test the model.

  • Results should be logical, consistent, and represent the real situation.

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 determines how much the results will change if the model or input data changes.

    • Sensitive models should be very thoroughly tested.

Implementing the Results

  • Implementation incorporates the solution into the company.

  • Implementation can be very difficult.

  • People may be resistant to changes.

  • Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented.

  • Changes occur over time, so even successful implementations must be monitored to determine if modifications are necessary.

Modeling in the Real World

  • Quantitative analysis models are used extensively by real organizations to solve real problems.

  • In the real world, quantitative analysis models can be complex, expensive, and difficult to sell.

  • Following the steps in the process is an important component of success.

How To Develop a Quantitative Analysis Model

  • A mathematical model of profit:

    • Profit = Revenue – Expenses

  • Expenses can be represented as the sum of fixed and variable costs.

  • Variable costs are the product of unit costs times the number of units.

    • Profit = Revenue – (Fixed cost + Variable cost)

    • Profit = (Selling price per unit)(number of units sold) – [Fixed cost + (Variable costs per unit)(Number of units sold)]

    • Profit = sX – [f + vX]

    • Profit = sX – f – vX

      • where:

        • s = selling price per unit

        • v = variable cost per unit

        • f = fixed cost

        • X = number of units sold

  • The parameters of this model are f, v, and s as these are the inputs inherent in the model

  • The decision variable of interest is X

Pritchett’s Precious Time Pieces Example

  • Profits = sX – f – vX

  • 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.

    • s = 10

    • f = 1,000

    • v = 5

  • Number of spring sets sold = X

  • If sales = 0, profits = -f = –1,000.

  • If sales = 1,000, profits = (10)(1,000) – 1,000 – (5)(1,000) = 4,000

Ray Bond – Yard Decorations Example

  • Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is 20 each, and he sells them for 50. The cost to rent a booth at the fair is 150.

  • How much is the profit if he sells 50 pieces?

Break-Even Point (BEP) Calculation

  • 0 = sX – f – vX, or 0 = (s – v)X – f

  • Companies are often interested in the break-even point (BEP).

  • The BEP is the number of units sold that will result in 0 profit.

  • Solving for X, we have:

    • f = (s – v)X

    • X = \frac{f}{s – v}

    • BEP = \frac{Fixed cost}{(Selling price per unit) – (Variable cost per unit)}

Pritchett’s Precious Time Pieces BEP Example

  • BEP = \frac{1,000}{10 – 5} = 200 units

  • Sales of less than 200 units of rebuilt springs will result in a loss.

  • Sales of over 200 units of rebuilt springs will result in a profit.

Ray Bond – Yard Decorations Questions

  • Ray Bond sells handcrafted yard decorations at county fairs. The variable cost to make these is 20 each, and he sells them for 50. The cost to rent a booth at the fair is 150.

    • If Ray sells 200 pieces, what is his total expenses?

    • If Ray sells, 50 pieces, how much is his total revenue?

    • How many of these must Ray sell to break even?

Advantages of Mathematical Modeling

  1. Models can accurately represent reality.

  2. Models can help a decision maker formulate problems.

  3. Models can give us insight and information.

  4. Models can save time and money in decision making and problem-solving.

  5. A model may be the only way to solve large or complex problems in a timely fashion.

  6. A model can be used to communicate problems and solutions to others.

Models Categorized by Risk

  • Deterministic models: Mathematical models that do not involve risk.

    • All of the values used in the model are known with complete certainty.

  • Probabilistic models: Mathematical models that involve risk, chance, or uncertainty.

    • Values used in the model are estimates based on probabilities.

Possible Problems in the Quantitative Analysis Approach

  • Defining the problem

    • Problems may not be easily identified.

    • There may be conflicting viewpoints

    • There may be an impact on other departments.

    • Beginning assumptions may lead to a particular conclusion.

    • The solution may be outdated.

  • Developing a model

    • Manager’s perception may not fit a textbook model.

    • There is a trade-off between complexity and ease of understanding.

  • Acquiring accurate input data

    • Accounting data may not be collected for quantitative problems.

    • The validity of the data may be suspect.

  • Developing an appropriate solution

    • The mathematics may be hard to understand.

    • Having only one answer may be limiting.

  • Testing the solution for validity

  • Analyzing the results in terms of the whole organization

Implementation – Not Just the Final Step

  • There may be an institutional lack of commitment and resistance to change.

    • Management may fear the use of formal analysis processes will reduce their decision-making power.

    • Action-oriented managers may want “quick and dirty” techniques.

    • Management support and user involvement are important.

  • There may be a lack of commitment by quantitative analysts.

    • Analysts should be involved with the problem and care about the solution.

    • Analysts should work with users and take their feelings into account.