Quantitative Analysis

Dr. Abdallah Abdallah

Fall Term 2014

1

Introduction to quantitative analysis

Ch. 1

2

What‘s quantitative analysis?

QA-approach

Application of the scientific method to managerial decision making

Typically via mathematical laws

Basic procedure

Developing models and testing them

Considering both quantitative and qualitative factors

3

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

4

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-Develop a clear statement of the problem is the most important step -Develop specific measurable objectives

5

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-A model is a representation of reality -Mathematical models are relevant for QA, i.e., set of mathematical relationships -Basic terminology: variable=measurable entity that may vary (controllable vs. uncontrollable variables) parameter=measurable entity given by the problem -suitable input data should be available!

6

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-garbage in, garbage out! -make use of statistical sampling procedures

7

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-via solving equations, per trial and error, or through complete enumeration of solutions -accuracy of the solution is determined by the input data and by the model

8

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-before analyzing and implementing the results! -testing includes: a. Testing accuracy and

completeness of data b. Testing the model‘s internal

validity

9

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-sensitivity analysis, determining how different parameters and/ or data will change the solution

10

The QA-approach Defining the

problem

Developing a model

Aquiring input data

Developing a solution

Testing the solution

Analyzing the results

Implementing the results

-it is not straithforward to implement the obtained solution into an organization -implementation should be closely monitored

11

Example

Developing a profit model and calculate the break even point

Profit=revenues-expenses

=revenues-(fixed costs+variable costs)

12

Basic terminology

QA: scientific approach using quantitative techniques as a tool in decision making

Model: representation of reality

Mathematical model: set of mathematical relations

Algorithm: set of logical and mathematical operations performed in a specific sequence

Deterministic model: a model in which all value used are known with certainty

Probabilistic (or stochastic) model: all values used involve some chance or risk (probability)

13

Basic terminology

Variable vs. Parameter

Sensitivity analysis: a process involving the determination of how sensitive a solution is to changes in the formulation of the problem

14

The Pies are then processed and sold to local grocery stores in order to generate a profit.

Example 1: Simon Pie

Two ingredients combine to make Apple Pies: Fruit and frozen dough

performance measure variable

Profit Start here:

Decompose this variable into the intermediate variables Revenue and Total Cost

Profit

Revenue Total Cost

Now, further decompose each of these intermediate variables into more related intermediate variables ...

Profit

Revenue Total Cost

Pies Demanded

Pie Price Unit Pie

Processing Cost Fixed Cost

Processing

Cost

Ingredient

Cost

Unit Cost

Filling

Unit Cost

Dough

Required

Ingredient

Quantities

Step 3: Model Construction

Based on the previous Influence Diagram, create the equations relating the variables to be specified in the spreadsheet.

Profit

Revenue Total Cost

Profit = Revenue – Total Cost

Profit

Revenue

Pie Price

Pies Demanded

Revenue = Pie Price * Pies Demanded

Fixed Cost

Processing

Cost

Ingredient

Cost

Profit

Total Cost

Total Cost =

Processing Cost + Ingredients Cost + Fixed Cost

Processing Cost =

Pies Demanded *

Unit Pie Processing Cost

Processing

Cost

Total Cost

Pies Demanded

Unit Pie

Processing Cost

Profit

Ingredients Cost =

Qty Filling * Unit Cost Filling +

Qty Dough * Unit Cost Dough Ingredient

Cost

Profit

Total Cost

Unit Cost

Filling

Unit Cost

Dough

Required

Ingredient

Quantities

Simon’s Initial Model Input Values

Pie Price

Pies Demanded and sold

Unit Pie Processing Cost ($ per pie)

Unit Cost, Fruit Filling ($ per pie)

Unit Cost, Dough ($ per pie)

Fixed Cost ($000’s per week)

$8.00

16

$2.05

$3.48

$0.30

$12

Initial Simon Pie Weekly Profit Model

“What if?” Projection Allows you to determine what would happen if you used alternative inputs.

For example, what would the resulting Profit be if the Profit for Pie Price and Pies Demanded changed to $7.00 and 20,000 or $9.00 and 12,000, respectively.

Simply change the values of these parameters in the spreadsheet to view the resulting Profit.

What if we change the values of two parameters?

What effect will that have on Total Cost and Profit?

29

Home work Problems 1 - 18 1 – 19 1 – 20 1 – 21