Chapter 1

Meaningful

Information

Quantitative

Analysis

A data driven approach to managerial decision making

Raw Data

“Big data” is a term that describes the large volume of data that inundates a business on a day-to-day basis.

Raw Data

The internet of things (IoT) in US, Industrie 4.0 in Germany and 物联网 (wù lián wăng) in China are all centered on the application of big data to business decision making

But….

The more data companies have the even more complex the problems of managing it can become. Do you buy hardware? Do you store it in the cloud? How often will you need to access it?

The more data you have, sometimes the harder it can be to find true value from the data.

Five of the six most damaging data thefts of all time have happened in the last two years. At the same time, failing to comply with data protection laws can lead to expensive lawsuits.

Python is an important programming language for data science and data mining because it is free, open source, easy to learn, easy to read, and scalable.

Python is particularly well suited when data analysis tasks involve integration with web apps or when there is a need to incorporate statistics into databases

Implementing the Results

Analyzing the Results

Testing the Solution

Developing a Solution

Acquiring Input Data

Developing a Model

Between “data in” and “information out” analysts are involved…

Defining the Problem

A specific and measurable statement of the problem

Provides clear direction

Goes beyond symptoms and identifies true causes

Avoids assumptions

Defining the Problem

Models are realistic & solvable mathematical representations of a situation

\$ Sales

Y = b0 + b1X

Models contain variables and parameters

Variables are the unknown

“How do sales increase with advertising?”

Parameters are the known inputs

“What amount was spent on sales each quarter?”

Developing a Model

Input data must be available & accurate

Data sources include: company reports, documents, employee interviews, direct measurement, statistical sampling

Acquiring Input Data

Run data through the model to arrive at the optimal solution

Developing a Solution

Validate the input data

Collect additional data from other sources to see if inputs remain the same

Validate the model

With consistent input data determine if model outputs are consistent

Testing the Solution

Determine the implications to the organization of implementing modeled solution

Conduct a sensitivity analysis to determine how results change if the model or input data changes (i.e. robustness means little change in the outputs based on large changes in the inputs)

Analyzing the Results

Incorporate the solution into the company

Management of Change in light of resistant

Monitor results to determine if modifications are necessary

Implementing the Results

Its not just enough to model data and reach conclusions analysts understand. Analysts must be able to present their conclusions in ways others understand.

Effective Data Visualization

Which graph types are the easiest for people to interpret accurately?

1. Dots on a line

2 . Graphs of dots on side by side lines with a common scale

3. Bar Charts

4. Pie charts

How to Develop a Quantitative Analysis Model

A mathematical model of profit:

Profit = Revenue – Expenses

How to Develop a Quantitative Analysis Model

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

How to Develop a Quantitative Analysis Model

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.

Let’s look at an example……

Rebuilt springs sell for \$8 per unit

Fixed cost of equipment to build springs is \$1,000

Variable cost for spring material is \$3 per unit

s = 8 f = 1,000 v = 3

In Excel we can make a parameter table.

By highlighting cells B:3 – D:5 and placing the mouse curser over the “All Borders” icon we can outline each cell with a box.

In Excel we can also make a table of different values of springs sold (X)

The equation for profits is sX – f – vX

Using our values \$8X – \$1,000 – \$3X

s = 8 f = 1,000 v = 3

Number of spring sets sold = X

In Excel we can make a table of profit for different values of springs sold (X)

To calculate profit look at cell C15 (-375):

(D3*D8) – D4 – (D5*D8)

(8*125) – 1000 – (3*125)

When we sell 125 we lose \$375

Why are “\$” around \$D\$3, \$D\$4,\$D\$5?

We want to solve the profit equation \$8X – \$1,000 – \$3X for each value of X.

For each value of X, the spring price (\$D\$3) fixed cost (\$D\$4) and variable cost (\$D\$5) do not change. The \$ in front of column (D) and the \$ in front of row (3,4,5) keep the values constant when we “copy – paste” the equation in C15 across (C16-C19)

Step1 Copy

Step 2 Paste

We can graph profit earned (Y) vs springs sold (X) by:

Highlighting the values for X and Y (cells B15-C19)

On the “Insert” tab selecting “Scatter” plot

To see our “Profit vs sales” linear equation we:

“Right click” the mouse and select “Format Trendline”

Then inside the “Format Trendline” pop-up-box we select “Display Equation on chart” and then “close” the pop-up box

Profit (Y) equals 5 times sales minus 1000.

The break-even point (BEP), is the number of units sold that will result in \$0 profit

0 = sX – f – vX, or 0 = (s – v)X – f

Solving for X, we have

f = (s – v)X

X = f/(s – v)

BEP = \$1,000/(\$8 – \$3) = 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

We could also see this on our linear equation

Y= 5x – 1000

0=5x-1000

1000=5x

200=x

We could also solve this using Python

We can open a file (attached to variable p) which we call breakeven

We use the suffix .dat because our file will have text and numbers

We write information to the file (called w)

The break even is when Y=0; so we assign y=0

we solve for x

In our answer we want to see the label The break even quantity is: prior to our answer

We then close the breakeven file associated with variable p

At this point we can print out the label and the answer

Models can accurately represent reality.

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

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

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

Models Categorized by Risk

Mathematical models that do not involve risk or chance are called deterministic models

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

Mathematical models that involve risk or chance are called probabilistic models

Values used in the model are estimates based on probabilities

The future vision is where the factory only produces a product when there is customer demand or an operation is only performed when there is a “data” signal.

We are shifting to a different paradigm: event-triggered control.

In this model, factories respond to events as they occur.

A machine that was planned to perform the next manufacturing step goes into (unplanned) maintenance mode which triggers the handling system to read parts’ Radio Frequency ID tags to determine the best way through the factory floor.