Abu Dhabi School of Management Decision Analysis Project

This project analyzes a decision-making scenario for a social media platform, evaluating whether to sell user data or perform data analysis. The assignment utilizes various decision criteria, including Maximax, Maximin, Regret, Maximum Likelihood, and Expected Value, to determine the optimal course of action. It also incorporates a decision tree to assess the value of hiring a consultant. Furthermore, the project extends to a production optimization problem, employing Excel Solver to maximize profit by determining the optimal production quantities for chairs, tables, and sofas, considering departmental capacity constraints. The analysis includes sensitivity and limits reports to provide a comprehensive understanding of the decision-making process and optimization outcomes, with references to key decision analysis texts.

Abu Dhabi School of Management
Decision Analysis
Group out of Class assessment
May 2018

Q1
A company runs a social media platform
Courses of action; sell the users data
Perform the analysis
If the firm perform the analysis there is 2/3 probability of obtaining an interesting pattern.
Data analysis process cost $ 100,000
The payoff table
Courses of actions States of nature
Obtaining a
pattern
No pattern
Sell the users data $ 50,000 $ 50,000
Perform the analysis $ 300,000 ($ 100,000)
Probability 2/3 1/3
 Optimal decision under the Maximax Criterion
Courses of actions States of nature
Obtaining a
pattern
No pattern Max
Sell the users data $ 50,000 $ 50,000 $ 50,000
Perform the analysis $ 300,000 ($ 100,000) $ 300,000
Probability 2/3 1/3
The optimal decision is to perform the analysis
 Optimal decision under the Maximin Criterion
Courses of actions States of nature
Obtaining a
pattern
No pattern Min
Sell the users data $ 50,000 $ 50,000 $ 50,000
Perform the analysis $ 300,000 ($ 100,000) $ (100,000)

Probability 2/3 1/3
The optimal decision will be to sell the data to a data analysis firm
 Optimal decision under the Regret Criterion
The regret table
Courses of actions States of nature
Obtaining a pattern No pattern Maximum
Sell the users data ($ 250,000) $ 0 $ 0
Perform the analysis $ 0 $ 150,000 $ 150,000
Probability 2/3 1/3
The optimal decision will be to sell the data to a data analysis company.
 Optimal decision under the Maximum Likelihood Criterion
Courses of actions States of nature
Obtaining a
pattern
No pattern
Sell the users data $ 50,000 $ 50,000
Perform the analysis $ 300,000 ($ 100,000)
Probability 2/3 1/3
The optimal decision is for the company to undertake the analysis.
 Optimal decision based on the expected Value Criterion
Courses of actions States of nature
Obtaining a
pattern
No pattern Expected value
Sell the users data $ 50,000 $ 50,000 $ 50,000
Perform the analysis $ 300,000 ($ 100,000) $ 166,666.67
Probability 2/3 1/3
The optimal decision is for the company to undertake the analysis

A company can hire a consultant before the analysis to gauge the possible behavior of their
data. The expense of hiring a consultant is $ 20,000.
A drawing a decision tree
Signifies course of action
Signifies states of nature interesting $ 280,000
0.5
0.4 Not interesting ($ 20,000)
Successful 0.5
Hire Not successful useless data ($20,000)
0.5 0.6 6/7
Useful 1/7
Not hire 0.5 interesting $ 280,000 $ 280,000
2/3
Not interesting
1/3 ($ 120,000)
From the decision tree hiring a consultant before doing the analysis gives an expected
return of $ 65,714
Failing to hire a consultant prior to conducting the analysis gives an expected return of
$ 146,666.67
The expected value of doing the analysis is $ 106,190.48
Receiving a higher offer of $ 70,000 to sell the data does not change the nature of the
decision tree.
The decision tree will remain as

interesting $ 280,000
0.5
0.4 Not interesting ($ 20,000)
Successful 0.5
Hire Not successful useless data ($20,000)
0.5 0.6 6/7
Useful 1/7
Not hire 0.5 interesting $ 280,000 $ 280,000
2/3
Not interesting
1/3 ($ 120,000)
The expected value of doing the analysis still stands at $ 106,190.48 which is higher than the
amount received upon selling data. The firm will therefore choose to do the analysis on their
own.
The breakeven amount is the price at which the firm will make neither a profit nor a loss
The expected profit from doing the analysis is $ 106,190.48. if the firm is to receive a zero
profit then the new consultant will have to be paid $ 126,190.48
The probability range at which the optimal decision remains unchanged

interesting $ 280,000
0.5
0.4 Not interesting ($ 20,000)
Successful 0.5
Hire Not successful useless data ($20,000)
0.5 0.6 6/7
Useful 1/7
Not hire 0.5 interesting $ 280,000 $ 280,000
2/3
Not interesting
1/3 ($ 120,000)
The optimal decision will remain unchanged for all the probability values of successful
For instance, at 0 probability of being successful the tree diagram remains the same, but the
expected profit reduced to $ 84,762.57. Thus, though is still hire than the probability of
selling the data hence the firm decision remains unchanged
Q2
The first step is to define the constraints that will affect the production
Let one unit of chair be defines by c, tables by t and sofas by s
This are
Construction
0.5 c +1.5 t+1.5 s ≤115
Assembly

2 c+ 4 t +1 s ≤ 230
Testing
5 c +1t +0.5 s ≤155
Second will have to define the total time needed to construct each item and cost per hour of
the items
After setting the conditions we’ll apply the use of excel solver to optimize the scenario
This gives
The time required in each department for each unit and the corresponding
profit
products
units
produced
Constructi
ng Assembly
Testin
g Profit
chairs 24 12.07 48.28
120.6
9
181.0
3
$
217
Tables 0 0.00 0.00 0.00 0.00
$
-
Sofas 69 102.93 68.62 34.31
205.8
6
$
1,029
Department capacity
(hrs) 115
116.89655
2 155
$
1,247
The answer report is
Microsoft Excel 16.0 Answer Report
Worksheet: [Decision Analysis group.xlsx] Sheet1
Report Created: 22/05/2018 15:54:45
Result: Solver found a solution. All Constraints and optimality conditions are
satisfied.
Solver Engine
Engine: GRG Nonlinear

Solution Time: 0.047 Seconds.
Iterations: 0 Subproblems: 0
Solver Options
Max Time Unlimited, Iterations Unlimited, Precision 0.000001
Convergence 0.0001, Population Size 100, Random Seed 0, Derivatives Central
Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume Nonnegative
Objective Cell (Max)
Cell Name
Original
Value
Final
Value
$G$
7 Department capacity (hrs) Profit
$
1,247
$
1,247
Variable Cells
Cell Name
Original
Value
Final
Value Integer
$B$
4 chairs units produced 24 24 Contin
$B$
5 Tables units produced 0 0 Contin
$B$
6 Sofas units produced 69 69 Contin
Constraints
Cell Name Cell Value Formula Status Slack
$C$
7
Department capacity (hrs)
Constructing 115
$C$7<=11
5 Binding 0
$D$
7
Department capacity (hrs)
Assembly
116.896551
7
$D$7<=23
0
Not
Binding
113.103448
3
$E$ Department capacity (hrs) Testing 155 $E$7<=15 Binding 0

7 5
The sensitivity report is
Microsoft Excel 16.0 Sensitivity Report
Worksheet: [Decision Analysis group.xlsx] Sheet1
Report Created: 22/05/2018 15:54:56
Variable Cells
Final Reduced
Cell Name Value Gradient
$B$
4 chairs units produced
24.137931
03 0
$B$
5 Tables units produced 0
-
3.4137931
03
$B$
6 Sofas units produced
68.620689
66 0
Constraints
Final Lagrange
Cell Name Value Multiplier
$C$
7
Department capacity (hrs)
Constructing 115
9.7241379
31
$D$
7
Department capacity (hrs)
Assembly
116.89655
17 0
$E$
7 Department capacity (hrs) Testing 155
0.8275862
07
The limits report is

Microsoft Excel 16.0 Limits Report

Worksheet: [Decision Analysis group.xlsx]
Sheet1
Report Created: 22/05/2018
15:55:09
Objective
Cell Name Value
$G$
7
Department capacity (hrs)
Profit
$
1,247
Variable
Lowe
r
Objecti
ve
Upp
er
Objecti
ve
Cell Name Value Limit Result
Limi
t Result
$B$
4 chairs units produced 24 0 1029 24 1247
$B$
5 Tables units produced 0 0 1247 0 1247
$B$
6 Sofas units produced 69 0 217 69 1247
The correct number of each unit needed to optimize the profit as given by the solver is
Chairs 24
Tables 0
Sofas 69
The amount of profit in dollars is $ 1,247