Decision Making with Probability Report for Boutique Catering

This report analyzes the potential expansion of Boutique Catering into the frozen meal market, utilizing probability and decision-making techniques. It begins with an executive summary and table of contents, followed by calculations of expected value and variance for frozen meal sales based on survey data. A memorandum to the marketing team is included, highlighting the need for market research to understand demand for vegetarian and specialty meals. The report then presents an alternative analysis using a decision tree to evaluate the profitability of the frozen meal business under favorable and unfavorable market conditions. Finally, the report explores decision-making under uncertainty using maximax, maximin, equally likely, and minimax decision rules to determine the optimal area to purchase for a conference center expansion. The conclusion emphasizes the importance of market analysis and recommends purchasing 100 square meters of area based on the equally likely and minimax decisions.

Running head: DECISION MAKING WITH CONCEPT OF PROBABILITY
Decision Making with Concept of Probability
Name of the Student:
Name of the University:
Author Note:

1DECISION MAKING WITH CONCEPT OF PROBABILITY
Executive Summary
There are few technical steps what is used in analysing the market to take decision while
expanding the business. Here, expected value and variance is used to write a memorandum to
the marketing team of the business. The analysis of decision is making is easy with the help
of decision tree and decision table. An example and few techniques like, minmax decision,
maximin decision, equally likely decision and maximax decision are shown in this report.

2DECISION MAKING WITH CONCEPT OF PROBABILITY
Table of Contents
Answer to Question 1.1: Expected value and variance of number of frozen meals..................3
Answer to Question 1.2: Memorandum on the basis of previous anlaysis................................4
Answer to Question 2: Alternative analysis with decision tree.................................................5
Answer to Question 3.1: Maximax Decision.............................................................................5
Answer to Question 3.2: Maximin Decision..............................................................................5
Answer to Question 3.3: Equally Likely Decision.....................................................................6
Answer to Question 3.4: Minimax Decision..............................................................................6
Conclusion..................................................................................................................................7
Reference....................................................................................................................................8

3DECISION MAKING WITH CONCEPT OF PROBABILITY
Answer to Question 1.1: Expected value and variance of number of frozen meals
Number of frozen
meals
Probability
1 0.05
2 0.10
3 0.15
4 0.20
5 0.20
6 0.15
7 0.10
8 0.05
The sum of expected value for the (1+2+3+4+5+6+7+8) =36 frozen meals:
( 1∗0.05 ) + ( 2∗0.10 )+ ( 3∗0.15 )+ ( 4∗0.20 )+ (5∗0.20 )+ ( 6∗0.15 )+ ( 7∗0.10 ) + ( 8∗0.05 )
¿ 0.05+0.20+ 0.45+0.8+1+0.9+ 0.7+0.4
¿ 4.5
The variance of the (1+2+3+4+5+6+7+8) =36 frozen meals:
{ ( 1−4.5 )2∗0.05 }+ { ( 2−4.5 )2∗0.1 }+ { ( 3−4.5 )2∗0.15 }+ { ( 4−4.5 )2∗0.20 }+ { ( 5−4.5 )2∗0.2 }+ { ( 6−4.5 )2∗0.15 }+ { ( 7−4
¿ 0.6125++0.625+0.3375+0.05+0.3375+0.625+0.6125
¿ 3.25

4DECISION MAKING WITH CONCEPT OF PROBABILITY
Answer to Question 1.2: Memorandum on the basis of previous anlaysis
MEMORANDUM
Date: 05.08.2019
To: Management of Boutique Catering
From: [Name, Designation]
Subject: Sales of frozen meals.
This memorandum is prepared to have an overview of possible sales while the
company will expand the business by preparing the frozen meals which will be home-
delivered. The analysis on the survey data estimated that in the long-term an average of 4.5
frozen meals will be home-delivered. The variance of the data set shows that the volatility of
sales is very high. As, the meals Boutique Catering is going to offer every day vegetarian
and specialty meals (for people who have allergies) which generates a variation in the ordered
meals. Hence, a proper market research is required to get an overview of the market. One
thing can be done through market research is to get the separate daily market demand and
supply of the two types of meal, vegetarian and specialty meals (for people who have
allergies). It will be very help for the Boutique Catering to set the price and amount of the
production to meet the daily demand for the vegetarian and specialty meals separately.

5DECISION MAKING WITH CONCEPT OF PROBABILITY
Favourable
demand Market is not favourable.
$200,000
No actionsLoss
Profit
$50,000 $ 0
Answer to Question 2: Alternative analysis with decision tree
The probability of success of the frozen meals business is 0.5. There are two
conditions one when the demand is favourable and the other one is not favourable. There are
3 outcomes from the two conditions. For favourable demand there is a profit of $200,000 and
for not favourable demand, there is a loss of $50,000 or nothing for not taking any action.
Here the decision tree is presented (Anderson et al., 2015).
Figure 1: Decision Tree for the analysis of the problem
The formula to calculate the expected value: p . x + ( 1− p ) . y
Where, p is the probability of the favourable market, (1-p) is the probability of the
unfavourable market, x is the outcome form the favourable market, y is the outcome from the
unfavourable market.
The expected value of the profit if they chose to do business where market is not
favourable: (200,000*0.5) - (50,000*0.5) = $75,000.
The expected value of the profit if they do nothing where market is not favourable:
(200,000*0.5) - (0*0.5) = $100,000.

6DECISION MAKING WITH CONCEPT OF PROBABILITY
Hence, the decision should be doing nothing where market is not favourable as the
expected value in that condition is higher.
Answer to Question 3.1: Maximax Decision
Area of conference
centre purchased Strong market Average
market Weak market Best
50 1,00,000 40,000 -20,000 1,00,000
100 1,60,000 60,000 -40,000 1,60,000
150 1,00,000 60,000 -80,000 1,00,000
200 4,00,000 50,000 -3,20,000 4,00,000
The maximax decision is purchasing the 200 square meter of area.
Answer to Question 3.2: Maximin Decision
Area of conference
centre purchased Strong market Average
market Weak market Worst
50 1,00,000 40,000 -20,000 -20,000
100 1,60,000 60,000 -40,000 -40,000
150 1,00,000 60,000 -80,000 -80,000
200 4,00,000 50,000 -3,20,000 -3,20,000
The minmax decision is purchasing the 50 square meter of area (Greco, Figueira & Ehrgott,
2016).
Answer to Question 3.3: Equally Likely Decision
Area of conference
centre purchased Strong market Average
market Weak market Average
50 1,00,000 40,000 -20,000 40,000
100 1,60,000 60,000 -40,000 60,000
150 1,00,000 60,000 -80,000 26,667
200 4,00,000 50,000 -3,20,000 43,333
The equally likely decision is purchasing the 100 square meter of area.

7DECISION MAKING WITH CONCEPT OF PROBABILITY
Answer to Question 3.4: Minimax Decision
Area of conference centre
purchased Strong market Average market Weak market
50 1,00,000 40,000 -20,000
100 1,60,000 60,000 -40,000
150 1,00,000 60,000 -80,000
200 4,00,000 50,000 -3,20,000
Regret Table
Area of
conference
centre
purchased
Strong market Average market Weak market Maximum
50 (4,00,000-1,00,000)
=3,00,000
(60,000-40,000)
=20,000
-20,000-(-20,000)
=0 3,00,000
100 (4,00,000-1,60,000)
=2,40,000
(60,000-60,000)
=0
-20,000-(-40,000)
=20,000 2,40,000
150 (4,00,000-1,00,000)
=3,00,000
(60,000-60,000)
=0
-20,000-(-80,000)
=60,000 3,00,000
200 (4,00,000-4,00,000)
=0
(60,000-50,000)
=10,000
-20,000-(-3,20,000)
=3,00,000 3,00,000
The Minimax decision is purchasing the 100 square meter of area.
Conclusion
The expected value and variance are not enough to make an overview of the sales of
the frozen meals for which a market analysis for demand and supply of the meals is
recommended. The decision of purchasing the 100 square meter of area is supported by the
equally likely decision and minimax decision method. Whereas maximax and maximin
decision supports the decision of purchasing 200 square meter and 50 square meter of area
repectively.

8DECISION MAKING WITH CONCEPT OF PROBABILITY
Reference
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2015). An
introduction to management science: quantitative approaches to decision making.
Cengage learning.
Greco, S., Figueira, J., & Ehrgott, M. (2016). Multiple criteria decision analysis. New York:
Springer.
Kassa, A. M. (2017). APPLICATION OF DECISION MAKING WITH UNCERTAINTY
TECHNIQUES: A CASE OF PRODUCTION VOLUME OF MAIZE IN ETHIOPIA.
International Journal for Quality Research, 11(2).
Tajima, S., Drugowitsch, J., & Pouget, A. (2016). Optimal policy for value-based decision-
making. Nature communications, 7, 12400.