Question

Probability and Decision Analysis

A smartphone supplier in Sydney is considering three alternative investment options: a large store, a small store, or an outlet in the shopping mall.  

Profits from selling smartphones will be affected by the customer demand for smartphones in Sydney. The following payoff table shows the profit that could result from each investment, in dollars ($).  

Investment type	Customer Demand
	Low	Medium	High
Large Store	7,000	6,000	5,000
Small Store	2,000	8,000	6,000
Outlet in Shopping Mall	8,000	15,000	20,000
Probability	0.2	0.5	0.3

1. What choice should be made by the optimistic decision maker?

2. What choice should be made by the pessimistic decision maker?

3. Compute the regrettable from the data.

4. What decision should be made under minimax regret approach?

5. What choice should be made under the expected value approach?

With excel

Answer 1

What choice should be made by the optimistic decision maker?

An optimistic decision-maker chooses the alternative whose maximum payoff is the maximum of the maximum payoffs of all the alternatives.

The maximum payoff of Large store = 7000

The maximum payoff of Small store = 8,000

The maximum payoff of outlet in the shopping mall = 20,000

The maximum of the maximum payoffs is 20,000 pertaining to an outlet in the shopping mall.

Therefore, the optimistic decision maker would choose an outlet in the shopping mall.

What choice should be made by the pessimistic decision maker?

The minimum payoff of Large store = 6,000

The minimum payoff of Small store = 2,000

The minimum payoff of outlet in the shopping mall = 8,000

The maximum of the minimum payoffs is 8,000 pertaining to an outlet in the shopping mall.

Therefore, the pessimistic decision maker would choose an outlet in the shopping mall.

Compute the regrettable from the data.

Regret table is the following:

Investment type	Low demand	Medium demand	High demand
Large store	MAX(7000,2000,8000)-7000 = 1000	MAX(6000,8000,15000)-6000    =9000	MAX(5000,6000,20000)-5000 =15000
Small store	MAX(7000,2000,8000)-2000 =6000	MAX(6000,8000,15000)-8000 =7000	MAX(5000,6000,20000)-6000 =14000
The outlet in the shopping mall	MAX(7000,2000,8000)-8000 =0	MAX(6000,8000,15000)-15000 =0	MAX(5000,6000,20000)-20000 =0

What decision should be made under minimax regret approach?

Maximum regret of Large store = MAX(1000,9000,15000) = 15000

Maximum regret of Small store = MAX(6000,7000,14000) = 14000

Maximum regret of Outlet in shopping mall = MAX(0,0,0) = 0

Minimum of the maximum regret is 0 pertaining to Outlet in a shopping mall

Therefore, under the minimax regret approach, the best decision is to open an Outlet in a shopping mall.

What choice should be made under the expected value approach?

Expected value of Large store	=0.2*7000+0.5*6000+0.3*5000=5900
Expected value of Small store	=0.2*2000+0.5*8000+0.3*6000=6200
Expected Value of Outlet in the shopping mall	=0.2*8000+0.5*15000+0.3*20000=15,100

The maximum expected Value is 15,100 pertaining to open Outlet in a shopping mall.

Therefore, under the expected Value approach, the best decision is to open an outlet in a shopping mall.