Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Advance sales are so small that Weiss has no way to estimate the demand for the red roses. She buys roses for $15 per dozen and sells them for $40 per dozen. Pay-off table for the problem is given below. Apply each of the criteria given below to determine the decision Weiss should make.
There is no payoff table below
To determine the decision Adele Weiss should make, we need to apply a decision-making criterion. There are several criteria that can be used, including the maximin, maximax, minimax regret, and criterion of realism. Let's apply each of these criteria to the given pay-off table:
Pay-off table:
Demand
Low (20 dozen) Medium (30 dozen) High (40 dozen)
Order (100 dozen) $0 $450 $900
Order (200 dozen) $300 $600 $1,200
Order (300 dozen) $600 $750 $1,800
1. Maximin criterion:
This criterion involves choosing the decision alternative that maximizes the minimum pay-off for each state of nature. To apply this criterion, we find the minimum pay-off for each decision alternative:
For ordering 100 dozen: The minimum pay-off is $0.
For ordering 200 dozen: The minimum pay-off is $300.
For ordering 300 dozen: The minimum pay-off is $600.
Based on the maximin criterion, Adele Weiss should choose to order 100 dozen roses since it has the highest minimum pay-off.
2. Maximax criterion:
The maximax criterion involves choosing the decision alternative that maximizes the maximum pay-off for each state of nature. To apply this criterion, we find the maximum pay-off for each decision alternative:
For ordering 100 dozen: The maximum pay-off is $900.
For ordering 200 dozen: The maximum pay-off is $1,200.
For ordering 300 dozen: The maximum pay-off is $1,800.
Based on the maximax criterion, Adele Weiss should choose to order 300 dozen roses since it has the highest maximum pay-off.
3. Minimax regret criterion:
The minimax regret criterion involves determining the regret for each decision alternative and selecting the one with the least maximum regret. To apply this criterion, we need to calculate the regret for each decision alternative (the difference between the maximum possible pay-off and the pay-off for each state of nature):
For ordering 100 dozen:
- Regret for low demand: $900 - $0 = $900
- Regret for medium demand: $1,200 - $450 = $750
- Regret for high demand: $1,800 - $900 = $900
For ordering 200 dozen:
- Regret for low demand: $900 - $300 = $600
- Regret for medium demand: $1,200 - $600 = $600
- Regret for high demand: $1,800 - $1,200 = $600
For ordering 300 dozen:
- Regret for low demand: $900 - $600 = $300
- Regret for medium demand: $1,200 - $750 = $450
- Regret for high demand: $1,800 - $1,800 = $0
Based on the minimax regret criterion, Adele Weiss should choose to order 300 dozen roses since it has the least maximum regret.
4. Criterion of realism:
The criterion of realism involves evaluating the decision alternatives based on other factors, such as budget constraints, market conditions, and practical considerations. It may incorporate subjective judgments and qualitative factors. This criterion is less objective than the previous three criteria but can still be considered when making a decision.
To apply the criterion of realism, Adele Weiss should consider factors such as her budget, the current demand trends for red roses, and any other practical considerations that may influence her decision. It is important to assess the specific context and limitations of the flower shop before making a final decision.
By considering all four criteria, Adele Weiss can make a more informed decision regarding the number of roses to order for her flower shop.