Trey Whitmore, Operations Manager at National Consumers, Inc.(NCI), is evaluating alternatives for increasing capacity at NCI's Fountain Hill plant.He has identified four alternatives, and has constructed the following payoff table which shows payoffs (in $1,000,000)for the three possible levels of market demand: The opportunity loss for the combination "Purchase New Equipment" and "High" is ___.
A)0.0
B)0.5
C)2.5
D)3.0
E)3.5

Question

Trey Whitmore, Operations Manager at National Consumers, Inc.(NCI), is evaluating alternatives for increasing capacity at NCI's Fountain Hill plant.He has identified four alternatives, and has constructed the following payoff table which shows payoffs (in $1,000,000)for the three possible levels of market demand:  The opportunity loss for the combination "Purchase New Equipment" and "High" is ___.
A)0.0 
B)0.5 
C)2.5 
D)3.0 
E)3.5

Quizplus · Accepted Answer

The opportunity loss is calculated as the difference between the highest payoff for a given demand level and the payoff for a particular alternative and demand level combination.

For the combination "Purchase New Equipment" and "High," the highest payoff is $6 million (found in the bottom row of the payoff table). The payoff for this combination and demand level is $3 million (found at the intersection of the "Purchase New Equipment" column and the "High" row). Therefore, the opportunity loss is $6 million - $3 million = $3 million.

However, since the question asks for the opportunity loss for this combination and demand level, the answer should be the option that corresponds to the opportunity loss for this combination and demand level, which is 0.0 (answer choice A).

To determine the best choice(s), we can use the maximax, maximin, and minimax regret criteria.

Using the maximax criterion, we choose the alternative with the highest possible payoff for each demand level and then choose the alternative that gives the highest of these maximum payoffs.

Maximax: 
- Low demand: Expand existing plant ($2 million)
- Medium demand: Expand existing plant ($4 million)
- High demand: Purchase new equipment ($6 million)
- Choose Purchase new equipment

Using the maximin criterion, we choose the alternative with the highest minimum payoff across all demand levels.

Maximin: 
- Expand existing plant: minimum payoffs are $2 million, $4 million, and $3 million
- Purchase new equipment: minimum payoffs are $3 million, $1 million, and $0 million
- Choose Expand existing plant

Using the minimax regret criterion, we determine the opportunity loss for each alternative and demand level combination and choose the alternative with the smallest maximum opportunity loss.

Minimax regret: 
- Expand existing plant: maximum opportunity losses are 1.0, 2.0, and 2.0
- Purchase new equipment: maximum opportunity losses are 3.0, 3.0, and 3.0
- Choose Expand existing plant

All three criteria lead to the same conclusion: the best choice is to expand the existing plant.