Reference no: EM131933378
Read and answer in detail #1, 2 and 3.
Problem 1.
Brenda Kelly runs a specialty ski clothing shop outside of Boone, North Carolina. She must place her order for ski parkas well in advance of ski season because the manufacturer produces them in the summer months. Brenda needs to determine whether to place a large (75 parkas), medium (50 parkas) or a small order (25 parkas).
The number sold will depend largely on whether the area receives a heavy, normal, or light amount of snow during the ski season. The following table summarizes the possible demand for parkas based on the weather condition.
|
Amount of Snow
|
|
Heavy
|
Normal
|
Light
|
|
Demand
|
75
|
50
|
20
|
Brenda estimates the probability of heavy, normal, and light snowfalls as 0.25, 0.6 and 0.15 respectively. Parkas are purchased from the supplier at a cost of $50 and sold for $100. Any parkas that are left over at the end of the season can be sold to a discount store for $10.
Construct the payoff table for this problem.
What decision should be made according to the maximax decision rule?
What decision should be made according to the maximin decision rule?
d. What decision should be made according to the minimax regret decision rule?
e. What decision should be made according to the expected value decision rule?
f. Assume that the probability of light snow is 0.15 but the probability of heavy or normal snow levels varies between 0 and 0.85. Assume the probability of heavy snow is denoted as Determine an algebraic expression for the expected payoffs for each alternative and find the crossover point where the expected payoff for making a large order is always the best.
Problem 2
The Hit and Miss Manufacturing Company produces items that have a probability of being defective. These items are produced in lots of 150. Past experience indicates that for the entire lot is either 0.05 or 0.25. Furthermore, in 80 percent of the lots produced, equals 0.05. (So = 0.25 in 20 percent of the lots).
These items are used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. Initially the company can either screen each item in a lot at a cost of $10 per item and replace defective items or use the items directly without screening. If the latter is chosen, the cost of rework is $100 per defective item. Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made two days before the screening can take place.
Develop a decision analysis formulation for this problem (define the states of nature, the alternatives, and the payoff table.
What decision should be made according to the maximax decision rule?
What decision should be made according to the maximin decision rule?
d. What decision should be made according to the minimax regret decision rule?
e. What decision should be made according to the expected value decision rule?
Problem 3
You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem.
Consider the following payoff matrix.
|
State of Nature
|
|
Decision
|
|
|
|
|
6
|
1
|
1
|
|
1
|
3
|
0
|
|
4
|
1
|
2
|
|
Prior Probability
|
0.3
|
0.4
|
0.3
|
Which alternative should be chosen according to Maximax criterion?
Which alternative should be chosen according to Maximin criterion?
Which
Problem 4.
Brenda Kelly runs a specialty ski clothing shop outside of Boone, North Carolina. She must place her order for ski parkas well in advance of ski season because the manufacturer produces them in the summer months.
Brenda needs to determine whether to place a large (75 parkas), medium (50 parkas) or a small order (25 parkas). The number sold will depend largely on whether the area receives a heavy, normal, or light amount of snow during the ski season. The following table summarizes the possible demand for parkas based on the weather condition.
|
Amount of Snow
|
|
Heavy
|
Normal
|
Light
|
|
Demand
|
75
|
50
|
20
|
Brenda estimates the probability of heavy, normal, and light snowfalls as 0.25, 0.6 and 0.15 respectively. Parkas are purchased from the supplier at a cost of $50 and sold for $100. Any parkas that are left over at the end of the season can be sold to a discount store for $10.
Construct the payoff table for this problem.
What decision should be made according to the maximax decision rule?
What decision should be made according to the maximin decision rule?
d. What decision should be made according to the minimax regret decision rule?
e. What decision should be made according to the expected value decision rule?
f. Assume that the probability of light snow is 0.15 but the probability of heavy or normal snow levels varies between 0 and 0.85. Assume the probability of heavy snow is denoted as Determine an algebraic expression for the expected payoffs for each alternative and find the crossover point where the expected payoff for making a large order is always the best.
Problem 5
The Hit and Miss Manufacturing Company produces items that have a probability of being defective. These items are produced in lots of 150. Past experience indicates that for the entire lot is either 0.05 or 0.25. Furthermore, in 80 percent of the lots produced, equals 0.05. (So = 0.25 in 20 percent of the lots). These items are used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. Initially the company can either screen each item in a lot at a cost of $10 per item and replace defective items or use the items directly without screening. If the latter is chosen, the cost of rework is $100 per defective item. Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made two days before the screening can take place.
a. Develop a decision analysis formulation for this problem (define the states of nature, the alternatives, and the payoff table.
b. What decision should be made according to the maximax decision rule?
c. What decision should be made according to the maximin decision rule?
d. What decision should be made according to the minimax regret decision rule?
e. What decision should be made according to the expected value decision rule?
Problem 6
You are given the following payoff table (in units of thousands of dollars) for a decision analysis problem.
Consider the following payoff matrix.
|
State of Nature
|
|
Decision
|
|
|
|
|
6
|
1
|
1
|
|
1
|
3
|
0
|
|
4
|
1
|
2
|
|
Prior Probability
|
0.3
|
0.4
|
0.3
|
Which alternative should be chosen according to Maximax criterion?
Which alternative should be chosen according to Maximin criterion?
Which alternative should be chosen according to expected value criterion?
Which alternative should be chosen according to Minimax Regret criterion?
alternative should be chosen according to expected value criterion?
Which alternative should be chosen according to Minimax Regret criterion?
7. The manager of a manufacturing plant is about to place an annual order for new material han- dling equipment for the plant. Every year he must determine which equipment to replace and which to keep for another year.
The factors involved in this decision include the cost of new equipment, the age of the current equipment, the equipment's useful life, and the salvage value of the equipment. A table displays the data for each of these factors. Any piece of equipment that is as old as its useful life must be replaced.
The manager will also replace any piece of equip- ment with a net cost (the cost for a new piece of equipment minus the equipment's salvage value) under $250. sing logical functions an the conditions mentioned above, complete the final column of the table with a "Yes" or a "No" to indicate whether or not the equipment should be replaced. (Refer to worksheet "4.9")