Brenda Kelly runs a specialty ski clothing shop outside of Boone, North Carolina
ID: 3202507 • Letter: B
Question
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, medium or a small order. 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. 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 maxima decision rule? What decision should be made according to the maximin decision rule? What decision should be made according to the minimax regret decision rule? What decision should be made according to the expected value decision rule? 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.Explanation / Answer
Solution
Preparatory Work
Pay-off = Order Quantity x {100(selling price) – 50(cost)} if demand order Quantity
= Demand x {100(selling price) – 50(cost)} – {(Order Quantity - Demand){50 – 10)}
if order Quantity Demand
EMV (Expected Monetary Value) = sum of (pay-off x probability)
Now, to answer the questions,
Pay-off table alongwith row max, row min and EMV is given below:
Order
Amount of snowfall (probability)(Demand)
Row
Row
EMV
Quantity
Heavy (0.25)(75)
Normal (0.6)(50)
Light (0.15)(20)
max
min
75
3750
1500
- 1200
3750
- 1200
1657.5
50
2500
2500
- 200
2500
- 200
2095.0
25
1250
1250
800
1250
800
1182.5
Since max of row max is 3750, order 75 under maxi-max criterion
Since min of row max is 1250, order 25 under mini-max criterion
Since max of row min is 800, order 25 under maxi-min criterion
Since maximum EMV is 2095.0, order 50 under EMV criterion.
Order
Amount of snowfall (probability)(Demand)
Row
Row
EMV
Quantity
Heavy (0.25)(75)
Normal (0.6)(50)
Light (0.15)(20)
max
min
75
3750
1500
- 1200
3750
- 1200
1657.5
50
2500
2500
- 200
2500
- 200
2095.0
25
1250
1250
800
1250
800
1182.5
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