Tiffany\'s Jewelers sell watches for $50 each. During the next month, they estim
ID: 3274252 • Letter: T
Question
Tiffany's Jewelers sell watches for $50 each. During the next month, they estimate that they might sell 15, 25, 35, or 45 watches. They can only buy watches in lots of ten from their dealer. 10, 20, 30, 40, and 50 watches cost $40, 39, 37, 36, and 34 per watch respectively. Every month, Tiffany has a clearance sale and will get rid of any unsold watches for $24 (watches are only in style for a month and so they have to buy the latest model each month). It any customer comes in during the month to buy a watch, but is unable to, this costs Tiffany $6 in lost goodwill.
a) applying each of the following approaches to find out wich decision is best for Tiffany under that approach
1. optimistic approach
2. pessimistic approach
3. Hurwicz approach (alpha=0.6)
4.minimax regret approach
5. equal likelihood approach
b). if they estimate that they will sell 15, 25, 35, or 45 watches with respective probabilities of 0.35, 0.25, 0.20, and ...(figure out), which is the best decision?
Explanation / Answer
Let n be the number of watches sold at $50, s be the number of watches in surplus after the month (sold at $24) and d be the number of watches in deficit which cost $6 for lost goodwill.
Then, the payoff of for each combination of decision and outcome is
n * profit - loss of surplus * s - 6d
So, the payoff table is,
1. optimistic approach -
Maximum payoff for each outcome is 70, 190, 360, 530, 670
Maximum of these payoff is 670. So the decision using optimistic approach is to get 50 watches from dealer.
2. pessimistic approach -
Minimum payoff for each outcome is -110, 70, 0, -90, -110
Maximum of these payoff is 70. So the decision using optimistic approach is to get 25 watches from dealer.
3. Hurwicz approach (alpha=0.6)
H for each decision is,
70 * 0.6 - 110 * 0.4 = -2
190 * 0.6 + 70 * 0.4 = 142
360 * 0.6 + 0 * 0.4 = 216
530 * 0.6 - 90 * 0.4 = 282
670 * 0.6 - 110 * 0.4 = 358
Maximum of these payoff is 358. So the decision using Hurwicz approach is to get 50 watches from dealer.
4. minimax regret approach
Regret table is,
Maximum regret for each decision is 780, 600, 370, 140, 0
Minimum of these is 0, so decision using minimax regret approach is to get 50 watches from dealer.
Profit loss of surplus DecisionOutcome 15 25 35 45 50-40=10 24 - 40 = -16 10 10*10-0-6*5 = 70 10*10-0-6*15 = 10 10*10-0-6*25 = -50 10*10-0-6*35 = -110 50-39=11 24 - 39 = -15 20 15*11-15*5-0 = 90 20*11-0-6*5 = 190 20*11-0-6*15 = 130 20*11-0-6*25 = 70 50-37=13 24 - 37 = -13 30 15*13-13*15-0 = 0 25*13-13*5 = 260 30*13-6*5 = 360 30*13-6*15 = 300 50-36=14 24 - 36 = -12 40 15*14 - 12*25 = -90 25*14 - 12*15 = 170 35*14 - 12*5 = 430 40*14 - 6*5 = 530 50-34=16 24 - 34 = -10 50 15*16 - 10*35 = -110 25*16 - 10*25 = 150 35*16 - 10*15 = 410 45*16 - 10*5 = 670