Finicky's Jeweler's

The Problem

Finicky's Jewelers sells watches for $50 each. During the next month, they estimate that they will sell 15, 25, 35, or 45 watches with respective probabilities of 0.35, 0.25, 0.20, and ... (figure it out). 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, Finicky's 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). Any customer that comes in during the month to buy a watch, but is unable to, costs Finicky's $6 in lost goodwill.

Find the best action under each of the four decision criteria.

The Solution

Creating the Payoff Table

  Buy 10   Buy 20   Buy 30   Buy 40   Buy 50  
Demand 15 10 bought at $40 -400 20 bought at $39 -780 30 bought at $37 -1110 40 bought at $36 -1440 50 bought at $34 -1700
  10 sold @ $50 500 15 sold @ $50 750 15 sold @ $50 750 15 sold @ $50 750 15 sold @ $50 750
  5 lost goodwill @ $6 -30 5 clearance at $24 120 15 clearance at $24 360 25 clearance at $24 600 35 clearance at $24 840
Total   70   90   0   -90   -110
                     
Demand 25 10 bought at $40 -400 20 bought at $39 -780 30 bought at $37 -1110 40 bought at $36 -1440 50 bought at $34 -1700
  10 sold @ $50 500 20 sold @ $50 1000 25 sold @ $50 1250 25 sold @ $50 1250 25 sold @ $50 1250
  15 lost goodwill @ $6 -90 5 lost goodwill @ $6 -30 5 clearance at $24 120 15 clearance at $24 360 25 clearance at $24 600
Total   10   190   260   170   150
                     
Demand 35 10 bought at $40 -400 20 bought at $39 -780 30 bought at $37 -1110 40 bought at $36 -1440 50 bought at $34 -1700
  10 sold @ $50 500 20 sold @ $50 1000 30 sold @ $50 1500 35 sold @ $50 1750 35 sold @ $50 1750
  25 lost goodwill @ $6 -150 15 lost goodwill @ $6 -90 5 lost goodwill @ $6 -30 5 clearance at $24 120 15 clearance at $24 360
Total   -50   130   360   430   410
                     
Demand 45 10 bought at $40 -400 20 bought at $39 -780 30 bought at $37 -1110 40 bought at $36 -1440 50 bought at $34 -1700
  10 sold @ $50 500 20 sold @ $50 1000 30 sold @ $50 1500 40 sold @ $50 2000 45 sold @ $50 2250
  35 lost goodwill @ $6 -210 25 lost goodwill @ $6 -150 15 lost goodwill @ $6 -90 5 lost goodwill @ $6 -30 5 clearance at $24 120
Total   -110   70   300   530   670

Payoff Table

    Buy
    10 20 30 40 50
Demand 15 70 90 0 -90 -110
25 10 190 260 170 150
35 -50 130 360 430 410
45 -110 70 300 530 670

Opportunistic Loss Table

    Buy
    10 20 30 40 50
Demand 15 20 0 90 180 200
25 250 70 0 90 110
35 480 300 70 0 20
45 780 600 370 140 0

Best Choices

  Buy Best Action
Criteria 10 20 30 40 50
Expected value -5 119 197 203 215 Buy 50
Maximax 70 190 360 530 670 Buy 50
Maximin -110 70 0 -90 -110 Buy 20
Minimax 780 600 370 180 200 Buy 40