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

qty	desc	unit	ext
10	bought	-40	-400
10	sold	50	500
5	goodwill	-6	-30
	total		70

qty	desc	unit	ext
20	bought	-39	-780
15	sold	50	750
5	clearance	24	120
	total		90

qty	desc	unit	ext
30	bought	-37	-1110
15	sold	50	750
15	clearance	24	360
	total		0

qty	desc	unit	ext
40	bought	-36	-1440
15	sold	50	750
25	clearance	24	600
	total		-90

qty	desc	unit	ext
50	bought	-34	-1700
15	sold	50	750
35	clearance	24	840
	total		-110

Demand 25

qty	desc	unit	ext
10	bought	-40	-400
10	sold	50	500
15	goodwill	-6	-90
	total		10

qty	desc	unit	ext
20	bought	-39	-780
20	sold	50	1000
5	goodwill	-6	-30
	total		190

qty	desc	unit	ext
30	bought	-37	-1110
25	sold	50	1250
5	clearance	24	120
	total		260

qty	desc	unit	ext
40	bought	-36	-1440
25	sold	50	1250
15	clearance	24	360
	total		170

qty	desc	unit	ext
50	bought	-34	-1700
25	sold	50	1250
25	clearance	24	600
	total		150

Demand 35

qty	desc	unit	ext
10	bought	-40	-400
10	sold	50	500
25	goodwill	-6	-150
	total		-50

qty	desc	unit	ext
20	bought	-39	-780
20	sold	50	1000
15	goodwill	-6	-90
	total		130

qty	desc	unit	ext
30	bought	-37	-1110
30	sold	50	1500
5	goodwill	-6	-30
	total		360

qty	desc	unit	ext
40	bought	-36	-1440
35	sold	50	1750
5	clearance	24	120
	total		430

qty	desc	unit	ext
50	bought	-34	-1700
35	sold	50	1750
15	clearance	24	360
	total		410

Demand 45

qty	desc	unit	ext
10	bought	-40	-400
10	sold	50	500
35	goodwill	-6	-210
	total		-110

qty	desc	unit	ext
20	bought	-39	-780
20	sold	50	1000
25	goodwill	-6	-150
	total		70

qty	desc	unit	ext
30	bought	-37	-1110
30	sold	50	1500
15	goodwill	-6	-90
	total		300

qty	desc	unit	ext
40	bought	-36	-1440
40	sold	50	2000
5	goodwill	-6	-30
	total		530

qty	desc	unit	ext
50	bought	-34	-1700
45	sold	50	2250
5	clearance	24	120
	total		670

Payoff Table

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

Opportunistic Loss Table

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

Best Choices

Criteria	Buy 10	Buy 20	Buy 30	Buy 40	Buy 50	Best Action
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