TABLE 13.3 Expected cost for each possible outcome And the demand probabilities are If the stocking The expected cost will be 2 3 prob. = .20 prob. =.40 prob. = .30 prob. =.10 level is 1 unit short .40(1) ($4,200) = $1,680 S=D 2 units short .30(2) 3 units short .10(3) $0 ($4,200) = $2,520 ($4,200) = $1,260 $5,460 1-unit excess .20(1) ($800) = $160 2 units short .10(2) ($4,200) = $840 S=D 1 unit short .30(1) ($4,200) = $1,260 $0 $2,260 2-unit excess .20(2) ($800) = $320 1-unit excess .40(1) ($800) = $320 S=D 1 unit short .10(1) ($4,200) = $420 $0 $1,060 2-unit excess .40(2) ($800) = $640 1-unit excess .30(1) ($800) = $240 3-unit excess .20(3) S=D ($800) = $480 $0 $1,360

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 21P
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A manager is going to purchase new processing equipment and must decide on the number of
spare parts to order with the new equipment. The spares cost $200 each, and any unused spares
will have an expected salvage value of $50 each. The probability of usage can be described by this
distribution:
Number 0 1 2 3
Probability .10 .50 .25 .15
If a part fails and a spare is not available, two days will be needed to obtain a replacement
and install it. The cost for idle equipment is $500 per day. What quantity of spares should be
ordered?
a. Use the ratio method.
b. Use the tabular method (see Table 13.3).

TABLE 13.3
Expected cost for each possible outcome
And the demand probabilities are
If the
stocking
The expected
cost will be
2
3
prob. = .20
prob. =.40
prob. = .30
prob. =.10
level is
1 unit short .40(1)
($4,200) = $1,680
S=D
2 units short .30(2)
3 units short .10(3)
$0
($4,200) = $2,520
($4,200) = $1,260
$5,460
1-unit excess .20(1)
($800) = $160
2 units short .10(2)
($4,200) = $840
S=D
1 unit short .30(1)
($4,200) = $1,260
$0
$2,260
2-unit excess .20(2)
($800) = $320
1-unit excess .40(1)
($800) = $320
S=D
1 unit short .10(1)
($4,200) = $420
$0
$1,060
2-unit excess .40(2)
($800) = $640
1-unit excess .30(1)
($800) = $240
3-unit excess .20(3)
S=D
($800) = $480
$0
$1,360
Transcribed Image Text:TABLE 13.3 Expected cost for each possible outcome And the demand probabilities are If the stocking The expected cost will be 2 3 prob. = .20 prob. =.40 prob. = .30 prob. =.10 level is 1 unit short .40(1) ($4,200) = $1,680 S=D 2 units short .30(2) 3 units short .10(3) $0 ($4,200) = $2,520 ($4,200) = $1,260 $5,460 1-unit excess .20(1) ($800) = $160 2 units short .10(2) ($4,200) = $840 S=D 1 unit short .30(1) ($4,200) = $1,260 $0 $2,260 2-unit excess .20(2) ($800) = $320 1-unit excess .40(1) ($800) = $320 S=D 1 unit short .10(1) ($4,200) = $420 $0 $1,060 2-unit excess .40(2) ($800) = $640 1-unit excess .30(1) ($800) = $240 3-unit excess .20(3) S=D ($800) = $480 $0 $1,360
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