a)
To determine: The probability that all three suppliers are disrupted using option 1.
Introduction:
a)
Answer to Problem 5P
The probability that three suppliers are disrupted using option 1 is 0.025062.
Explanation of Solution
Given information:
Option 1
Option 2
Formula:
Probability calculation when both suppliers are disrupted by option 1:
To find the probability of selection, one supplier substitutes the number of chosen suppliers, and the probability of super-event and unique-event in the above formula. Here, the number of suppliers chosen is ‘3’, S=0.025 and U=0.04, and is substituted in the above formula which gives probability as 0.025062.
Hence, the probability that two suppliers are disrupted using option 1 is 0.025062.
b)
To determine: The probability that all three suppliers are disrupted using option 2.
b)
Answer to Problem 5P
The probability that three suppliers are disrupted using option 1 is 0.011968.
Explanation of Solution
Given information:
Option 1
Option 2
Formula:
Probability calculation when both suppliers are disrupted by option 2:
To find the probability of selection, one supplier substitutes the number of chosen suppliers, anf the probability of super-event and unique-event in the above formula. Here, the number of suppliers chosen is ‘3’, S=0.004 and U=0.20, and is substituted in the above formula which gives probability as 0.011968.
Hence, the probability that two suppliers are disrupted using option 1 is 0.011968.
c)
To determine: The total annual expected cost for option 1.
c)
Answer to Problem 5P
The total expected cost for option 1 is $1,012,531.
Explanation of Solution
Given information:
Option 1
Option 2
Formula:
Calculation of total expected cost:
The total expected cost is calculated by taking the summation of the annual purchasing cost and expected disruption cost. The product of $500,000 and 0.025062 is added with $1,000,000, which gives $1,012,531 as the total expected cost for option 1.
Hence, the total expected cost using option 1 is $1,012,531.
d)
To determine: The total annual expected cost for option 2.
d)
Answer to Problem 5P
The total expected cost for option 2 is $1,015,984.
Explanation of Solution
Given information:
Option 1
Option 2
Formula:
Calculation of total expected cost:
The total expected cost is calculated by taking the summation of the annual purchasing cost and expected disruption cost. The product of $500,000 and 0.11968 is added with $1,010,000 which gives $1,015,984 as the total expected cost for option 2.
Hence, the total expected cost using option 2 is $1,015,984.
e)
To determine: The best options.
e)
Answer to Problem 5P
Option 1 is best.
Explanation of Solution
Given information:
Option 1
Option 2
On comparing equations (1) and (2), it can be inferred that option 1 has the least expected cost. Therefore, it is advisable for Company BJ to choose option 1.
Hence, Option 1 is best.
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Chapter 11 Solutions
Principles Of Operations Management
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