Concept explainers
a
Interpretation:Value of Q and R used to control the inventory of white dress shirts is to be determined.
Concept Introduction:
Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.
a
Answer to Problem 44AP
Order quantity (Q) is 240 units and Reorder point (R) is also 240 units.
Explanation of Solution
Given information:
Cost of each shirt = $6
Selling cost of each shirt = $15
Monthly demand = 120
Standard deviation of monthly demand = 32
Reorder point = Two months of demand,
Order quantity = two months of demand
Q refers to the order quantity and R refers to the reorder point.
Order quantity is two months of demand i.e. 120 units
The proprietor orders when stock falls below the two-month’s supply stock. The two month’s supply stock means 120 units
Order quantity (Q) is 240 units and Reorder point (R) is also 240 units.
b
Interpretation:Fill rate achieved with current policy is to be determined.
Concept Introduction:
Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.
b
Answer to Problem 44AP
The fill rate of 99.9% is being achieved in current policy.
Explanation of Solution
Given information:
Cost of each shirt = $6
Selling cost of each shirt = $15
Monthly demand = 120
Standard deviation of monthly demand = 32
Reorder point = Two months of demand,
Order quantity = two months of demand
Type 2 service:
Lead time given = 3 weeks =
Mean,
Standard deviation,
Therefore, the fill rate of 99.9% is being achieved in current policy.
c
Interpretation:Optimal value of Q and R is to be determined based on the 99% fill rate criteria.
Concept Introduction:
Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.
c
Answer to Problem 44AP
Optimal value of Q and R is (Q, R) = (455,107)
Explanation of Solution
Given information:
Cost of each shirt = $6
Selling cost of each shirt = $15
Monthly demand = 120
Standard deviation of monthly demand = 32
Reorder point = Two months of demand,
Order quantity = two months of demand
Iteration 1:
From
Iteration 2:
From
Iteration 3:
Since the Q value is repeating, we terminate further iteration
Hence, (Q, R) = (455,107)
d
Interpretation:Difference in average annual holding and set up costs is to be determined.
Concept Introduction:
Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.
d
Answer to Problem 44AP
Difference in average annual holding and set up costs is $257.
Explanation of Solution
Given information:
Cost of each shirt = $6
Selling cost of each shirt = $15
Monthly demand = 120
Standard deviation of monthly demand = 32
Reorder point = Two months of demand,
Order quantity = two months of demand
Considering (Q, R) from policy (b)
(Q, R) = (240,240)
Therefore, the annual holding cost and set up cost are $804.
Considering (Q, R) from policy (c)
(Q, R) = (455,107)
Therefore, the annual holding cost and set up cost are $547.
Saving on total = $804-$547 = $257
e
Interpretation:Time required paying for $25000 inventory
Concept Introduction:
Normal distribution is the probability function with continuous series. It is bell shaped distribution function where mean, median and mode are same.
e
Answer to Problem 44AP
Time required in paying $25,000 of inventory control is 4.86 yearsto the system.
Explanation of Solution
Given information:
Cost of each shirt = $6
Selling cost of each shirt = $15
Monthly demand = 120
Standard deviation of monthly demand = 32
Reorder point = Two months of demand,
Order quantity = two months of demand
Time required in paying $25,000 of inventory control is as shown below:
Assuming 20% of the annual interest rate to the estimate (Q, R)
Then the savings would be estimated as (20)($257) = $5,140
Here if the time value of money is ignored for the given inventory control of $25,000
Time required = 25,000/5140 = 4.86 years
Therefore, time required in paying $25,000 of inventory control is 4.86 yearsto the system.
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Chapter 5 Solutions
Production and Operations Analysis, Seventh Edition
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