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Anvils Works’ requires, on average, 2800 tons of aluminum each week, with a standard deviation of 1000 tons. The lead time to receive its orders is 10 weeks. The holding cost for one ton of aluminum for one week is $11. It operates with a 0.98 in-stock probability.
- a. On average, how many tons does it have on order? [LO11-5]
- b. On average, how many tons does it have on hand? [LO11-5]
- c. If its average inventory was 5000 tons, what would be its average holding cost per week? [LO11-5]
- d. If its average inventory was 10,000 tons, what would be its average holding cost per ton of aluminum? [LO11-5]
- e. Suppose its on-hand inventory is 4975 tons, on average. What instock probability does it offer to its customers? [LO11-5]
a)
To determine: The number of tons that are on order.
Explanation of Solution
Given information:
Weekly Demand (D) = 2,800 tons
Standard deviation (S) = 1,000 tons
Lead time (L) = 10 weeks
Holding cost per one ton of aluminum per week is (H) = $11
In-stock probability (P) = 0.98
Number of tons on order:
The number of tons on order is 28,000 tons.
b)
To determine: The number of tons that are on hand.
Explanation of Solution
Given information:
Weekly Demand (D) = 2,800 tons
Standard deviation (S) = 1,000 tons
Lead time (L) = 10 weeks
Holding cost per one ton of aluminum per week is (H) = $11
In-stock probability (P) = 0.98
Number of tons on hand:
For an in-stock probability of 0.98, the Z-value is 2.06
The number of tons on hand is 6,831 tons.
c)
To determine: The average holding cost per week.
Explanation of Solution
Given information:
Weekly Demand (D) = 2,800 tons
Standard deviation (S) = 1,000 tons
Lead time (L) = 10 weeks
Holding cost per one ton of aluminum per week is (H) = $11
In-stock probability (P) = 0.98
Average inventory (I) = 5,000 tons
Average holding cost per week:
The average holding cost per week is $55,000.
d)
To determine: The average holding cost per ton of aluminum.
Explanation of Solution
Given information:
Weekly Demand (D) = 2,800 tons
Standard deviation (S) = 1,000 tons
Lead time (L) = 10 weeks
Holding cost per one ton of aluminum per week is (H) = $11
In-stock probability (P) = 0.98
Average inventory (I) = 10,000 tons
Average holding cost per ton of aluminum:
The average holding cost per ton of aluminum is $39.29.
e)
To determine: The average holding cost per ton of aluminum.
Explanation of Solution
Given information:
Weekly Demand (D) = 2,800 tons
Standard deviation (S) = 1,000 tons
Lead time (L) = 10 weeks
Holding cost per one ton of aluminum per week is (H) = $11
In-stock probability (P) = 0.98
Average on-hand inventory (I) = 4,975 tons
Calculation of in-stock probability:
The Z-value is 1.50. From the table, the probability for a Z value of 1.50 is 0.93319
Therefore, the in-stock probability is 93.32%.
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