1. A firm desires to control inventory levels so as to minimize the sum of holding and order costs. It costs the firm $20 to place an order. The firm estimates its yearly inventory carrying costs at 20%. Weekly demand is 100 units, and there are 50 weeks in the work year. The item costs $10 per unit. The EOQ is approximately:
| A. 316 | |||||||||
| B. 224 | |||||||||
| C. 145 | |||||||||
| D. 45 | |||||||||
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E. 32 2. One end item A requires three component parts: B, C, and D. The bill of material indicates that for each completed A, 3 units of B, 2 units of C, and 1 unit of D are required. Current inventory for the four items is as follows: There are 18 As, 40 Bs, 50 Cs and 35 Ds in stock. If the lead time for all items is one week and there are no scheduled receipts for any item, how many units of product A can be delivered to customers at the start of next week (week 2)?
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1. To calculate the Economic order quantity EOQ), we have following information
Weekly demand = 100 units
Number of weeks in a work year = 50
Therefore, Annual Demand (D) = 50 * 100 units = 5000 units /year
Ordering Costs (S) = $20/order
Inventory carrying cost (H) = 20% of the cost of item
= 20% *$1o per unit = $2 per unit per year
Formula of economic order quantity (EOQ)
EOQ = ? (2 * Annual Demand * Ordering cost/ Inventory carrying cost)
Therefore
EOQ = ? (2 * 5000 *$20 / $2)
EOQ = ? (100,000)
EOQ = 316.23 or 316 units
The EOQ for this item is 316 units.
Therefore correct answer is option A. 316
2. The number of units of product A can be delivered to customers at the start of next week (week 2)
= Current Inventory of Item A + Units of item A can be produced by its component parts B, C and D at the start of next week
Where,
Current Inventory of Item A = 18 units
As the lead time for all items are one week, therefore A can be produced only by component parts B, C and D are available at week start of week 1
We know that there are 18 As, 40 Bs, 50 Cs and 35 Ds in stock and for each completed A, 3 units of B, 2 units of C, and 1 unit of D are required. As the maximum units of component B is requited for Item A, Therefore and total 13 units are possible to produce from 40 units of B (40/3 =13.33 =13 nearest whole number). Stocks of Cs and Ds are sufficient to produce 13 units of A.
Therefore,
The number of units of product A can be delivered to customers at the start of next week (week 2)
= 18 units + 13 units
= 31 units
Therefore correct answer is option B. 31
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