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A firm uses 14
A firm uses 14.000 units per year of a particular item. Holding costs are 18% per year and fixed costs of ordering are Tk. 135.50 and paper work cost Tk 12.75 per order. The demand is normally distributed with a standard deviation of 2200 units. The replenishment rate is infinite. The item costs Tk 9.50 per unit and lead time is 10 days with standard deviation of 3 days. If the product is stock out, it incurs Tk. 670 in stock out costs. Use 360 days year. Calculate: i The optimum order quantity and no of orders. The total cost of this inventory strategy per year. The optimum safety stock 11. 111
Expert Solution
b.
i. EOQ = Sq root of 2 * Annual Demand * Order cost per order / carrying cost per annum per unit
= sq root of 2 * 14,000 * 148.25 / (9.5 * 18%) = sq root of 4,151,000 / 1.71 = 1558 units per order
no. of orders = 14,000 / 1558 = 9 orders
ii. Total cost of inventory strategy = Ordering cost (9 orders * Tk 148.25 per order) + Carrying cost (1558 / 2 units * Tk. 9.5 * 18%) = 1334.25 + 1332.09 = Tk. 2666.34
iii. Optimum safety stock = Z × ΣLT × D AVG
Z is the desired service level, σLT is the standard deviation of lead time, and D avg is demand average.
Since the replenishment rate is infinite, desired service level is close to 100% (99.99%) with a Z score of 3.72
Optimum safety stock = 3.72 * 3 days * 14,000 units / 360 days = 434 units
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