Q 2(c) Suppose that an inventory has the following characteristics: [15 Marks] F
ID: 339379 • Letter: Q
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Q 2(c) Suppose that an inventory has the following characteristics: [15 Marks] Forecast of Demand Forecast error, std. dev. = 475 items per week Lead time3 weeks Carrying cost Purchase price, delivered €25 per item Replenishment order cost Stock-out cost6 per item = 1250 items per week -4% per year 40 per order 95% Probability of being in stock during the lead time, P Calculate the optimal order quantity and design a reorder point control system, given the assigned P. How would you state the inventory control policy if the ROP>Q?Explanation / Answer
d= 1250 per week, Annual demand, D = 1250*52 = 65000
S = 40 per order
H = 4% * 25 = 1
EOQ, Q* = sqrt (2DS/H) = 2280.35
Lead time, L = 3 weeks , Std. deviation per week, S = 475 , Z-score for probability of in stock of 95% = 1.96
ROP = Demand during lead time + Safety stock
ROP = d*L + z*s* sqrt (L) = 1250*3 + 1.96*475* sqrt(3) = 5362.53
Whenever the inventory touches 5362 an order is placed to get more units. Lead time to get these units is 3 weeks and the service level expected is 95%.
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