can u show me step by step instructions on how to solve this. Daily demand for p
ID: 376660 • Letter: C
Question
can u show me step by step instructions on how to solve this.
Daily demand for packages of five videotapes at a warehouse store is found to be normally distributed with mean 50 and st ordering cost is $42 and the orders take 4 days to arrive. Each pack of tapes costs $7.20 and there andard deviation 5. When the store orders more tapes, the is a 24% annual holding cost for inventory. Assume the store is open 360 days a year. a. What is the EOQ? b. If the store wants the probability of stocking out to be no more than 5%, and demand each day is independent of the day before, what reorder point should be set? How much of your reorder point in part b) is safety stock? c.Explanation / Answer
Given data -
Daily demand = d = 50, d = 5;
Ordering cost = S = 42 $;
Lead time = L = 4 days
Purchasing cost = 7.2 $
Holding cost = H = 0.24*7.2 = 1.728 $
Number of days = 360 => Annual demand = d*Number of days = 50*360 = 18000 units
a) EOQ = SQRT(2*D*S/H) = SQRT(2*18000*42/1.728) = 936 (approx)
b) Probability of stockout = 5 % => Service level = 100-5 = 95 % minimum
z value at 95% service level = 1.645
Reorder point = Lead Time Demand +Safety stock = L*d+z*d*SQRT(L) = (4*50)+(1.645*5*SQRT(4))
ROP = 216.45 = 217(approx)
c) Safety stock from part b = 16.45
SS % of ROP = (16.45/216.45)*100 = 7.6%(approx)
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