(3) Inventory Optimization Demand for refrigerators at a local Home Depot is 1,0
ID: 380519 • Letter: #
Question
(3) Inventory Optimization Demand for refrigerators at a local Home Depot is 1,000 per year. The cost of each refrigerator to HD is $300, and the holding cost is 3% per year. There is a fixed cost of $50 per order, regardless of size, to cover processing. # of refrigerators (3a) What is the Economic Order Quantity? (3b) t takes two weeks from time of order for a new refridgerator to be delivered to HD, and the coefficient of variation on demand for refrigerators is 30%. If HD's target Custormer Service Level (CSL) is 90%, what is the Reorder Point for inventory, the level at which new refrigerators should be ordered? # of refrigerators ROP (3c) If instead of CSL, HD targets Fill Rate (FR) is 95%, what is the Reorder Point? # of refrigerators ROPExplanation / Answer
(3a)
D = annual demand = 1000
S = ordering cost = $50
H = Holding cost = i.C = 3% x $300 = $9
EOQ = (2.D.S/H)1/2 = sqrt(2*1000*50/9) = 105.4 or 106 refrigerators
(3b)
Target service level = 90%, so, Z = NORMSINV(0.90) = 1.28
Coefficient of variation of demand = 30%
Mean weekly demand = d = 1000/50 = 20 (assuming 50 weeks a year)
So, Std. deviation of weekly deamand = = 20 x 30% = 6
L = average lead time = 2 weeks
Average lead time demand = d x L = 20 x 2 = 40
Safety Stock = Z x x L = 1.28 x 6 x sqrt(2) = 10.86 or 11 (rounded off)
ROP = Average lead time demand + Safety Stock = 40+11 = 51 (note that the answer will change if the number of weeks per year =50 assumption change).
(3c)
Fill Rate = 0.95; Q=106; L=8.49
i.e. 1 - (L x L(z) / Q) = 0.95 where L(z) is the unit normal loss corresponding to Z
or, 8.49*L(z) = (1-0.95)*106
or, L(z) = 0.05*106/8.49 = 0.63
From loss function table, Z = -0.4 So, no safety stock will be required.
ROP = Average lead time demand + Safety Stock = 40+0 = 40 (note that the answer will change if the number of weeks per year =50 assumption change).
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