Given the following information, formulate an inventory management system. The i
ID: 363237 • Letter: G
Question
Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.
a. Determine the order quantity and reorder point. (Use Excel's NORMSINV() function to find the correct critical value for the given -level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)
b. Determine the annual holding and order costs. (Round your answers to 2 decimal places.)
c. Assume a price break of $55 per order was offered for purchase quantities of 2,000 or more units per order. If you took advantage of this price break, how much would you save annually? (Round your answer to 2 decimal places.)
Item cost $ 12.00 Standard deviation of weekly demand 20 per week Order cost $ 224.00 Lead time 2 weeks Annual holding cost (%) 35 % of item cost Service probability 95 % Annual demand 24,700 Average demand 494 per weekExplanation / Answer
Annual demand, D = 24700
Order cost, K = 224
Hoding cost, H = 12*0.35 = 4.2
Demand rate, d = 494 per day
Std deviation of weekly demand, s = 20
Lead time, L = 2 weeks
-level = 0.95
a.
Critical value (z) for given -level = NORMSINV(0.95) = 1.645
Optimal order quantity = (2*D*K/H) = (2*24700*224/(4.2) = 1623
Reorder point = d*L + z*sL = 494*2 + 1.645*202 = 1035
b.
Annual holding cost = (Q/2 + ss)*H, where ss is safety stock = z*sL = 1.645*202 = 47
Annual holding cost = (1623/2 + 47)*4.2 = 3606
Annual ordering cost = (D/Q)*K = (24700/1623)*224 = 3409
c.
Total annual costs with the price break = (24700/2000)*55 + (2000/2+47)*4.2 = 5077
Annual savings = (3606+3409) - 5077 = $ 1938
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