Given the following information, formulate an inventory management system. The i

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 $50 per order was offered for purchase quantities of 2,200 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 $ 275.00 Lead time 1 week Annual holding cost (%) 32 % of item cost Service probability 90 % Annual demand 22,700 Average demand 454 per week

Explanation / Answer

a) Optimal order quantity Q = SQRT(2*D*S/H) = SQRT(2*22700*275/(0.32*12)) = 1803 units (approx)

Reorder point = Average demand during lead time + Safety stock = d*L+z**L = 454*1+(1.282*20*1)

ROP = 480 units (approx)

b) Annual holding costs = (Q/2)*H = (1803/2)*(0.32*12) = 3462 $ (approx)

Annual ordering costs = (D/Q)*S = (22700/1803)*275 = 3462 $ (approx)

Total costs = 3462+3463 = 6924 $

c) Purchase quantity Q = 2200

Total costs = Holding costs+Ordering costs = (Q/2)*H+(D/Q)*S = (2200/2)*(0.32*12)+(22700/2200)*50 = 4740 $ (approx)

Annual savings = 6924-4740 = 2184 $ (approx)

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