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. Standard deviation of weekly 30 per weelk 9.00 $230.00 Item cost Order cost Annual holding cost (%) Annual demand Average demand demand Lead time Service probability 3 weeks 98% 34% of item cost 27,500 550 per week a. Determine the order quantity and reorder point. (Use Excel's NORMSINV) function to find your z- value and then round that z-value to 2 decimal places. Do not round any other intermediate calculations. Round your final answers to the nearest whole number.) Optimal order quantity Reorder point units units b. Determine the annual holding and order costs. (Do not round any intermediate calculations. Round your final answers to 2 decimal places.) Holding cost Ordering cost c. Assume a price break of $50 per order was offered for purchase quantities of 2,100 units per order. If you took advantage of this price break, how much would you save annually? (Do not round any intermediate calculations (including number of setups per year). Round your final answer to 2 decimal places.) Annual savings

Explanation / Answer

Item cost, C = $ 9

Order cost, S = $ 230

Annual holding cost, H = 9*0.34 = $ 3.06

Average weekly demand, d = 550

Std deviation of weekly demand, s = 30

Lead time, L = 3 weeks

Service level, apha = 98 %

z = NORMSINV(0.98) = 2.05

a)

Order Quantity, Q = SQRT(2DS/H) = SQRT(2*27500*230/3.06) = 2033

Reorder point, R = d*L + z*s*SQRT(L) = 550*3 + 2.05*30*SQRT(3) = 1757

b)

Holding cost = (Q/2)*H + z*s*SQRT(L)*H = (2033/2)*3.06 + 2.05*30*SQRT(3)*3.06 = $ 3436.45 (this includes cost of holding safety stock)

Ordering cost = (D/Q)*S = (27500/2033)*230 = $ 3111.17

c)

Total cost without price break offer = (D/Q)*S + (Q/2)*H = (27500/2033*230 + (2033/2)*3.06 = 6221.66

Total cost with price break offer = (D/Q)*S + (Q/2)*H = (27500/2100)*(230-50) + (2100/2)*3.06 = 5570.14

Annual savings = 6221.66 - 5570.14 = $ 651.51

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