Given the following information, formulate an inventory management system. The i
ID: 2747317 • 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. (Round your answers to the nearest whole number.)
b. Determine the annual holding and order costs. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)
c. If a price break of $50 per order was offered for purchase quantities of over 2,000, what would be the annual savings? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Given the following information, formulate an inventory management system. The item is demanded 50 weeks a year.
Item cost $ 9.00 Average demand 516 per week Order cost $ 256.00 Standard deviation of weekly demand 25 per week Annual holding cost (%) 32% of item cost Lead time 1 week Annual demand 25,800 Service probability 96%a. Determine the order quantity and reorder point. (Round your answers to the nearest whole number.)
b. Determine the annual holding and order costs. (Round your answers to 2 decimal places. Omit the "$" sign in your response.)
c. If a price break of $50 per order was offered for purchase quantities of over 2,000, what would be the annual savings? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Explanation / Answer
Annual Demand 25800 Ordering Cost $ 256.00 Holding Cost - 32% of Price = 32% * 9 $ 2.88 a. EOQ = 2AO / H where A = Annual Demand O = Ordering Cost per order H = Holding Cost per unit per annum EOQ = 2AO / H = (2 * 25800 * 256) / 2.88 = 2141.65 or, 2142 units Mean Demand 516 Standard Deviation of Weekly Demand (SDd) 25 Lead Time (weeks) 1 Standard Deviation of Lead Time (SDl) = SDd * Lead Time = 25*1 = 25 25.00 Service Level Desired 96% Z Value at 96% 1.751 Safety Stock for 96% service level Z value * Standard Deviation (Demand Lead Time) (25 * 1.751) 44 Lead Time Demand ( Lead Time * Avg Demand) 516 Reorder Point = Lead Time Demand + Safety Stock 560 Total Holding Cost (Average Inventory * Holding Cost per unit) $3,084.48 Total Ordering Cost (No of orders * Ordering Cost) $3,083.47 Total Cost $6,167.95 No of orders = Annual Demand/EOQ = 25800/ 2142 = 12.04 Ordering Cost per order = $256 Average Inventory = EOQ / 2 = 2142 / 2 = 1071 units Holding Cost per unit = 32% of Price = 25% * 9 = $2.88
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