Fixed Period, EOQ, and Single Period Basics A product sells at the rate of 5 per
ID: 448754 • Letter: F
Question
Fixed Period, EOQ, and Single Period Basics
A product sells at the rate of 5 per day and the company operates 250 days per year. The carrying cost is $3 per unit per year and the set-up charge is $80 per set-up. There is a five day lead tie with a desired service level of 90%.
What is the EOQ?
What is the maximum inventory assuming zero safety stock?
What is the average inventory assuming zero safety stock?
What is the annual carrying cost?
What is the annual order cost?
What is the optimal period if a fixed period model were desired? (Time between EOQ and orders)
What is the target in a fixed period model if the period is 20 days?
What is the safety stock if sigma is 4 per day in the above target?
A quantity discount is available of 10% off the cost of $10.00 per unit. At a minimum order quantity of 1,000 what should the company order? (Keep H constant at $3.00)
Explanation / Answer
a. Annual Demand (250 * 5) 1250 Set Up Cost $ 80.00 Carrying Cost $ 3.00 EOQ = 2AS / C where A = Annual Demand S = Set Up Cost C = Carrying Cost per unit per annum EOQ = 2AS / C = (2 * 1250 * 80) / 3 = 258.1989 units or, 258 units b. Maximum Inventory = EOQ = 258 units c. Average Inventory = EOQ/2 = 258/2 = 129 units d. Annual Carrying Cost = Average Inventory * Carrying Cost per unit per annum = 129 units * $3 = $387 e. Annual Ordering Cost = Annual Demand / EOQ * Set Up cost = 1250 / 258 * 80 = $387.60 f. No of orders Orders = Annual Demand / EOQ = 1250 / 258 = 4.8449 or 5 orders Order Cycle Length = 250 days/ # Orders = 250 days / 5 orders = 50 days/per order If # orders are not rounded off Order Cycle Length = 250 days/ # Orders = 250 days / 4.8449 orders = 51.6 days/per order g. In a periodic review system, find target inventory T, given: P = 20 days L = 5 days Safety stock = z * std Dev (P,L) Std Dev (P,L) = Std Dev Demand * P+L = 4 * 20 + 5 = 4 * 5 units = 20 units Z Value at 90% - 1.282 Safety stock = 1.282* (20) = 25.64 or 26 units T = Average demand during the protection interval + Safety stock T = 5(20 + 2) + 26 T = 126 units h. Safety stock = 1.282* (20) = 25.64 or 26 units i. Order Size (a) 258 1000 1250 Price per unit (b) $10 $9 $9 No of Orders (c = annual demand / a) 5 1 1 Ordering Cost (d = a * $80) $387.60 $100.00 $80.00 Holding Cost (e = a/2 * $3) $387.00 $1,500.00 $1,875.00 Product Cost (f = 1250*b) $12,500.00 $11,250.00 $11,250.00 Total Cost (d+e+f) $13,274.60 $12,850.00 $13,205.00 Company Can take the offer of 10% discount as total cost is lower in that order size
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