Greg Oison stocks an important but slow-moving items in his variety store. The d
ID: 2748433 • Letter: G
Question
Greg Oison stocks an important but slow-moving items in his variety store. The demand is 24 per year on average and the Poisson distribution is a reasonable fit for it. The cost of an item is $400, and the cost of placing a new item is considered negligible. The lead time to replenish an order is 2 weeks, and the company use a holding cost of 0.24 $ per dollar of inventory carrying one year in inventory. The cost of carrying one unit of backorder is $240 per unit per year. What should be the optimal inventory policy if Greg Oison wants to minimize the total annual inventory costs? What is the total annual inventory cost? What is the fill rate, average backorder level, and average inventory level that corresponds to the inventory policy? A new competitor has arrived to town, and Greg needs to improve his customer service level to at least 90%. What should be his new inventory policy? Find the fill rate, average inventory level, bac^onier level, and total inventory costs for the new policy.Explanation / Answer
Answer:
Here the inventory demand = 24 units per annum
cost of one item = $400
Holding cost = $0.24
ordering cost = negligible
therefore EOQ = Q = sqrt((2*24)/0.24) = 14.14 units
Total inventory cost = back order cost + annual holding cost = $240 + 14.14/2 * $0.24 = $241.69
Fill rate = re order point = demand x lead time + Z value x satndard deviations
Here z value = 1.28
Fill rate = 24 x 2 + 1.28 x 1 = 49.28
average back orger level = average inventory on hand = 241.69/2 = 120.845 units
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