Ollah\'s Organic Pet Shop sells about 8,500 bags of free-range dog biscuits ever
ID: 428661 • Letter: O
Question
Ollah's Organic Pet Shop sells about 8,500 bags of free-range dog biscuits every year. The fixed ordering cost is $10, and the cost of holding a bag in inventory for a year is $0.50. Click the icon to view the table of z values. a. What is the economic order quantity for the biscuits? The EOQ is 583. (Enter your response rounded to the nearest whole number.) b. Suppose Ollah decides to order 380 bags at a time. What would the total ordering and holding costs for the year be? (For this problem, don't consider safety stock when calculating holding costs.) The total ordering and holding costs are S 319. (Enter your response rounided to the nearesf dollar.) c. Average weekly demand for free-range dog biscuits is 68 bags per week, with a standard deviation of 15 bags. Ollah uses a continuous inventory review systern to manage inventory of the biscuits. Ollah wants to set the reorder point high enough that there is only a 5% chance of running out before the next order comes in. Assuming that the lead time is a constant 5 weeks, what should the reorder point be? The reorder point is 395 bags. (Eter your response rounded to the nearest whole number) d. Suppose Ollah decides to use a periodic review system to manage the free-range dog biscuits, with the vendor checking inventory levels every week. Under this scenario, what would the restocking level be, assuming the same demand and lead time characteristics listed in part c and lhe same 95% service level? Not that because the standard deviation of oekly demand is 15, basic statistics tells us the standard deviation of demand over 6 eeks will be 37 The restocking level is 456 bags. (Enter your response rounded up to the nearest whole number) i Reference z value 0.84 1.28 1.65 2.33 3.08 Associated service level 80% 90% 95% 99% 99.9% Done Enter your answer in the answer box and then click Check Answer.Explanation / Answer
(a) Annual demand, D = 8500
Ordering cost, S = $ 10
Holding cost, H = $ 0.5
EOQ = SQRT(2DS/H) = SQRT(2*8500*10/0.5) = 583 bags
(b) Q = 380
Total ordering and holding cost = (D/Q)*S + (Q/2)*H
= (8500/380)*10 + (380/2)*0.5
= $ 319
(c) Weekly Demand, d = 68 bags per week
Standard deviation of weekly demand, s = 15 bags
Lead time, L = 5 weeks
Desired service level = 1 - 5% = 95%
z = 1.65
Reorder point = Lead time demand + Safety stock (safety stock = z*standard deviation of demand over lead time)
= d*L + z*s*SQRT(L)
= 68*5 + 1.65*15*SQRT(5)
= 395 bags
(d) Review period, P = 1 week (vendor checks inventory levels every week)
Reorder point = d*(L+P) + z*s*SQRT(L+P)
= 68*(5+1) + 1.65*15*SQRT(5+1)
= 469 bags
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