Scenario 9.10
Demand = 52,000 units/year
Standard deviation of weekly demand = 110 units
Ordering costs = $45/order
Holding costs = $0.50/unit/year
Cycle-service level = 90%
Lead time = 2 weeks
Number of weeks per year = 52 weeks
A normal distribution table is appended to this exam.
-Use the information in Scenario 9.10.A firm uses the periodic review system to control the item depicted above.It reviews the item's status every three weeks (P = 3).At the most recent inventory review,an inventory clerk found 1,500 units.There were no scheduled receipts and no backorders.How many units should be ordered? (Hint: You must calculate T before answering this question. )
A)0 units
B)greater than 0 but less than or equal to 3,750 units
C)greater than 3,750 but less than or equal to 4,000 units
D)greater than 4,000 units

Question

Quizplus · Accepted Answer

First, we need to calculate T by using the formula T = d + zσ√(L + P), where:
- d = demand per period = demand per year / number of periods per year = 52,000 / 52 = 1,000 units/week
- z = z-value corresponding to the cycle-service level of 90%, which is 1.28 (found from the normal distribution table)
- σ = standard deviation of weekly demand = 110 units
- L = lead time = 2 weeks
- P = review period = 3 weeks

Plugging in the numbers, we get:
T = 1,000(3) + 1.28(110)√(2+3) = 3,000 + 1.28(110)√5 ≈ 3,774 units

Since the current inventory level is 1,500 units, we need to order:
Order quantity = T - on-hand inventory = 3,774 - 1,500 = 2,274 units

However, since the answer options are in ranges, we need to choose the closest range that includes the calculated order quantity. The range that includes 2,274 units is "greater than 3,750 but less than or equal to 4,000 units" (option C). Therefore, the best choice is C.

Scenario 9.10 Demand = 52,000 Units/year