Question

Same problem statement:

Weekly demand for DVD-Rs at a retailer is normally distributed with a mean of 1,000 boxes and a standard deviation of 150. Currently, the store places orders to the supplier, with a reorder point of 4,200 boxes. The order quantity to the supplier is fixed at 5,000 boxes. Replenishment lead time is 4 weeks, fixed order cost per order is $100, each box costs the retailer $10, and the inventory holding cost is 25% per year.

Under the current order quantity of 5,000 boxes and current reorder point of 4,200 boxes, what would be the order-up-to level S that the retailer should use as a baseline to calculate how much inventory to order when conducting a periodic review?

Answer 1

Periodic Review System:

As there is only demand uncertainty, restocking level or inventory to order when conducting a periodic review is given as follows:

R = demand during lead time and review period + Safety stock

R = d(L + T) + zσT+L

Thus, here we have to determine Order interval, T and z-score for cycle service level (CSL)

Determine Order interval, T:

For periodic system the order interval (T) = time between the orders according to continuous review model

time between the orders according to continuous review model = (52 weeks per year) / (no. of orders per year)

No. of orders per year = annual demand / order quantity

Annual Demand = 52 weeks x weekly demand = 52 x 1000 = 52,000 units per year

Order Quantity according to Continuous review model = 5000 units

No. of orders per year = (52,000 / 5000) = 10.4 order per year

Time between the orders according to continuous review model = 52 / 10.4 = 5 weeks between orders

To determine cycle service level:

d = average weekly demand = 1,000 per week

σd = standard deviation in average weekly demand = 150 units per week

Reorder point = 4,200 boxes

Lead time = L = 4 weeks

Reorder point = weekly demand x lead time + Safety stock

ROL = (1000)(4) + SS

4200 = 4000 + SS

SS = 4200 – 4000 = 200

Safety stock = 200 boxes

Safety stock is given as follows:

Safety Stock = zσd√L

If safety stock = 200 boxes, CSL = ?

Safety Stock = zσd√L = 200

z = 200/(150 x √4) = 0.67

for z-score of 0.667, the probability is 0.7485

for ROL of 4200 and SS = 200, CSL is 74.85%

For periodic review model:

d = weekly demand = 1000 units

σd = S.D of weekly demand = 150 units

L = Lead Time = 4 weeks

T = order interval = 5 weeks

CSL = 0.7485

z-score for 74.85% service level = 0.67

As there is only demand uncertainty, restocking level as follows:

R = demand during lead time and review period + Safety stock

R = d(L + T) + zσT+L

σT+L = σd√(L + T) = (150)√(4 + 5) = 450 units

Safety stock = (0.67)(450) = 301.5 units

Safety stock of periodic review system = 301.5 units

R = d(L + T) + zσT+L

R = (150)(4 + 5) + 301.5

R = 1350 + 301.5

R = 1651.5 units

Order up-to level for periodic review model = 1651.5 units