Question

A company begins a review of ordering policies for its continuous review system by checking the current policies for a sample of SKUs. Following are the characteristics of one item:
Demand (D) = 72 units/week (Assume 48 weeks per year)
Ordering and setup cost (S) = $55 /order
Holding cost (H) = $18 /unit/year
Lead time (L) = 3 week(s)
Standard deviation of weekly demand = 18 units
Cycle-service level = 90 percent
EOQ = 145 units
Under the same information as above, develop the best policies for a periodic review system.
1. The value of P that gives the same approximate number of orders per year as the EOQ is weeks (Hint: please round your answer to the nearest positive integer number).
2. The target inventory level that provides an 88 percent cycle-service level is units (Hint: please round your answer to the nearest positive integer number).

Answer 1

Answer:

Explanation:

Given that:

weekly demand = 72 units

no of weeks in 1 year = 48

Then; total demand = 72 × 48 = 3456 units

No of orders = $\dfrac{\text{total demand }}{EOQ}$

= $\dfrac{\text{3456}}{145}$

∴

The periodic review (P) = $\dfrac{1}{no \ of \ orders}$

= $\dfrac{1}{\dfrac{3456}{145}}$

$= \dfrac{145}{3456}$

= 0.041956 year

≅ 2 weeks

Z score based on 88 percent service level = NORMSINV(0.88) = 1.18

Here;

Lead time = 3 wks

P = 2 weeks

Thus protection interval = ( 3+2) weeks

= 5 weeks

Safety stock = z-score × std dev. of demand at (P+L) days

std dev = $\sqrt{5 } \times 18$ = 2.236 × 18

std dev = 40.248 units

Safety stock = 1.18 × 40.248

safety stock = 47.49 units

Safety stock ≅ 48 units

Average demand during(P + L) = 5 × 72 units

= 360 units

Target inventory level = average demand + safety stock

= 360 units + 48 units

= 408 units