The annual demand for a product is 15,600 units. The weekly demand is 300 units with a standard deviation of 90 units. The cost to place an order is $31.20, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.10 per unit. Find the reorder point necessary to provide a 98% service probability. Suppose the production manager is asked to reduce the safety stock of this item by 50%. If she does so, what will the new service probability be?

If the production manager wants to have a 50% reduction in the safety stock, then the service probability is 84.7%

The first thing to do is to calculate the standard deviation with a lead time of 4 weeks. This will be:

= ✓Lead time × Standard deviation

= ✓4 × 90

= 2 × 90.

= 180

Since there's a 98% service probability, the value of z will be 2.05. Then, the new order will be:

= 300 × 4 + (2.05 × 180)

= 1569 units.

Then, the safety stock will be:

= (0.50) × (2.05 × 180)

= 185 units

Finally, we'll calculate the value of z when the safety stock is 185 units. This will be;

185 = z × 180

185 = 180z

z = 185/180.

z = 1.02.

Then, the z value will be checked in the table and thus will be 84.7%.

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Reorder point necessary to provide 98% service probability is 1569 units

If the production manager is asked to reduce the safety stock of the item by 50%, the new service probability will be 84.7%

Explanation:

Data:

Weekly demand (d)= 300 units

Lead time (L)= 4 weeks

Standard Deviation (SD) = 90units

(A) To find reorder point.

-standard deviation (SDw) with lead time of 4 weeks = x (90) = 180units

-98% probability is needed, use the formular NORMSINV (0.98) in Excel Spread sheet and get value of "z" to be 2.05

R = d*L + z*(SDw)

R = 300 x (4) + (2.05) x (180)

R = 1,569 units

Note; determining the safety cost "SS"

SS = z * SDw = 2.05 x 180 = 369 units

for a 50% reduction, 369 x 0.50 = 184.5 ≅ 185 units

(B) now calculate "z" when safety stock is 185 units

SS = z * SDw

185 = z (180)

z = 1.02

In table, the corresponding probability value of 1.02 is 84.7%

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