Question

Store B orders on a weekly basis. Its weekly demand is 50 units with a standard deviation of five units. The holding cost is $10 per unit per week and a 0.99 in-stock probability is desired.

a) What is Store B’s weekly inventory holding cost if lead time is two weeks?

b) What is Store B’s weekly inventory holding cost per unit?

Answer 1

Given :

Expected Weekly demand, = 50 units

Standard deviation, = 5 units

Probability of in-stock = 0.99 (Service level = 99%)

Stock out level = (100-99)% = 1% Stockout policy

From Normal distribution table for an area under the curve of 99%, the Z- value = 2.33

Reorder point is the minimum inventory level required for store B which triggers replenishment of stocks.

Reorder Point = Average Weekly demand * Lead time + Safety Stock

= Average weekly demand * Lead time + Z * Standard deviation of demand * √(Lead time)

=  *Lead time + Z * * √(Lead Time)

= 50 units/week * 2 weeks + 2.33 * 5 * √2

= 100 + 16.47

= 116.47 units ~117 units

Holding cost per unit per week = $10

Weekly inventory holding cost = 117 units * $10/unit/week

= $1170 /week

Weekly holding cost per unit = 1170/117 = $10