Store B orders on a weekly basis. Its weekly demand is 50 unitswith a standard...

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?

Expert Solution

(a) Weekly inventory cost = 414.75 $/week

(b) Weekly inventory cost per unit = 8.3 $/unit

Explanation:

D = 50 units/week

σ = 5 units/week

h = 10 $/unit/week

Lead Time = 2 weeks

Since the store orders weekly, its Q = weekly demand = 50 units per order

For a 99% in stock probability, form standard normal distribution table, we find that k = 2.33

σ_DL= σ*SQRT(LT) = 5*SQRT(2) = 7.07 units

Weekly inventory cost = h* [(Q/2)+ k*σ_DL = 10* [ (50/2) + (2.33* 7.07)] = 10*(25+16.47) = 414.75 $/week

Weekly inventory cost per unit = Weekly inventory cost / Q = 414.75 / 50 = 8.3 $/unit

keosha answered 2 years ago

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