Weekly demand for DVD-Rs at a retaller is normally distributed with a mean of 10

Question

Weekly demand for DVD-Rs at a retaller is normally distributed with a mean of 1000 hoxes and a standard devlation of 150 Currently, the store places orders to the suppler, 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 ls $100 each box costs the retailer $10, and the inventory holding cost Is 25% per year Glven the problem parameters, what is the optimal order quantity the retaller should order?

Explanation / Answer

Average weekly demand = 1000 boxes

Annual demand (D) = 1000 x 52 = 52000(Assuming 52 weeks in a year )

Ordering cost (S) = $100

Cost per box = $10

Holding cost (H) = 25% of cost = 25% of $10 = $2.5

Optimal order quantity = sqrt of (2DS / H)

= sqrt of [(2 x 52000 x 100) / 2.5]

= sqrt of 4160000

= 2039.61 or rounded to 2040 boxes

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