Question

A pharmacy has estimated that the average daily demand for a particular medication is 30 packages, with a standard deviation of 4 packages. The wholesale cost of each package to the pharmacy is $12. The pharmaceutical company from which the pharmacy purchases the medication has a lead time of 4 days, and the cost of placing an order is $9. The carrying cost to hold one package of medication per quarter is 2% of the wholesale cost of the package. The pharmacy is open 300 days per year (it is closed on Sundays and some holidays). If the manufacturer wishes to ensure a 96% service level, what is the optimal order quantity, and what is the reorder point?

Answer 1

Average daily demand(d) = 30 packages

Number of days per year = 300 days

Annual demand (D) = d × Number of days per year = 30 × 300 = 9000 packages

Standard deviation of daily demand ($\sigma$d) = 4 packages

Ordering cost (S) = $9

Carrying cost(H) = 2% of wholesale cost = 2% of $12 = $0.24

Lead time(L) = 4 days

At 96% service level value of Z = 1.75

a)Optimal order quantity = √(2DS/H)

= √[(2 × 9000 × 9) / 0.24]

= √(162000/0.24)

= √675000

= 822 packages

b) Reorder point = d × L + (Z x $\sigma$d x √L)

= 30 × 4 + (1.75 × 4 × √4)

= 120 + (1.75 × 4 × 2)

= 120 + 14

= 134 packages