Question

University Drug Pharmaceuticals orders its antibiotics every two weeks (14 days) when a salesperson visits from one of the pharmaceutical companies. Tetracycline is one of its most prescribed antibiotics, with average daily demand of 2,700 capsules. The standard deviation of daily demand was derived from examining prescriptions filled over the past three months and was found to be 750 capsules. It takes four days for the order to arrive. University Drug would like to satisfy 90 percent of the prescriptions. The salesperson just arrived, and there are currently 24,000 capsules in stock.

How many capsules should be ordered? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Do not round intermediate calculations. Round "z" value to 2 decimal places and final answer to the nearest whole number.)

Number of capsules ordered

Answer 1

L = lead time = 4 days

d-bar = average daily demand = 2700 capsules

Inventory stock = 24000 capsules

Standard deviation of daily demand = 750 capsules

T = 14 days

Ordering quantity = d-bar*(T+L)+z*standard deviation for period (T+L)-Inventory stock

= 2700*(14+4)+normsinv(0.9)*standard deviation of daily demand * sqrt(T+L)-24000

= 48600+normsinv(0.9)*750*sqrt(14+4)-24000

= 28677.87211 = 28678 (Rounded to nearest whole number)

Answer 2

To determine the number of capsules that should be ordered, we need to consider the demand during the lead time (four days) plus a safety stock to account for variability in demand.

First, let's calculate the demand during the lead time:

Demand during lead time = Average daily demand * Lead time = 2,700 capsules/day * 4 days = 10,800 capsules

Next, we need to calculate the safety stock, which is based on the desired service level and the standard deviation of daily demand:

Safety stock = z * Standard deviation of daily demand = z * 750 capsules

To find the value of "z" corresponding to a 90 percent service level, we can use the NORMSINV function in Excel or any other statistical tool. NORMSINV(0.9) gives us the z-value.

z = NORMSINV(0.9) ≈ 1.2816 (rounded to 4 decimal places)

Now we can calculate the safety stock:

Safety stock = 1.2816 * 750 capsules ≈ 961.2 capsules (rounded to 1 decimal place)

Finally, to determine the total number of capsules to order, we sum the demand during the lead time and the safety stock:

Total capsules to order = Demand during lead time + Safety stock = 10,800 capsules + 961.2 capsules = 11,761.2 capsules

Rounding the final answer to the nearest whole number, the number of capsules to order is approximately 11,761.