Question

Daily demand for a product is 100 units, with a standard deviation of 35 units. The review period is 10 days and the lead time is 5 days. At the time of review there are 40 units in stock.

If 95 percent service probability is desired, how many units 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.)

Ordered Quantity- __________

Answer 1

Given values:

Daily demand (d) = 100 units

Standard deviation, (d) = 35 units

Time between orders (T) = 10 days

Lead time (L) = 5 days

Current Inventory (I) = 40 units

Service level = 95% or 0.95

Solution:

Using NORMSINV function in MS Excel, value of Z can be determined.

Z = NORMSINV (Service level)

Z = NORMSINV (0.95)

Z = 1.64

Order Quantity (Q) is calculated as,

Q = d (T + L) + Z (T + L) - I

(T + L) = (d) x SQRT (T + L)

(T + L) = 35 x SQRT (10 + 5)

(T + L) = 135.55

Putting the given values in the above formula, we get,

Q = d (T + L) + Z (T + L) - I

Q = [100 x (10 + 5)] + [1.64 x 135.55] - 40

Q = 1500 + 222.30 - 40

Q = 1682.30 or 1682 (Rounding off to the nearest whole number)

Order Quantity = 1682 units