Question

For a product A, if the average daily demand is 40 units, and it takes a supplier nine days to deliver

an order once it has been placed and the standard deviation of daily demand is 4, in order to have 95%

service level, what should be the reorder point?

Answer 1

Ans) The reorder point for the product A should be 379.68 units (Not rounding off as it is not mentioned in the question)

Let us list down the given data

Average daily demand for product A - d = 40 units

Lead time to deliver the product LT = 9 days

Standard deviation of daily demand $\sigma$ _d = 4 units

Service level = 95%

This is a fixed order quantity model with safety stock as a service level of 95% is required.

So

Reorder Point R is given by

R = Demand during lead time + Safety stock

R = d*LT + z*$\sigma$_LT ---------------Eq. 1

In the above equation, the unknowns are z & $\sigma$ _LT

z = number of standard deviations for a service probability

$\sigma$_LT = Standard deviation during lead time (in units)

Let us calculate z

For a service level of 95%

Let us determine the value of z

For a service level of 95% the value of z = 1.64

This is calculated using excel function “NORMSINV”

In excel type

=NORMSINV (0.95)

=1.64

Above value is the value of z

Now calculate the value of $\sigma$ _LT

Standard deviation during lead time is given by

$\sigma$_LT = Standard deviation of daily demand * Lead time

$\sigma$_LT = $\sqrt{}$ ($\sigma$_d )²  * LT -------------Eq. 2

Substituting the value of $\sigma$ _d & LT from given data in Eq. 2, we get

$\sigma$_LT = $\sqrt{}$ 4² * 9

$\sigma$_LT = 12 units

Now substitute the value of d, LT, z & $\sigma$ _LT in Eq. 1, we get

R = 40 * 9 + 1.64 * 12

R = 360 + 19.68

R = 379.68 units

This is the reorder point.

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