Question

If demand for an inventory item is normally distributed with a mean of 150 units per day and standard deviation of 2 units/day, lead time is normally distributed with an average of 4 days and standard deviation of 0.5, and service level is 95% (z=1.65) , at what point should it be reordered?

128

328

548

748

850

Answer 1

ROP (xy) = 724 units to be recorded

Explanation:

Given:-

- Demand for an inventory item(x) is normally distributed with :

mean ux = 150 units/day

standard deviation sx = 2 units/day

- lead time(y) is normally distributed with:

mean uy = 4 days

standard deviation sy = 0.5 days

- Service level is 95% (zs=1.65):

Find:-

at what point should it be reordered?

Solution:-

- We will deonte (xy) the number of units to be serviced to be normally distributed with mean and standard deviation:

uxy = ux*uy = 150*4 = 600 units

sxy = √[(uy*sx^2) + ux^2*sy^2 ]

=√[(4*2^2) + 150^2*0.5^2 ]

= 75.10659

- At the service level of 95% the confidence interval would be:

ROP (xy) = uxy + zs*sxy )

ROP (xy) = 600 + 1.65*75.10659

ROP (xy) = 724 units to be recorded