Question

Average for a normally distributed demand of a product is 35 units per day. Standard deviation of lead time demand is 10. Lead time is 3 days. Service level is 95%.

a) Calculate reorder point and safety stock.

b) Reconsider 10 units as daily standard deviation of demand and re-calculate reorder point.

c) Reconsider that demand is constant, but lead time varies with a standard deviation of 1 day. Recalculate reorder point.

d) Assume both demand and lead time are variable. Re-calculate reorder point.

Answer 1

Answer:

Normal interest, d = 35 units for every day

Standard deviation of lead time request, σLT = 10 units

Lead time, L = 3 days

Administration level, F(z) = 0.95 for example z = 1.645

a)

Security stock = z.σLT

substitute values

= 1.645*10

= 16.45 or 17 units (gathered together)

ROP = d.L + security stock

substitute values

= 35*3 + 17

= 122 units

b)

Standard deviation of day by day request, σ = 10 units

In this way,

Standard deviation of lead time request, σLT = σ.√L

substitute values

= 10*√3

= 17.32 units

Security stock = z.σLT

substitute values

= 1.645*17.32

= 29 units (gathered together)

ROP = d.L + security stock

substitute values

= 35*3 + 29

= 134 units

c)

Standard deviation of day by day request, σ = 0 units

Standard deviation of lead time, σL = 1 day

In this way, Standard deviation of lead time request,

σLT = [σ2.L + (d.σL)2]1/2

substitute values

= SQRT(0^2*3 + (35*1)^2)

= 35 units

Well-being stock = z.σLT

substitute values

= 1.645*35

= 58 units (gathered together)

ROP = d.L + well-being stock

substitute values

= 35*3 + 58

= 163 units

d)

Standard deviation of every day request, σ = 10 units

Standard deviation of lead time, σL = 1 day

Along these lines, Standard deviation of lead time request, σLT = [σ2.L + (d.σL)2]1/2

substitute values

= Sqrt((10^2)*3 + (35*1)^2)

= 39.05 units

Well-being stock = z.σLT

substitute values

= 1.645*39.05

= 65 units (gathered together)

ROP = d.L + wellbeing stock

substitute values

= 35*3 + 65

= 170 units