Question

(T, S) Policy (Periodic Review)

A vendor sells on average 100 bottles of water per day with a standard deviation of 25. He reviews inventory every Friday and places a replenishment order Friday evening. New bottles arrive before the business is open on Monday. The vendor wishes to maintain a 99% service level.

1.) What should be his order-to to level S?

2.) What is the safety stock?

3.) Plot safety stock vs service level (safety stock as a function of service level changes)

Answer 1

Average daily demand, d = 100 bottles
Stdev of daily demand, σ = 25 bottles
Review period, P = 1 week or 5 days
Replenishment lead time, L = 0 day

1)

z = normsinv(0.99) = 2.326

Order up-to level, S = d.(P+L) + z*σ*sqrt(P+L) = 100*(5+0) + 2.326*25*sqrt(5+0) = 630 units

2)

Safety stock = z*σ*sqrt(P+L) = 2.326*25*sqrt(5+0) = 130 units

3)