Question

Sous-la-Table is a small wine shop selling many imported products.   One of their biggest year-round sellers is a Tuscan Chianti called TroppodalVino, with a weekly demand of 40 bottles on average and a weekly standard deviation of 18 bottles. Bottles take 9 weeks to arrive from Italy.   Sous-la-Table estimates their annual holding costs for wine is $2 per bottle, and they aim to have a 90% service level.

1. If Sous-la-Table can order TroppodalVino at will (remembering that it still takes a while to get a delivery in), at what inventory level should they reorder?
2. If nothing else has changed but it turns out that Sous-la-Table can only place orders for TroppodalVino at the start of every business trimester (effectively 16 weeks, as they close for August), how much should they reorder on Sept 1st, when the inventory level is 400 bottles?
3. What is the chance they will run out of TroppodalVino before this order will arrive in November?
4. What is the annual difference in safety stock costs between the 2 ordering policies?

Answer 1

Average demand, d = 40 units per week
Stdev of weekly demand, σ = 18 units
Lead time, L = 9 weeks
Unit holding cost, h = $2 per annum
Required service level = 90% which means z = 1.28

a.

Reorder point, R = d.L + z.σ.√L = 40*9 + 1.28*18*√9 = 429 units

So, they need to reporder when the inventory level is 429 units

b.

Review and reorder period, P = 16 weeks.

Order up-to-level, T = d.(L+P) + z.σ.√(L+P) = 40*(9+16) + 1.28*18*√(9+16) = 1115 units

On-hand inventory was 400 units.

So, the order quantity should be 1115 - 400 = 715 units

c.

Average demand of 9 weeks = 9*40 = 360 units
Stdev of 9-week demand = 18*√9 = 54 units

Z = (400 - 360)/54 = 0.741

So, F(z) = 0.77

So, Prob{Stock-out} in the coming 9 months = 1 - 0.77 = 0.23 or 23%

d.

The difference in safety stock = z.σ.√(L+P) - z.σ.√L = z.σ.(√(L+P) - √L) = 1.28*18*(√(9+16) - √9) = 46 units

So, the difference in terms of annual carrying cost = 46 * h = 46*$2 = $92