Question

Question 3

The restaurant works with several national and foreign wine suppliers. One of the best-selling wines is supplied by a wine cellar located in the Douro region, in boxes of 6 bottles at the price of 24 euros per box. The monthly needs of this wine are 600 bottles. Currently the Pousada Palacio de Estoi uses a continuous review system, ordering 100 boxes of wine each time an order is placed. Based on recent studies, it was concluded that the cost of holding a box of this wine in stock for one year amounts to 2 euros. On the other hand, it is known that the delivery time is one month and the administrative costs of placing an order, including transport costs, are 75 euros.

a) Evaluate whether the current stock management policy for this wine is optimal. In case the current

policy is not optimal, determine the optimum quantity of wine to be ordered each time, the number

of orders to be placed per year and the reorder point.

b) The wine supplier has informed the restaurant that if all the wine needed during the year is ordered

at once, the supplier is prepared to offer a discounted price for each box. In your opinion, what

should the minimum amount of the discount per box be, in order to be advantageous for the

restaurant to order all the wine at once.

Answer 1

(a) Annual Demand = D = (600/6)*12 = 1200 boxes /year
Ordering Cost = C_o = €75
Holding Cost = C_c = €2/year
Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*1200*75/2) = 300
Hence, the current policy is not optimal and the restaurant should order 300 boxes when an order is placed

Number of orders/year = 1200/300 = 4 orders/year
Reorder Point =  dL, where d = demand rate per period and L = lead time
d = 1200/12 = 100 boxes per month, L = 1 month
Hence, Reorder Point = 100*1 = 100 boxes

(b) Using the optimal Quantity Q* = 300,
Average Inventory = Q*/2 = 150
Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (300/2)*2 = €300
Number of Annual orders = D/Q* = 1200/300 = 4
Annual Order cost = Number of orders * cost/order = (D/Q*) C_o = (1200/300)*75 = €300
Hence, Total Annual Cost as per best policy = Annual Inventory Holding Cost + Annual Order Cost = 300 + 300 = €600

If all the wine is ordered at once, Q = 1200 boxes,
Total Annual Cost if all wine is order at once= Annual Inventory Holding Cost + Annual Order Cost = (1200/2)*2 + (1200/1200)*75 = €1200

To match the best price, a discount of 1200 - 600 = €600 should be given
Total boxes ordered = 1200
Discount / box = 600/1200 = €0.50

Hence a minimum discount of €0.5 per box should be given in order to be be advantageous