Question

Gentle Ben's Bar and Restaurant uses 6,700 quart bottles of an imported wine each year. The effervescent wine costs $4 per bottle and is served only in whole bottles because it loses its bubbles quickly. Ben figures that it costs $25 each time an order is placed, and holding costs are 15 percent of the purchase price. It takes three weeks for an order to arrive. Weekly demand is 134 bottles (closed two weeks per year) with a standard deviation of 30 bottles. Ben would like to use an inventory system that minimizes inventory cost and will provide a 95 percent service probability.

Required:
a. What is the economic quantity for Ben to order? (Round your answer to the nearest whole number.)
b. At what inventory level should he place an order? (Round your answer to the nearest whole number.)

Answer 1

Answer:

a. The answer is:762 bottlé.

b. The answer is: 487 bottles.

Explanation:

a. The economic order quantity is calculated as: $\sqrt{(2xDxS/H)}$ = $\sqrt{2 x 6968 x 25)/0.6$ = 762 units because: D = annual demand = Weekly demand x week opening per year = 134 x 52 = 6968; S = Cost per order = 25; H = Holding cost per unit = 15% x purchase price = 15% x 4 = 0.6

b. Inventory level to place order:

With the inventory system providing a 95 percent service probability, z level is 1.64 (using the NORM.S.INV function in excel).

So Inventory level to place order = 134 * 3 + 1.64 * 30 * 3^0.5= 487 bottles.