Question

The Olde Town Microbrewery makes Townside beer, which it bottles and sells in its adjoining restaurant and by the case. It costs $1700 to set up, brew, and bottle a batch of the beer. The annual cost to store the beer in inventory is $1.25 per bottle. The annual demand for the beer is 21,000 bottles and the brewery has the capacity to produce 30,000 bottles annually.

a.Determine the optimal order quantity, total annual inventory cost, the number of production runs per year, and the maximum inventory level.

What is the total cost for pat a?

Answer 1

Setup cost, K = $1,700
Unit carrying cost, h = $1.25 per annum
Annual demand, D = 21,000 bottles
Production capacity, P = 30,000 bottles per annum

Economoc production quantity, Qp = [2.D.K.P / h.(P - D)]^1/2 = sqrt(2*21000*1700*30000/(1.25*(30000 - 21000))) = 13,799 bottles.

Max Inventory, I_max = Qp * (1 - D/P) = 13,799 * (1 - 21/30) = 4,140 bottles.

Total annual carrying cost = (I_max /2) * h = (4140/2) * 1.25 = $2,587.3

Total annual setup cost = (D / Qp) * K = (21000/13799) * 1700 = $2,587.1

So, total annual cost = $2,587.3 + $2,587.1 = $5,174.4

Number of production runs per year = D / Qp = 21000/13799 = 1.52