The mythical Hacker Microbrewery in Rosenheim, Germany, makes a brand of beer called Golden Eagle, which bottles and sells in cases to adjoining pubs and stores in Rosenheim. The setup cost of brewing and bottling a batch of beer is the US $1,800 per setup. The annual demand for the Golden Eagle brand of beer is 20,000 bottles. Hacker Microbrewery brews and bottles beer at a rate of 655 bottles per day. The brewery operates 250 days per year.
a. What is the economic production quantity (EPQ)?
b. What is the average inventory level for this optimum pro quantity? c. How many production setups would there be in a year?
d. What is the optimal length of the production run in days?
e. What would be the savings in annual inventory co can be reduced to $1,500 per setup?

Explanation:

Annual demand (D) = 20000 units

Number of days per year = 250

Demand rate(d) = D/number of days per year = 20000/250 = 80 units

Production rate(p) = 655 units

Set up cost(S) = $1800

Holding cost (H) = $1.50

A) Optimum run size(Q) = sqrt of {2DS / H [1-(d/p)]}

= sqrt of {(2x20000x1800) /1.50[1-(80/655)]}

= Sqrt of [7200000/1.50(1-0.1221) ]

= sqrt of [72000000/(1.50 x 0.8779)]

= sqrt of (7200000/1.31685)

= Sqrt of 5467593.1199

= 2338 units

b) Maximum inventory ( I - max) = (Q/p) (p-d) = (2338/655)(655-80) = 3.5695 x 575 = 2052.46 or rounded off to 2052 units

Average inventory = I-max/2 = 2052/2 = 1026 units

C) Number of production setups per year = D/Q = 20000/2338 = 8.55 or rounded up to 6

d) optimal length of production run  = optimal run size /production rate = 2338/655 = 3.56 or rounded up to 4 days