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?

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