Mountain Nectar Brewing Company produces an India pale ale which it stores in ba

Question

Mountain Nectar Brewing Company produces an India pale ale which it stores in barrels in its warehouse and supplies to distributors on demand. The demand for India pale ale is 1800 barrels per day and the company can produce 3000 barrels per day. It costs $750 to set up a production run of India pale ale. Once brewed, the ale is stored in their refrigerated warehouse at an annual cost of $60 per barrel. Annual demand equals 1800 barrels per day times 250 operating days per year which equals 450,000 barrels annually Can daily production keep up with daily demand? What quantity should be produced in each production run in order to minimize total annual inventory costs? Calculate the minimum total annual inventory costs. How many days is each production run of India pale ale?

Explanation / Answer

Demand rate, d = 1800 barrels

Production rate, p = 3000 barrels

Setup cost, S = $ 750

Annual holding cost, H = $ 60 per barrel

Annual demand, D = 1800*250 = 450,000 barrels

1) Yes, daily production rate is greater than demand rate. Therefore, production can very well keep up with the demand.

2) Economic Production Quantity = SQRT(2DS/(H*(1-d/p)))

= SQRT(2*450000*750/(60*(1-1800/3000)))

= 5303 barrels

3) Minimum total annual inventory costs = (D/Q)*S + (Q/2)*H*(1-d/p)

= (450000/5303)*750 + (5303/2)*60*(1-1800/3000)

= $ 127,279

4) Production run length = 5303/3000 = 1.77 days

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