Question

Cadbury has a chocolate factory in Dunedin, New Zealand. For Easter, it makes two kinds of “Easter Eggs”: milk chocolate and dark chocolate. It cycles between producing milk and dark chocolate eggs. The table below provides data on these two products.

	Milk	Dark
Demand (lbs per hour)	500	200
Switchover time (minutes)	60	30
Production rate per hour	800	800

For example, it takes 30 minutes to switch production from milk to dark chocolate. Demand for milk chocolate is higher (500lbs per hour versus 200 lbs per hour), but the line produces them at the same rate (when operating): 800 lbs per hour.

Suppose Cadbury produces 1,992lbs milk chocolate and 1,362 lbs of dark chocolate in each cycle. What would be the maximum inventory (lbs) of milk chocolate?

Answer 1

Overall time to complete one cycle = 60 + (1992 / 800)*60 + 30 + (1392 / 800)*60 = 343.8 minutes

So,

Effective production rate of milk chocolate, p = 1992 lbs in 343.8 minutes = 5.794 lbs per minute = 347.64 lbs. per hour

Demand rate, d = 500 lbs per hour

So,

Max inventory level = batch size * (1 - d/p) = 1992 * (1 - (347.64/500)) = 607 lbs.