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 1,491lbs milk chocolate and 1,148 lbs of dark chocolate in each cycle. What would be the maximum inventory (lbs) of milk chocolate? 10 points QUESTION 3 Continue from Q2: How many lbs of milk and dark chocolate should be produced with each cycle so as to satisfy demand while minimizing inventory?

Answer 1

Batch size of milk chocolate = 1491 lbs

Production rate, p = 800 lbs/hr

Demand rate, d = 500 lbs/hr

Maximum inventory of milk chocolate = Q*(1-d/p)

Maximum inventory of milk chocolate = 1491*(1-500/800)

Maximum inventory of milk chocolate = 559.125 lbs

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In order to satisfy demand while minimizing inventory, production cycle time must be equal to demand cycle time

Let X be the combined batch size of milk and dark chocolate.

Production cycle time = X/800+(60+30)/60

Demand cycle time = X/(500+200)

Equating the production and demand cycle time, we get,

X/800+(60+30)/60 = X/700

X(1/700-1/800) = 1.5

X(1/5600) = 1.5

X = 1.5*5600

X = 8400 lbs

Quantity of milk chocolate = 8400*500/700 = 6000 lbs

Quantity of dark chocolate = 8400*200/700 = 2400 lbs