Battle Creek Cereal Company has four main products: Corn Flakes, Frosted Flakes,

Question

Battle Creek Cereal Company has four main products: Corn Flakes, Frosted Flakes, Bran Flakes and Strawberry Flakes. The average daily demand for the products is: Corn Flakes: 1,695 CS Frosted Flakes: 1,830 CS Bran Flakes: 1,180 CS Strawberry Flakes: 2,600 CS These products are manufactured on a single assembly line with a daily production rate of 12,980 CS. It takes Battle Creek one day to set up for each product. If they run production in a cyclic schedule, what is the minimum cycle time in hours assuming Battle Creek runs 24 hours per day?

Answer: 220

How is this calculated?

Explanation / Answer

Let the cycle time be x days,

when the production starts for Corn flakes it has to produce the total demand during cycle = 1695*x CS

Time taken to produce this demand (daily production 12980) = 1695*x/12980

similarly time taken to produce Frosted flakes demand = 1830*x/12980

time taken to produce for bran flakes demand = 1180*x/12980

time taken to produce for Strawberry Flakes demand = 2600*x/12980

The setup time for each = 1 day

total time taken =

1 + 1695*x/12980 + 1 + 1830*x/12980 + 1 + 1180*x/12980 + 1 + 2600*x/12980

Now this time is nothing but the cycle time since it is sum of all the production times in one cycle, hence it is equal to x

1 + 1695*x/12980 + 1 + 1830*x/12980 + 1 + 1180*x/12980 + 1 + 2600*x/12980 = x

4 + 7305x/12980 = x

x - 7305x/12980 = 4

5675x/12980 = 4

x= 4*12980/5675

x = 9.15 (approx)

Hence the cycle time = 9.15 days = 9.15*24 hours = 219.6 hours = 220 hours

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