Question

Suppose there is a two-machine line, where each machine has a 1 minute operation time. There is also a buffer with 1 Kanban card between the machines.

Part 1

How many parts are produced in the 1st hour? Assume the buffer is empty at time 0.

How many parts are produced in the second hour?  

Part 2

Suppose now that Machine 1 now fails every hour, 10 minutes into the hour, for 10 minutes.

How many parts are produced in the first hour? Assume the buffer is empty.  

How many parts are produced if we increase the Kanban count from 1 to 10 in the first hour? Assume the buffer is empty.  

Part 3

Assuming the same conditions are still in place from part 2. Suppose the second machine fails 40 minutes in the hour, every hour for 10 minutes.

Assuming the Kanban size is now 2, and the buffer is empty at time 0. How many parts are produced in the first hour?   

If we increase the Kanban to 10, how many parts are produced in the second hour?

Answer 1

Part 1: In first hour 58 parts will be produced. An hour consists of 60 mins. First machine required 1 min to process the part. 1 kanban card is present. Second machine starts production by end of start of third minute and completes by end of third minute. Following continuous supply, a total of 58 parts will be produced in first hour.

For second hour, total 60 parts will be produced.

Part 2: The machine breaks down in every hour. 10 mins into the hour. That kanban size is increased to 10. The second machine won't have part till end of tenth minute. Second machine will start production by start of eleventh minute and will continue production. Since machine 1 does not break down for another hour, first machine will continue to supply parts at rate of 1 part per min. Hence total parts produced, as per scenario, are 50.

Part 3:

Assuming conditions of part 2, machine 1 fails 10 mins into the hour, kanban size is 10. Now the second machine fails 40 mins into the hour. Breakdown is for 10 mins. Then parts produced will be 40. By the end of 40th minute on second machine, it had produced 30 parts. It goes into breakdown after 40th min for 10 mins. The second machine comes back online by 51th min.in remaining 10 mins it produces 10 parts. So the total of 40 parts.

Now if the kanban size is 2, parts produced in same situation will be 28. First 10 parts will be made, then machine 1 breaks down. Then inventory is used up by second machine. By end of 40th min, second machine goes into breakdown. By then only 8 parts have been produced, 2 are in inventory. When the machine comes back online, it can only produce 10 parts by end of hour. So total works out to be 28 parts.

Now if the kanban size is changed to 10, then only 20 parts will be produced. For starting 10 mins, second machine won't be producing any part. On eleventh minute, it will start production and will use up all inventory by end of 20 min. On start of eleventh min, machine 1 goes into breakdown and will not produce any parts. After machine 1 coming online, it will start producing the parts. Total 10 parts will be made by end of 30th min. These parts will be available for second machine and production will commence. The second machine goes into breakdown after 40th min and comes back online after end of 50th min and starts producing parts.

For second hour, 30 parts will be produced. For first 10 mins the second machine will be using parts produced on first machine during first hour. After start of eleventh min, machine 1 fails and second machine uses up all the inventory, thereby producing 20 units till now. From start of 21st min, machine 1 comes back online and starts producing parts. Kan ban size is 10, so second machine won't have parts till end of 40th min. After that second machine goes onto breakdown and come back online by end of 50th min. From 50th min to end of hour 10 parts are made. So the total works out to be 30.

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