Question

Calculate the cycle time of the below business process. The cycle times of included tasks and the probabilities for the branches after XOR split gateways are all given. Please list the math steps of your calculation. (8 marks) Task name Task cycle time Task 1 1 day Task 2 2 days Task 3 3 days Task 4 4 days

Answer 1

To calculate the cycle time of the business process, we need to identify the critical path, which is the longest sequence of tasks required to complete the process. The critical path will determine the minimum cycle time needed to complete the process.

From the given information, the possible paths through the process are:

- Path 1: Task 1 -> Task 2 -> XOR Split -> Task 3 -> Task 4

- Path 2: Task 1 -> Task 3 -> Task 4

Path 1 has a cycle time of 1 day + 2 days + max(3 days, 4 days) = 7 days. The XOR split gateway indicates that either Task 3 or Task 4 will be executed next, depending on the outcome of the previous task. The maximum of the cycle times of Task 3 and Task 4 is chosen for Path 1.

Path 2 has a cycle time of 1 day + max(3 days, 4 days) = 5 days.

Since Path 1 has a longer cycle time than Path 2, it is the critical path. Therefore, the cycle time of the business process is 7 days.

Math steps:

- Path 1 = Task 1 + Task 2 + XOR Split + max(Task 3, Task 4)

- Path 1 = 1 day + 2 days + XOR Split + max(3 days, 4 days)

- Path 1 = 1 day + 2 days + XOR Split + 4 days

- Path 1 = 7 days

- Path 2 = Task 1 + XOR Split + max(Task 3, Task 4)

- Path 2 = 1 day + XOR Split + max(3 days, 4 days)

- Path 2 = 1 day + XOR Split + 4 days

- Path 2 = 5 days

Therefore, the cycle time of the business process is 7 days.