(a) Average WIP (work in progress): To calculate the average WIP, we need to know the number of cases that are in progress at any given time. We can do this by looking at each step of the process and determining how many cases are in that step on average.
Step 1: Collect This is an automated task and therefore does not require any resources or time. Therefore, there will be zero cases in progress at this step.
Step 2: Assess Each case has a 15% chance of being reassessed, which means that on average, 85% of cases will move on to the next step after one assessment. This means that the average number of cases in progress at this step is:
Average number of cases in Assess = (Number of cases x 0.85)
Step 3: Approve or Reject All cases that make it to this step will either be approved or rejected. Therefore, the average number of cases in progress at this step is equal to the average number of cases in Assess that have not been reassessed yet. This can be calculated as:
Average number of cases in Approve/Reject = (Number of cases x 0.85) x 0.85
Therefore, the total average WIP can be calculated by adding the average number of cases in each step:
Average WIP = 0 + (Number of cases x 0.85) + (Number of cases x 0.85 x 0.85) Average WIP = Number of cases x 1.1525
(b) Average flow time (throughput time): To calculate the average flow time, we need to know the amount of time it takes for a case to go through the entire process. We can do this by adding up the average time spent at each step.
Step 1: Collect This step is automated and therefore does not require any time or resources.
Step 2: Assess The average time spent in this step will depend on whether the case is reassessed or not. If the case is not reassessed, it will spend an average of 2 days in this step (1 day for assessment and 1 day waiting for approval/rejection). If the case is reassessed, it will spend an additional 1 day in this step. Therefore, the average time spent in this step can be calculated as:
Average time in Assess = (Number of cases x 0.85 x 2) + (Number of cases x 0.15 x 3)
Step 3: Approve or Reject All cases that make it to this step will either be approved or rejected. Therefore, the average time spent in this step is equal to the average time spent in Assess that have not been reassessed yet. This can be calculated as:
Average time in Approve/Reject = (Number of cases x 0.85 x 2)
Therefore, the total average flow time can be calculated by adding the average time spent at each step:
Average flow time = 0 + [(Number of cases x 0.85 x 2) + (Number of cases x 0.15 x 3)] + (Number of cases x 0.85 x 2) Average flow time = Number of cases x 2.55
Therefore, the average flow time for this process is 2.55 days.
