(a) Average WIP (work in progress):
To calculate the average work in progress, we need to determine how many cases are in each step of the process at any given time. We will assume that the process is in steady-state, meaning that the input rate equals the output rate and there is no backlog.
Let’s begin by defining some variables:
- λ = input rate (number of cases per day)
- μ = output rate (number of completed cases per day)
- p = probability of a case being re-assessed (15% or 0.15)
- C = number of cases in the Collect step
- A1 = number of cases in the first Assess step
- A2 = number of cases in the second Assess step
- R = number of cases in the Review step
- T = total number of cases in the system (WIP)
We can set up a system of equations based on the flow of cases through the process: λ = C μ = R A1 = C(1-p) A2 = C*p + A1(1-p) R = A2
Using these equations, we can solve for the unknowns: C = λ A1 = λ(1-p) A2 = λ*p/(1-p) R = λ*p/(1-p) T = C + A1 + A2 + R T = λ + λ(1-p) + λ*p/(1-p) + λ*p/(1-p) T = λ(3-p)/(1-p)
Therefore, the average work in progress is T/4: Average WIP = λ(3-p)/(4*(1-p))
(b) Average flow time (throughput time):
The average flow time is the total time it takes for a case to go through the entire process, including any re-assessments.
Let’s define some additional variables:
- tC = time spent in Collect step (0, since it is automated)
- tA1 = time spent in first Assess step (assume 2 days)
- tA2 = time spent in second Assess step (assume 2 days)
- tR = time spent in Review step (assume 1 day)
The total flow time for a case is: Flow time = tC + tA1 + tA2 + tR + p*(tA1 + tA2) = tC + tA1 + (1+p)*tA2 + p*tR
Using the assumptions we made above: Flow time = 0 + 2 + (1+0.15)*2 + 0.15*1 = 5.3 days
Therefore, the average flow time is: Average flow time = Flow time = 5.3 days
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