$11.$ Investigating the Effect of Rework Rates$$A proposed business process consists of

five serial workstations. One caseworker is positioned in each workstation. The

processing times at each workstation are exponentially distributed with mean

values of $11,10,11,11,$ and $12$ minutes, respectively. The interarrival times are

uniformly distributed between $13$ and $15$ minutes. The workstations have an

unlimited queuing capacity, and it is assumed that the downstream transfer time

is negligible. The unique aspect of this process is that between Workstations $2$ and

$5,$ it is possible that the job will need to be reprocessed by the workstation immediately preceding the current one. For example, after Workstation $3,$ it is possible

A$1$ B$1$

A$2$ B$2$

A$3$ B$3$

Type $1$

C$1$

C$2$

C$3$

Type $2$

Type $3$

FIGURE $8\mathrm{.}66$

Investigating the effect of pooling resources.

TABLE $8\mathrm{.}4$

Probability Distributions for Processing Times $($in minutes$)$

Activity Distribution

Job Type

$123$

A Exponential $282040$

B Normal $(34,5)(38,7)(21,3)$

C Lognormal $(19,3\mathrm{.}5)(28,2\mathrm{.}3)(17,3\mathrm{.}1)$

$($Mean$,$ Standard Deviation$)$

$352$ Business Process Modeling, Simulation and Design

that the job will be sent back to the queue in Workstation $2.$ When this occurs, the

transfer requires $3$ minutes. The probability of rework remains the same regardless of the number of times a job is sent back for reprocessing. The rework probability is considered to be the same for all workstations and is currently estimated

to be between $5$ and $10$ percent.

a$.$ Develop a simulation model of this process that is capable of running $10,000$

minutes of operation.

b$.$ Run $10,000$ minutes of operation for rework probabilities of $5,6,7,8,9,$ and $10$

percent. Collect cycle time data for each run.

c$.$ Construct a plot of the average cycle time $($y$-$axis$)$ versus the rework probability $($x$-$axis$).$ Also, construct a plot of the maximum cycle time versus the rework

probability.

d$.$ Assume that the processing times are constant. Rerun the simulation six times

with the rework probabilities in Part $($b$).$

e$.$ Construct plots of average cycle time and maximum cycle time versus the

rework probability. Compare these plots with the ones obtained in Part $($c$).$