# Developing simulation models

**1-**Measuring cycle times of different types of jobs- Three types of jobs arrive to a process at a rate of four jobs per hour. The interarrival times are exponentially distributed. The arrivals are not equally likely for each job type. Typically 40% of the jobs are type I 35% are type II and 25% are type III. It can be assumed that all of the processing times are exponentially distributed; however the mean times depend on the job type. Table 8.3 shows the mean processing time for the activities associated with each job type. (All times are given in minutes.)

A flowchart of the process is depicted in Figure 8.65. Note that type I jobs are routed through activities B and C and job types II and III are routed through activities D and E. The percentage of rework also depends on the job type. About 5% of the type I jobs are reworked about 4% of the type II jobs are reworked and about 6% of the typeIII jobs are reworked. In terms of resources the process has three types of workers. Five super workers can handle any job; therefore managers employ them to work on activities A F or G. Three type I specialists can handle only type I jobs; therefore management employs them to work on activities B and C. Finally three type II and III specialists can handle only type II and type III jobs; therefore management employs them to work on activities D and E:

a. Develop a simulation model for this process.

b. Run the simulation for 250 h to generate approximately 1000 job arrivals and collect data on cycle times for each job type separately.

c. Assess the performance of the process based on your analysis in part (b).

**2-**Investigating the effect of pooling resources—Three types of jobs arrive to a process at a rate that randomly varies between 2 and 4 jobs/h; that is, the interarrival times are governed by a uniform distribution with mean equal to three and a half jobs per hour.

The process is currently configured in a way such that each arrival is sent to a team of specialists according to the type of job. Each team consists of three members. A team performs three activities in order to complete each job, and any team member can work on any of the three activities (A, B, or C). Figure 8.66 shows a flowchart of the process.

The arrivals are not equally likely for each job type. Typically, 30% of the jobs are type 1, 35% are type 2, and 35% are type 3. Processing times (in minutes) associated with the activities depend on the job type and are summarized in Table 8.4.

Management is concerned with the current performance of the process and is considering cross-training the teams so team members can work on any job type:

a. Develop a simulation model of this process that can be used to model 1 day of operation; that is, one run of the model will consist of 8 h of operation.

b. Use your model to assess performance with the following measures: cycle times, resource utilization, and overtime (the time needed to finish all jobs after the process closes). Simulate 10 days of operation to collect data for your analysis.

c. Assume that the teams are cross-trained and that all nine people can perform any of the activities in the process. Compare this design with the original process using the measures in part (b).

**3-**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 min, respectively. The interarrival times are uniformly distributed between 13 and 15 min. 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 that the job will be sent back to the queue in workstation 2. When this occurs, the transfer requires 3 min. 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%:

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

b. Run 10,000 min of operation for rework probabilities of 5%, 6%, 7%, 8%, 9%, and 10%. 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. Run 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).