8.5: Summary

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Modeling the flow of multiple job types in a job shop has been presented. Each type of job has a unique route through the workstations.

Simulation experiments are used to set the number of machines at each workstation in order to meet a service level criteria. Little's law is applied to determine the average number of busy machines at each station. These values are used as the initial number of machines at each station in the simulation. After each experiment, the bottleneck station is identified. The next experiment involves increasing the number of machines at this station by one. The series of experiments ends when the service level criteria is met.

Simulation results show how the bottleneck station changes as the result of adding capital equipment.

Problems

Based on the simulation experiment results that follow for a job shop similar to the one discussed in this chapter, give verification evidence.

Arrivals: \(\ \quad\quad\)Type 1 \(\ \quad\quad\)Type 2 \(\ \quad\quad\)Type 3	-- 581 -- 373 -- 482
Number completing operations \(\ \quad\quad\)Lathe \(\ \quad\quad\)Shaper \(\ \quad\quad\)Polisher \(\ \quad\quad\)Planer	-- 1063 -- 1065 -- 1426 -- 859
Number waiting for operations at the end of the simulation \(\ \quad\quad\)Lathe \(\ \quad\quad\)Shaper \(\ \quad\quad\)Polisher \(\ \quad\quad\)Planer	--0 --0 --5 --0
State of resource at the end of the simulation \(\ \quad\quad\)Lathe \(\ \quad\quad\)Shaper \(\ \quad\quad\)Polisher \(\ \quad\quad\)Planer	-- 2 busy -- 6 busy -- 8 busy -- 7 busy
Total number of jobs completed	--1426

Suppose the situation in the job shop is changed as follows. The time between arrivals jobs is 0.25 hours. Two thirds of the jobs are of job type 1 and one-third are of job type 3. Develop an analytic estimate of the required number of each type of machine.

Develop a process model of the following small job shop. The shop processes two types of jobs in equal numbers. The time between job arrival is exponentially distributed with a mean of 3 hours. The first type of job visits stations 1 and 2. The second type of job visits stations 2, 1, and 3. Processing times are constant and as follows:

Job Type	First Station Time	Second Station Time	Third Station Time
1	2.0	1.2
2	0.8	1.7	2.6

Model the serial line discussed in the application study of Chapter 7 using the job shop model developed in this chapter.
List systems with job shop organizations that you deal with in the course of your everyday life. Develop a single list for the entire class.
Provide validation evidence based on the outputs presented in this chapter.
Add an additional planer as well as a shaper and a polisher to the job shop in the case study in this chaper. Is the improvement due to the additional shaper worthwhile?
The lower limit of the approximate 99% confidence interval for the service level in Table 8-5 is less than the required average service level of 99%. As an alternative, estimate and interpret the approximate 90% confidence interval.
Re-run the simulation experiment with the following performance measure added: lead time for entities who lead time exceed the service level target cycle time. Interpret your results.

Case Problem

Management wishes to move the job shop toward a lean system in which there would be three workcells, one for each job type. Due to current budget constraints, no more machines than were found necessary in the case study above can be used, a total of 11. As a first step toward lean in the short term, the following options are to be evaluated with respect to service level and total number of machines.

A serial line to produce type 3 jobs and smaller job shop to produce type 1 and 2 jobs with 10 total machines.
A serial line to produce type 3 jobs and smaller job shop to produce type 1 and 2 jobs with 11 total machines.
Three serial lines, one for each type of job, with 11 total machines.

Build the simulation models and conduct the simulation experiments to evaluate the above options.

Case Problem Issues

Suppose each type of job is run on its own dedicated serial line (#3 above). How many machines of each kind are needed for each type of job?
Can this analysis be done using the model developed in this chapter? If so, tell how.
For item 1 above, how would the 10 total machines be allocated by machine type and location (serial line for jobs of type 3 and job shop for jobs of type 1 and 2)?
For item 2 above, how would the 11 total machines be allocated by machine type and location (serial line for jobs of type 3 and job shop for jobs of type 1 and 2)?