# 10.4: Summary

- Page ID
- 31004

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This chapter emphasizes how simulation is used to evaluate the operating strategies for systems. In addition, simulation is helpful in setting the parameters of such operating strategies. The use of simulation in modeling a pull production strategy is shown. The evolution of previously existing models is illustrated.

**Problems**

- Develop the process model for the lathe station.
- Develop the process model for the polisher station.
- Develop a process model of a single workstation producing one item type that uses a pull production strategy.
- Find verification evidence for the model discussed in this chapter.
- Provide additional validation evidence for the model discussed in this chapter.
- Compare the routing process used in the model in this chapter to that used in chapter 8.
- Compare the process at each workstation used in the model in this chapter to that in the model in chapter 8.
- Provide a justification for using different inventory levels at different stations and the FGI for the same product.
- Find an inventory level between the lower and upper inventory sizes that provides a 99% service level. How much inventory is required?
- Conduct additional simulation experiments using the model developed in this chapter to determine the product inventory levels that yield a 95% service level.
- For one customer demand, augment the model to produce a trace of the movement of the entities through the model.

**Case Problem -- CONWIP**

Convert the assembly line presented in the chapter 7 application problem to a CONWIP production strategy. The assembly line was described as follows.

A new serial system consists of three workstations in the following sequence: mill, deburr, and wash. There are buffers between the mill and the deburr stations and between the deburr and the wash stations. It is assumed that sufficient storage exists preceding the mill station. In addition, the wash station jams frequently and must be fixed. The line will serve two part types. The production requirements change from week to week. The data below reflect a typical week with all times in minutes.

Time between arrivals - | Part type 1: Exponentially distributed with mean 2.0 Part type 2: Exponentially distributed with mean 3.0 |

Time at the mill station - | Part type 1: 0.9 Part type 2: 1.4 |

Time at the deburr station - | Uniform (0.9, 1.3) for each part type |

Time at wash station - | 1.0 for each part type |

Time between wash station jams - | Exponentially distributed with mean 30.0 |

Time to fix a wash station jam - | Exponentially distributed with mean 3.0 |

Arrivals represent demands for completed products. Demands are satisfied from finished goods inventory. Each demand creates a new order for the production of a product of the same type after it is satisfied. The completed product is place in the finished goods inventory.

Three quantities must be determined through simulation experimentation:

- The CONWIP level, that is the maximum number of parts allowed on the line concurrently.
- The target FGI level for part type 1.
- The target FGI level for part type 2.

Two approaches to setting these values could be taken. Choose either one you wish.

- Approach one.
- Set the FGI inventory level for each product as described in this chapter. Set the CONWIP level to infinite (a very high number). Use an infinite (again a very high number) FGI inventory level to determine the minimum number of units needed for a 100% service level.
- Determine the inventory level needed for a 99% service level during the average replacement time analytically. The average replacement time is the same for each part type. Determine the average lead time using the VUT equation for each station. Sum the results. Remember that ca at a following station is equal to cd at the preceding station. Hints: 1) The VUT equation assumes that there is only one part type processed at a station. Thus, the processing time to use a the mill station is the weighted average processing time for the two part types. The weight is the percent of the total parts processed that each part type is of the total: 60% part type 1 and 40% part type 2. The formulas for the average and the variance for this situation are given in the discussion of discrete distributions in chapter 3. 2) The formula for the variance of a uniform distribution is given in chapter 3. 3) Ignore the downtime at the was station for this analysis.
- Assess the service level for the inventory level midway between the lower and upper bound.
- Pick the lowest level of inventory of three that you have tested that yields close to a 99% service level. Note average and maximum WIP on the serial line for this value.
- Set the CONWIP level to the lowest value that doesn't negatively impact the service level. The minimum feasible CONWIP level is 3. Try values of 3, 4, 5, until one is found that does not impact the service level. Confirm your choice with a paired-t analysis.
- Compare the maximum WIP before the CONWIP level was establish to the CONWIP level you selected.

- Approach two:
- Find the minimum CONWIP level that maximizes throughput. Set the two FGI levels to infinite (a very high number) so that the service level is 100%. The minimum feasible CONWIP level is 3. Try values of 3, 4, 5, ... until one is found such that the throughput is no longer increasing. Confirm your choice with a paired-t analysis.
- Compare the maximum WIP in the serial line without the CONWIP control to the CONWIP level you select. The former could be determined by setting the CONWIP level to a large number.
- Estimate the finished goods inventory level need to satisfy customer demands using the approach described in this chapter and after the CONWIP level has been established. Use an infinite (again a very high number) FGI inventory level to determine the minimum number of units needed for a 100% service level.
- Determine the inventory level needed for a 99% service level during the average replacement time analytically. The average replacement time is the same for each part type: the average lead time at station j is given by the following equation discussed in Chapter 9 where M = 3 stations and N is the CONWIP level you selected: \(\ \left(\frac{N-1}{M}\right) C T_{j}+C T_{j}\)
- Assess the service level for the inventory level midway between the lower and upper bound and pick the lowest level that yields close to a 99% service level.

Terminating Experiment: Use a simulation time interval of 184 hours.

Application Problem Issues

- How should the CONWIP control be modeled?
- What should the ratio of the two FGI levels be if prior information is used?
- Should the mean or maximum WIP level on the serial line with no CONWIP control be compared to the CONWIP level?
- Given the CONWIP control, is it necessary to model the finite buffer space between the stations on the serial line? Why or why not?
- How will verification and validation evidence be obtained?

**Case Problem -- POLCA**

Convert the assembly line presented in the chapter 7 application problem to a set of QRM Cell pairs as follows.

A QRM analysis determined that there will be three QRM cells processing two part types.

- Mill and deburr serving both part type 1 and part type 2
- Wash station 1 serving part type 1
- Wash station 2 serving part type 2

The wash stations jam frequently and must be fixed.

Time between wash station jams - | Exponentially distributed with mean 30.0 |

Time to fix a wash station jam - | Exponentially distributed with mean 3.0 |

Production requirements change from week to week. The data below reflect a typical week with all times in minutes.

Time between arrivals - | Part type 1: Exponentially distributed with mean 2.0 Part type 2: Exponentially distributed with mean 3.0 |

Time at the mill station - | Part type 1: 0.9 Part type 2: 1.4 |

Time at the deburr station - | Uniform (0.9, 1.3) for each part type |

Time at wash station 1 for part type 1- | 1.7 |

Time at wash station 2 for part type 2 - | 2.5 |

Arrivals represent demands for completed products. Demands are satisfied from finished goods inventory. Each demand creates a new order for the production of a product of the same type after it is satisfied. The completed product is place in the finished goods inventory.

Three quantities must be determined through simulation experimentation:

- The number of POLCA cards of each type (A-B and B-C).
- The target FGI level for part type 1.
- The target FGI level for part type 2.

Approach

- Determine an upper bound on the needed inventory for each part type as follows. Set the POLCA cards levels to infinite (a very high number). Use an infinite (again a very high number) FGI inventory level to determine the minimum number of units needed for a 100% service level.
- Determine a lower bound on the needed inventory for each part type as follows. Determine the inventory level needed for a 99% service level during the average replacement time analytically. Determine the average replacement time separately for each part type. Remember however that the average time in QRM Cell A will be the same for each part type when determine using the VUT equation as described in items a, b, and, c. Remember that c
_{a}at a following station is equal to c_{d}at the preceding station.- The VUT equation assumes that there is only one part type processed at a station. Thus, the processing time to use at the mill station is the weighted average processing time for the two part types. The weight is the percent of the total parts processed that each part type is of the total: 60% part type 1 and 40% part type 2. The formulas for the average and the variance for this situation are given in the discussion of discrete distributions in chapter 3.
- The formula for the variance of a uniform distribution is given in chapter 3.
- Ignore the downtime at the wash stations for this analysis.

- Assess the service level for the inventory level midway between the lower and upper bounds.
- Pick the lowest level of inventory of three that you have tested that yields close to a 99% service level.
- Set the POLCA levels to the lowest values that don't negatively impact the service level. Confirm your choice with a paired-t analysis.

Terminating Experiment: Use a simulation time interval of 184 hours.

Application Problem Issues

- How should the POLCA control be modeled?
- What should the ratio of the two FGI levels be if prior information is used?
- What should the ratio of the number of A-B POLCA cards to the number of A-C POLCA cards be if prior information is used?
- Given the POLCA control, is it necessary to model the finite buffer space between the stations on the serial line? Why or why not?
- How will verification and validation evidence be obtained?