**1-**record your numerical answers (in order) to the nearest tenth of jph. (Enter numbers only):

a. A station with three (3) machines operating in parallel with 20-minute process times (te) at each machine.

b. A balanced line with single-machine stations, all with average processing times (te) of 15 minutes.

c. A line with four (4) single machine stations in series, where the average processing times are:

15, 20, 10, & 12 minutes respectively.

d. A four (4) station line with multi-machine stations A, B, C, & D, where the number of parallel machines are 2, 6 10, & 3 respectively. The average processing times (te) at each station are 10, 24, 40, & 18 minutes respectively (see table below).

**Process Line with series stations & parallel machines per station Question (d)**

Station | te(minutes) | te(hours) | Machine jph(1/te) | Machines/ station | Station jph |

1 | 10 | 0.167 | 6 | 2 | |

2 | 24 | 0.40 | 4 | 6 | |

3 | 40 | 0.67 | 4 | 10 | |

4 | 18 | 0.3 | 6 | 3 |

**2-**Consider a three (3) station line with single-machine stations 1, 2, & 3. The average natural processing times (t0) at each station are 15, 12, and 12 minutes respectively. However, machine 2 is subject to random failures, which causes its Availability to be only 75%. Assuming 100% Availability for the other 2 stations, find te for station 2 and answer the following questions (see table below for problem summary):

a. Find **T0** of this line by adding the effective process times, te’s, together and enter to 2 decimal places in the first answer box below (if less than 1, show leading zero).

b. What is bottleneck rate, **rb**, of the line to two decimal places? Enter the value to 2 decimal places in the second answer box below.

**Process Line with series stations with one machine per station**

Station/Machine | t0(minutes) | t0(hours) | te(hours) | jph (1/te) | |

1 | 15 | 0.25 | 0.25 | 4.0 | |

2 | 12 | 0.20 | ? | ? | |

3 | 12 | 0.20 | 0.20 | 5.0 | |

T0 =rb = |

c. Then use **T0 **and the bottleneck rate, **rb**, and calculate **W0** to one decimal place for entry into the answer box.

d. If the Availablility of station 2 is reduced to 50%, what is the new critical WIP, **W0**? (to one decimal place)

e. What happens to the line throughput, TH? Indicate in either the work “up” or “down” (don’t show quotation marks).

**3-**Answer the following questions and enter answers with format indicated into the respective answer boxes:

a. Which is preferable – long, but infrequent machine outages; or, short, but more frequent outages? Answer format: enter either long or short.

b. **t0 **is the average natural (no detractors) process time at a workstation and is increased to the effective process time **te** by “detractors” such as machine downtime (availability) and more lengthy setup times between jobs. Calculate **te** given a **t0** = 4 minutes with an Availability of 80% and a setup time of 20 minutes of every 50 jobs. Give your **answer in minutes** to one decimal place.

c. What is the coefficient of variation CV for the **te **from (b) and a standard deviation of effective process time at a station of 2.7 minutes. Give answer to two decimal places with a leading zero before the decimal.

d. Is the CV from (c) a low, moderate, or high variability class. Enter low, moderate, or high in answer box.

e. In a high utilization (bottleneck) station, what determines the variability of the flow out of that station? Select either the parts arrival variability or the stationvariability. Enter either arrival or station.

**4-**Floor-On Ltd., operates a line that produces self-adhesive tiles. This line consists of single-machine stations that are balanced (station rates equal). A Manufacturing Technologist has estimated the bottleneck rate, rb, of the line to be 1,600 cases per 16-hour day, and the raw process time, T0, to be 15 minutes. The actual throughput of the line, TH, averages 1,200 cases per 16-hour day, and cycle time, CT, has averaged 4 hours. Find the following and enter into the respective answer boxes below with the exact format stated:

a. Critical WIP, W0 = rb * T0 to the nearest whole number of cases (enter only the number in the answer box).

b. Actual average throughput, TH, to the nearest whole number of cases per hour (enter only the number, no letters).

c. Actual average work-in-process, using Little’s Law: WIP = TH X CT (to the nearest whole number of cases).

d. Best-case Throughput, THbest.

e. Practical-worst-case Throughput, THpwc. (Enter numerical answer to one decimal place).

f. Based on actual TH vs THpwc is the operation considered “lean?” (Answer should be entered as either a yes or a no).

**5-**This process line has the following overall actual production data as follows:

Average actual throughput **TH** is 120 jobs per 16-hour production day.

Cycle time **CT** is 4 hours

Assume 100% machine availability and no setup times so that te is the same as to

Answer the questions after filling in your copy of the table below to find rb and T0:

**Process Line with series stations with one or more machines per station**

Station/Machine | Machine ratejph | te(hours) | Number of MachinesPer Station | Station Ratejph | |

1 | 12 | 1 | |||

2 | 5 | 2 | |||

3 | 6 | 2 | |||

T0 = | rb = |

1. Use Little’s Law to find the average actual **WIP** (round to nearest whole job and enter in the first answer box below). Continue with next answer in the next respective box.

2. What is bottleneck rate **rb** as calculated from the slowest jph station in table above? (Enter as number with rounding to nearest whole number)

3. What is the raw process time **T0** found from summing the te’s from table above (Enter to 2 decimal places with leading zero before the decimal)

4. Calculate the **THpwc **(Enter to nearest whole number jph – no written characters). Compare with actual to see how it compares (no answer required)

5. Calculate the **CTpwc** (Show to 2-decimal places in hours – no written characters). Compare with actual to see how it compares (no answer required)

6. Is the operation considered “lean” relative to actual TH vs THpwc? (Answer with either the word **yes** or the word **no**).

**6-**Compute the average capacity in jobs per day (jpd) for the following situations (enter the data in the respective boxes with format indicated):

1. A workstation with 10 machines in parallel each having a mean process time t0 of 2.5 hours. There are two (2) 8-hour shifts. Lunch and breaks take 1.25 hours per shift giving a total productive time of 2 shifts/day *(8 hr/shift – 1.25 hr/shift) = 13.5 hr/day that you can use for converting jph to jpd. (Enter answer in first box to nearest whole job).

2. Same situation as above except that the machines have a mean-time-to-failure of 100 hours with a mean time to repair of 4 hours (use availability formula to find uptime %). And, the machines are set up every 10 jobs with a mean setup time of 3 hours. (Given t0, calculate te taking availability, and setup time into account and convert to jph for the station and then convert to jpd). (Enter into the 2nd box to nearest whole jpd).

3. Same situation as (2) above but factor in worker utilization. Because the operators have to attend training meetings and the like, we cannot plan more than 85% utilization of the workers operating the machines. Compute the capacity taking this factor into account. (Likewise, enter the jpd to nearest whole jpd into the 3rd box below).

4. By considering “practical detractors” how much has the jpd rate dropped from situations 1 to 3 (take the difference and enter to the nearest whole jpd and enter into the 4th box below).

What is bottleneck rate, rb, of the line to two decimal places? was first posted on July 11, 2019 at 1:53 pm.

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