Chapter 7.S, Problem 15P

10 minutes per unit. Part 2 is simultaneously processed at work-station C for 20 minutes per unit. Work stations B and C feed the parts to an assembler at workstation D. w here the two parts are assembled. The time at workstation D is 15 minutes.

a) What is the bottleneck of this process?

b) What is the hourly capacity of the process?

•• S7.15 A production process at Kenneth Day Manufacturing is shown in Figure S7.9. The drilling operation occurs separately from, and simultaneously with, sawing and sanding, which are independent and sequential operations. A product needs to go through only one of the three assembly operations (the operations are in parallel).

a) Which operation is the bottleneck?

b) What is the bottleneck time?

c) What is the throughput time of the overall system?

d) If the firm operates 8 hours per day. 20 days per month, what is the monthly capacity of the manufacturing process?

Summary Introduction

To determine: The bottleneck operation.

Introduction:

Bottleneck time:

The bottleneck time of the system is the process in the system which takes the most amount of time to complete its activity. The bottleneck time will reduce the overall efficiency of the system.

Answer to Problem 15P

The bottleneck operation is Welding.

Explanation of Solution

Given information:

Formula to convert capacity into process time:

$\text{Process time of each operation}=\frac{\text{Number of minutes per hour}}{\text{Capacity}}$

Formula to calculate overall assembly operation process time:

$\text{Process time of overall assembly}=\frac{\text{Process time at one assembly operation}}{\text{Number of assembly operations}}$

Calculation of process time for each operation:

The process time of each station is calculated by dividing the number of minutes with the production capacity of the station.

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Sanding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Drilling:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2.4}\\ =25\text{ minutes / unit}\end{array}$

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Welding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2}\\ =30\text{ minutes / unit}\end{array}$

Assembly at one operation:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{0.7}\\ =85.71\text{ minutes / unit}\end{array}$

Calculation of overall assembly operation process time:

The overall assembly operation process time is calculated by dividing the process time at one assembly operation by the Number of assembly operations.

$\begin{array}{c}\text{Process time of overall assembly}=\frac{\text{85}\text{.71}}{\text{3}}\\ =\text{28}\text{.57}\end{array}$

Identification of the bottleneck time of the system:

The bottleneck time of the system is the operation which has the highest process time. Welding has the highest process time when compared to the other operations (30>10, 10, 25, 10, 28.57). Hence, the bottleneck time of the system is 30 minutes per unit.

Therefore, the bottleneck operation is Welding.

Summary Introduction

To determine: The bottleneck time of the bottleneck operation.

Introduction:

Bottleneck time:

The bottleneck time of the system is the process in the system which takes the most amount of time to complete its activity. The bottleneck time will reduce the overall efficiency of the system.

Answer to Problem 15P

The bottleneck time of the bottleneck operation is 30.

Explanation of Solution

Given information:

Formula to convert capacity into process time:

$\text{Process time of each operation}=\frac{\text{Number of minutes per hour}}{\text{Capacity}}$

Formula to calculate overall assembly operation process time:

$\text{Process time of overall assembly}=\frac{\text{Process time at one assembly operation}}{\text{Number of assembly operations}}$

Calculation of process time for each operation:

The process time of each station is calculated by dividing the number of minutes with the production capacity of the station.

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Sanding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Drilling:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2.4}\\ =25\text{ minutes / unit}\end{array}$

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Welding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2}\\ =30\text{ minutes / unit}\end{array}$

Assembly at one operation:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{0.7}\\ =85.71\text{ minutes / unit}\end{array}$

Calculation of overall assembly operation process time:

The overall assembly operation process time is calculated by dividing the process time at one assembly operation by the number of assembly operations.

$\begin{array}{c}\text{Process time of overall assembly}=\frac{\text{85}\text{.71}}{\text{3}}\\ =\text{28}\text{.57}\end{array}$

Identification of the bottleneck time of the system:

The bottleneck time of the system is the operation which has the highest process time. Welding has the highest process time when compared to the other operations (30 > 10, 10, 25, 10, 28.57).  The bottleneck operation is Welding.

Hence, the bottleneck time of the bottleneck operation is 30 minutes per unit.

Summary Introduction

To determine: The throughput time of the time of the overall system.

Introduction:

Throughput time:

The throughput time of a system is the time taken for a product to pass from the raw materials stage to the finished goods stage. The higher the throughput time the more efficient the system will be.

Answer to Problem 15P

The throughput time of the overall system is 140.71 minutes.

Explanation of Solution

Given information:

Formula to convert capacity into process time:

$\text{Process time of each operation}=\frac{\text{Number of minutes per hour}}{\text{Capacity}}$

Formula to calculate throughput time:

$\text{Throughput time}=\text{Maximum }\left(\left(\begin{array}{l}\text{Sum of process times of Sawing,}\\ \text{ Sanding, Welding, Assembly}\end{array}\right)\text{,}\left(\begin{array}{l}\text{Sum of process times of}\\ \text{ Drilling, Welding, Assembly}\end{array}\right)\right)$

Calculation of process time for each operation:

The process time of each station is calculated by dividing the number of minutes with the production capacity of the station.

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Sanding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Drilling:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2.4}\\ =25\text{ minutes / unit}\end{array}$

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Welding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2}\\ =30\text{ minutes / unit}\end{array}$

Assembly at one operation:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{0.7}\\ =85.71\text{ minutes / unit}\end{array}$

Calculation of throughput time:

The throughput time is calculated by identifying the maximum value of the summation of process times of Sanding, Sawing, Welding, assembly and the summation of process times of Drilling, Welding, and Assembly.

$\begin{array}{c}\text{Throughput time}=\text{Maximum}\left(\left(10+10+30+85.71\right),\left(25+30+85.71\right)\right)\\ =\text{Maximum}\left(135.71,140.71\right)\\ =\text{140}\text{.71}\end{array}$

Hence, the throughput time of the overall system is 140.71 minutes.

Summary Introduction

To determine: The monthly capacity of the manufacturing process.

Introduction:

Bottleneck time:

The bottleneck time of the system is the process in the system which takes the most amount of time to complete its activity. The bottleneck time will reduce the overall efficiency of the system.

Monthly capacity:

The monthly capacity is the number of units the firm is able to produce in a month’s time. It will be calculated taking into consideration of the resources and constraints present in the manufacturing process.

Answer to Problem 15P

The monthly capacity of the manufacturing process is 320 units per month.

Explanation of Solution

Given information:

Operating time = 60 minutes / 8 hour / day

Number of days = 20 / month

Formula to convert capacity into process time:

$\text{Process time of each operation}=\frac{\text{Number of minutes per hour}}{\text{Capacity}}$

Formula to calculate overall assembly operation process time:

$\text{Process time of overall assembly}=\frac{\text{Process time at one assembly operation}}{\text{Number of assembly operations}}$

Formula to calculate monthly capacity:

$\text{Monthly capacity}=\frac{\text{Operating time}\times \text{Number of days per month}}{\text{Bottleneck time}}$

Calculation of process time for each operation:

The process time of each station is calculated by dividing the number of minutes with the production capacity of the station.

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Sanding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Drilling:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2.4}\\ =25\text{ minutes / unit}\end{array}$

Sawing:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{6}\\ =10\text{ minutes / unit}\end{array}$

Welding:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{2}\\ =30\text{ minutes / unit}\end{array}$

Assembly at one operation:

$\begin{array}{c}\text{Process time }=\frac{\text{60}}{0.7}\\ =85.71\text{ minutes / unit}\end{array}$

Calculation of overall assembly operation process time:

The overall assembly operation process time is calculated by dividing the process time at one assembly operation by the Number of assembly operations.

$\begin{array}{c}\text{Process time of overall assembly}=\frac{\text{85}\text{.71}}{\text{3}}\\ =\text{28}\text{.57}\end{array}$

Identification of the bottleneck time of the system:

The bottleneck time of the system is the operation which has the highest process time. Welding has the highest process time when compared to the other operations (30 > 10, 10, 25, 10, 28.57). Hence, the bottleneck time of the system is 30 minutes per unit.

Calculation of monthly capacity:

The monthly capacity is calculated by multiplying the operating time per day with the number of days per month and dividing the resultant value with the bottleneck time of the system.

$\begin{array}{c}\text{Monthly capacity}=\frac{\text{Operating time}\times \text{Number of days per month}}{\text{Bottleneck time}}\\ =\frac{\text{8}\times \text{60}\times \text{20}}{\text{30}}\\ =\frac{\text{9,600}}{\text{30}}\\ =\text{320}units\end{array}$

Hence, the monthly capacity of the manufacturing process is 320 units per month.