Chapter 3, Problem 4PA

a)

Summary Introduction

To draw: A process flow diagram for this process.

Explanation of Solution

Given information:

Process flow diagram:

b)

Summary Introduction

To determine: The capacity at the resource “Apply a lid”.

Explanation of Solution

Given information:

Calculation of capacity:

$\begin{array}{c}\text{Capacity}=\frac{\text{Number of machines×Seconds per hour}}{\text{Seconds per bottle}}\\ \text{=}\frac{\text{1×3,600}}{\text{3}}\\ \text{=1,200 bottles}\end{array}$

The capacity is 1,200 bottles.

c)

Summary Introduction

To determine: The bottleneck in the process.

Explanation of Solution

Given information:

Determination of bottleneck:

The process step with the longest processing time “seconds per bottle” is the bottleneck in the process. Packaging has the highest time of 3 seconds per bottle.

Hence, the bottleneck is Packaging.

d)

Summary Introduction

To determine: The flow rate.

Explanation of Solution

Given information:

Determination of flow rate:

$\begin{array}{c}\text{Flow rate}=\frac{\text{Seconds per hour}}{\text{Bottleneck capacity}}\\ =\frac{3,600}{4}\\ =900\text{ bottles}\end{array}$

The flow rate is 900 bottles.

e)

Summary Introduction

To determine: The utilization of resource “Apply a lid”

Explanation of Solution

Given information:

Calculation of utilization:

$\begin{array}{c}\text{Utilization}=\frac{\text{Flow rate}}{\text{Capacity}}\times 100\\ =\frac{\text{900}}{\frac{\text{Number of machines}\times \text{Seconds per hour}}{\text{Seconds per bottle}}}\times 100\\ =\frac{900}{\frac{1\times 3,600}{3}}\times 100\\ =\frac{900}{1,200}\times 100\\ =75\%\end{array}$

The utilization is 75%.

f)

Summary Introduction

To determine: The utilization of bottling.

Explanation of Solution

Given information:

Calculation of utilization:

$\begin{array}{c}\text{Utilization}=\frac{\text{Flow rate}}{\text{Capacity}}\times 100\\ =\frac{\frac{\text{Number of machines}}{\frac{\text{Seconds per minute}}{\text{Demand per minute}}}}{\text{Seconds per bottle}}\times 100\\ =\frac{\frac{\text{1}}{\frac{\text{60}}{\text{12}}}}{1}\times 100\\ =\frac{\frac{1}{5}}{1}\times 100\\ =20\%\end{array}$

The utilization is 20%.

g)

Summary Introduction

To determine: The cycle time of the process.

Explanation of Solution

Given information:

Calculation of cycle time:

The demand is constrained and has a flow rate of

$\begin{array}{c}\text{Flow rate}=\frac{\text{Number of machines}}{\frac{\text{Seconds per minute}}{\text{Demand per minute}}}\\ =\frac{\text{1}}{\frac{\text{60}}{\text{12}}}\\ =0.20\text{ bottle per second}\end{array}$

$\begin{array}{c}\text{Cycle time}=\frac{1}{\text{Flow rate}}\\ =\frac{\text{1}}{0.2}\\ =5\text{ seconds}\end{array}$

The cycle time is 5 seconds.

h)

Summary Introduction

To determine: The time taken to produce 500 bottles.

Explanation of Solution

Given information:

Calculation of time taken to produce 500 bottles:

$\begin{array}{c}\text{Time taken}=\left(4\times 5\right)+\left[\left(500-1\right)\times 5\right]\\ =20+\left(499\times 5\right)\\ =20+2,495\\ =2,515\text{ seconds}\end{array}$

The time taken to produce 500 bottles is 2,515 seconds.