Chapter 7, Problem 7PA

a)

Summary Introduction

To determine: The process capacity of dolls per hour with a batch size of 500 dolls.

Explanation of Solution

Given information:

Capacity of Molding:

$\begin{array}{c}\text{Capacity}=\frac{\text{Batch size}}{\text{Setup time}+\left(\text{Batch size}\times \text{Time per unit}\right)}\times 60\text{ minutes}\\ =\frac{500}{15+\left(500\times \text{0}\text{.25}\right)}\times 60\text{ minutes}\\ =\frac{500}{140}\times 60\text{ minutes}\\ \text{=3}\text{.571}\times 60\text{ minutes}\\ =214\text{ units per hour}\end{array}$

Capacity of painting:

$\begin{array}{c}\text{Capacity}=\frac{\text{Batch size}}{\text{Setup time}+\left(\text{Batch size}\times \text{Time per unit}\right)}\times 60\text{ minutes}\\ =\frac{500}{30+\left(500\times \text{0}\text{.15}\right)}\times 60\text{ minutes}\\ =\frac{500}{105}\times 60\text{ minutes}\\ =4.76\times 60\text{ minutes}\\ =285\text{ units per hour}\end{array}$

Capacity of dressing:

$\begin{array}{c}\text{Capacity}=\frac{\text{Batch size}}{\text{Setup time}+\left(\text{Batch size}\times \text{Time per unit}\right)}\times 60\text{ minutes}\\ =\frac{500}{0+\left(500\times \text{0}\text{.3}\right)}\times 60\text{ minutes}\\ =\frac{500}{150}\times 60\text{ minutes}\\ =3.333\times 60\text{ minutes}\\ =200\text{ units per hour}\end{array}$

The capacity of dressing is the lowest of all. Hence, it will be the capacity of the process.

The capacity of the process is 200 units per hour.

b)

Summary Introduction

To determine: The utilization of depositing for 800 dolls.

Explanation of Solution

Given information:

Capacity of Molding:

$\begin{array}{c}\text{Capacity}=\frac{\text{Batch size}}{\text{Setup time}+\left(\text{Batch size}\times \text{Time per unit}\right)}\times 60\text{ minutes}\\ =\frac{800}{15+\left(800\times \text{0}\text{.25}\right)}\times 60\text{ minutes}\\ =\frac{800}{215}\times 60\text{ minutes}\\ \text{=3}\text{.72}\times 60\text{ minutes}\\ =223\text{ units per hour}\end{array}$

Capacity of painting:

$\begin{array}{c}\text{Capacity}=\frac{\text{Batch size}}{\text{Setup time}+\left(\text{Batch size}\times \text{Time per unit}\right)}\times 60\text{ minutes}\\ =\frac{800}{30+\left(800\times \text{0}\text{.15}\right)}\times 60\text{ minutes}\\ =\frac{800}{150}\times 60\text{ minutes}\\ =5.33\times 60\text{ minutes}\\ =320\text{ units per hour}\end{array}$

Capacity of dressing:

$\begin{array}{c}\text{Capacity}=\frac{\text{Batch size}}{\text{Setup time}+\left(\text{Batch size}\times \text{Time per unit}\right)}\times 60\text{ minutes}\\ =\frac{800}{0+\left(800\times \text{0}\text{.3}\right)}\times 60\text{ minutes}\\ =\frac{800}{240}\times 60\text{ minutes}\\ =3.333\times 60\text{ minutes}\\ =200\text{ units per hour}\end{array}$

Calculation of utilization of molding:

The flow rate is the minimum demand and process capacity. The capacity of the process is 200 units per hour. The demand is 4,000 dolls in 40 work hours which gives 100 dolls per hour. Therefore, the number of dolls per minute will be:

$\begin{array}{c}\text{Dolls per minute}=\frac{100}{60}\\ =1.67\text{ dolls per minute}\end{array}$

The flow rate is 1.67 dolls per minute.

Calculation of utilization:

$\begin{array}{c}\text{Utilization}=\text{Flow rate}\times \text{Processing time}\\ =1.67\times 0.25\\ =0.4175\end{array}$

The utilization of molding is 41.75%.

c)

Summary Introduction

To determine: The determine the batch size that would minimize the inventory without decreasing the flow rate.

Explanation of Solution

Given information:

Calculation of batch size for molding:

$\begin{array}{c}\text{Batch size}=\frac{\text{Capacity}\times \text{Setup time}}{\text{1}-\left(\text{Capacity}\times \text{Processing time}\right)}\\ =\frac{3.333\times \text{15}}{\text{1}-\left(3.333\times 0.25\right)}\\ =\frac{49.995}{\text{1}-0.83325}\\ =\frac{49.995}{0.16675}\\ =300\end{array}$

Calculation of batch size for painting:

$\begin{array}{c}\text{Batch size}=\frac{\text{Capacity}\times \text{Setup time}}{\text{1}-\left(\text{Capacity}\times \text{Processing time}\right)}\\ =\frac{3.333\times 30}{\text{1}-\left(3.333\times 0.15\right)}\\ =\frac{99.99}{\text{1}-0.49995}\\ =\frac{99.99}{0.50005}\\ =200\end{array}$

The batch size is 300 units.

d)

Summary Introduction

To determine: The determine the batch size that would minimize the inventory without decreasing the flow rate.

Explanation of Solution

Given information:

Calculation of batch size for molding:

$\begin{array}{c}\text{Batch size}=\frac{\text{Flow rate}\times \text{Setup time}}{\text{1}-\left(\text{Flow rate}\times \text{Processing time}\right)}\\ =\frac{1.67\times \text{15}}{\text{1}-\left(1.67\times 0.25\right)}\\ =\frac{25.05}{\text{1}-0.4175}\\ =\frac{25.05}{0.5825}\\ =43\end{array}$

Calculation of batch size for painting:

$\begin{array}{c}\text{Batch size}=\frac{\text{Flow rate}\times \text{Setup time}}{\text{1}-\left(\text{Flow rate}\times \text{Processing time}\right)}\\ =\frac{1.67\times 30}{\text{1}-\left(1.67\times 0.15\right)}\\ =\frac{50.1}{\text{1}-0.2505}\\ =\frac{50.1}{0.7495}\\ =67\end{array}$

The batch size is 67 units.