Chapter 20, Problem 34OQ

a)

Summary Introduction

To determine: The optimal order quantity of cotton.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine the optimal order quantity of cotton:

Setup cost (S) is given as $100.

$\begin{array}{c}\text{Total demand}=3\text{ colors}\times \text{12 months}\times \text{3,000 units}\times \text{0}\text{.5 pound}\\ =54,000\end{array}$

$\begin{array}{c}\text{Total purchasing cost}=\$2.5+\$0.20\\ =\$2.70\end{array}$

$\begin{array}{c}\text{Holding cost}=2.70\times 20\%\\ =\$0.54\end{array}$

$\begin{array}{c}\text{Q}=\sqrt{\frac{\left(2\right)\left(54,000\right)\left(100\right)}{0.54}}\\ =4,472\text{ pounds}\end{array}$

Hence, the optimal order quantity of cotton is 4,472 pounds.

b)

Summary Introduction

To determine: How frequently the firm should order.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine how frequently the firm should order:

$\begin{array}{c}\text{Number of orders per year}=\frac{\text{Total demand}}{\text{EOQ}}\\ =\frac{54,000}{4,472}\\ =12.08\end{array}$

Hence, the firm would order 12.08 times a year and 0.99 times (12÷12.08) a month.

c)

Summary Introduction

To determine: The time the firm should place the order when they need the order on April 1.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine the time the firm should place the order when they need the order on April 1:

It is given that the lead time is 2 weeks. Hence, the firm should order the cotton two weeks before in order to receive it on 1^st April. It is about March 15.

d)

Summary Introduction

To determine: The number of orders to be placed during the next year.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine the number of orders to be placed during the next year:

$\begin{array}{c}\text{Number of orders per year}=\frac{\text{Total demand}}{\text{EOQ}}\\ =\frac{54,000}{4,472}\\ =12.08\end{array}$

Hence, the number of orders to be placed during the next year is 12.08.

e)

Summary Introduction

To determine: The resulting annual holding cost.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine the annual holding cost:

$\begin{array}{c}\text{Annual holding cost}=H\times \frac{Q}{2}\\ =0.54\times \frac{4,472}{2}\\ =\$1,207\text{per year}\end{array}$

Hence, the annual holding cost is $1,207.

f)

Summary Introduction

To determine: The resulting annual ordering cost.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine the annual ordering cost:

$\begin{array}{c}\text{Annual ordering cost}=\text{Number of orders}\times \text{Ordering cost}\\ =12.08\times 100\\ =\$1,208\end{array}$

Hence, the annual ordering cost is $1,208.

g)

Summary Introduction

To determine: The way the change in annual interest cost would influence the optimal batch size, average inventory, and an annual number of orders.

Explanation of Solution

Given information:

The monthly demand of each color (red, blue, and white) T-shirts is 3,000 units. 0.5 pounds of cotton is required for each shirt and the purchasing price is given as $2.50. transportation cost by sea is $0.20, the lead time is 2 weeks, ordering cost is $100, and the annual interest rate is 20 percent.

Determine the way the change in annual interest cost would influence the optimal batch size, average inventory, and an annual number of orders:

If the annual interest cost reduced to 5 percent, the holding cost would be lower. Hence, the batch size and average inventory would be larger and the number of orders would be smaller.