Chapter 12, Problem 15P

Joe Henry’s machine shop uses 2,500 brackets during the course of a year. These brackets are purchased from a supplier 90 miles away. The following information a known about the brackets:

a) Given the above information, what would be the economic order quantity (EOQ)?

b) Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost?

c) Given the EOQ, how many orders would be made each year? What would be the annual order cost?

d) Given the EOQ, what is the total annual cost of managing the inventory?

e) What is the time between orders?

f) What is the reorder point (ROP)?

Summary Introduction

To calculate: The economic order quantity (EOQ).

Introduction:

Economic order quantity (EOQ):

EOQ is the quantity of units a company must add to its inventory so as to minimize the total inventory costs. It will determine the ideal order quantity which will decrease the inventory management costs.

Answer to Problem 15P

The economic order quantity (EOQ) is 250 brackets.

Explanation of Solution

Given information:

Annual demand= 2,500 units / year

Order cost= $18.75 / order

Holding cost = $1.50 / bracket / year

Number of days = 250 / year

Lead time = 2 days

Formula to calculate EOQ:

$\text{EOQ}=\sqrt{\frac{2\times \text{Order}\text{cost}\times \text{Annual}\text{demand}}{\text{Holding}\text{cost}}}$

Calculation of EOQ:

$\begin{array}{c}\text{EOQ}=\sqrt{\frac{2\times 2,500\times 18.75}{1.50}}\\ =\sqrt{\frac{93,750}{1.50}}\\ =\sqrt{62,500}\\ =250\text{ brackets}\end{array}$

Hence, the economic order quantity (EOQ) is 250 brackets.

Summary Introduction

To calculate: The average inventory and annual holding cost at EOQ.

Answer to Problem 15P

The average inventory is 125 units and the annual holding cost is $187.50.

Explanation of Solution

Given information:

Annual demand= 2,500 units / year

Order cost= $18.75 / order

Holding cost = $1.50 / bracket / year

Number of days = 250 / year

Lead time = 2 days

Formula to calculate average inventory:

$\text{Average inventory}=\frac{\text{EOQ}}{\text{2}}$

Formula to calculate annual holding cost:

$\text{Annual holding cost}=\frac{\text{EOQ}}{\text{2}}\text{×Holding cost}$

Calculation of average inventory:

$\begin{array}{c}\text{Average inventory}=\frac{250}{2}\\ =125\text{ units}\end{array}$

Hence, the average inventory is 125 units.

Calculation of annual holding cost:

$\begin{array}{c}\text{Annual holding cost}=\frac{250}{2}\times 1.50\\ =125\times 1.50\\ =\$187.5\end{array}$

Hence, the annual holding cost is $187.50.

Summary Introduction

To determine: The optimal number of orders per year and annual ordering cost.

Answer to Problem 15P

The optimal number of orders per year is 10 orders and annual ordering cost is $187.50.

Explanation of Solution

Given information:

Annual demand= 2,500 units / year

Order cost= $18.75 / order

Holding cost = $1.50 / bracket / year

Number of days = 250 / year

Lead time = 2 days

Formula to calculate optimal number of orders:

$\text{Optimal number of orders}=\frac{\text{Annual demand}}{\text{EOQ}}$

Formula to calculate annual order cost:

$\text{Annual ordering cost}=\frac{\text{Annual demand}}{\text{EOQ}}\times \text{Order cost}$

Calculation of optimal number of orders:

$\begin{array}{c}\text{Optimal number of orders}=\frac{2,500}{250}\\ =10\text{ orders}\end{array}$

Hence, the optimal number of orders per year is 10 orders.

Calculation of annual ordering cost:

$\begin{array}{c}\text{Annual ordering cost}=\frac{2,500}{250}\times 18.75\\ =10\times 18.75\\ =\$187.50\end{array}$

Hence, the annual ordering cost is $187.50 and annual ordering cost is $187.50.

Summary Introduction

To determine: The total annual cost of managing the inventory.

Introduction:

Total cost of inventory:

The total cost involved in ordering and carrying an inventory and the costs associated with the management and handling of associated activities.

Answer to Problem 15P

The total annual cost of managing the inventory is $375 per year.

Explanation of Solution

Formula to calculate the total cost of inventory:

$\text{Total cost}=\left(\frac{\text{EOQ}}{\text{2}}\text{×Holding cost}\right)+\left(\frac{\text{Annual demand}}{\text{EOQ}}\times \text{Order cost}\right)$

Calculation of total cost:

$\begin{array}{c}\text{Total cost}=\left(\frac{250}{2}\times 1.50\right)+\left(\frac{2,500}{250}\times 18.75\right)\\ =\left(125\times 1.50\right)+\left(10\times 18.75\right)\\ =187.50+187.50\\ =\$375/\text{year}\end{array}$

Hence, the total annual cost of managing the inventory is $375 per year

Summary Introduction

To determine: The time between any two orders.

Introduction:

Optimal number of orders:

The optimal number of orders is the number of orders a firm has to make such that the overall inventory cost is minimized.

Answer to Problem 15P

The time between any two orders is 25days.

Explanation of Solution

Given information:

Annual demand= 2,500 units / year

Order cost= $18.75 / order

Holding cost = $1.50 / bracket / year

Number of days = 250 / year

Lead time = 2 days

Formula to calculate time between any two orders:

$\text{Time between orders}=\frac{\text{Number of days}}{\frac{\text{Annual demand}}{\text{EOQ}}}$

Calculation of optimal number of orders:

$\begin{array}{c}\text{Time between orders}=\frac{\text{250}}{\frac{2,500}{250}}\\ =\frac{250}{10}\\ =25\text{ days}\end{array}$

Hence, the time between any two orders is 25 days.

Summary Introduction

To calculate: The reorder point.

Introduction:

Reorder point (ROP):

The reorder point is the level of the firm’s inventory which triggers the firm to act and replenish the stock of the particular item. It will be the minimum quantity of the item; the firm must hold in its stock.

Answer to Problem 15P

The reorder point is 20 units.

Explanation of Solution

Given information:

Annual demand= 2,500 units / year

Order cost= $18.75 / order

Holding cost = $1.50 / bracket / year

Number of days = 250 / year

Lead time = 2 days

Formula to calculate reorder point (ROP):

$\text{ROP}=\text{Daily demand}\times \text{Lead time}$

Calculation of reorder point (ROP):

$\begin{array}{c}\text{ROP}=\text{Daily demand}\times \text{Lead time}\\ \text{=}\frac{\text{Annual}\text{demand}}{\text{Number}\text{of}\text{days}}\times \text{Lead time}\\ \text{=}\frac{2,500}{250}\times 2\\ =20\text{units}\end{array}$

Hence, the reorder point is 20 units.