Chapter 12, Problem 18P

a)

Summary Introduction

To calculate: The economic production quantity (EPQ).

Introduction:

Economic production quantity (EPQ):

The economic production quantity is used to determine the amount a company or a retail outlet should purchase at every order so as to minimize the associated total inventory costs. It is done by balancing the holding cost and the ordering cost.

Answer to Problem 18P

The economic production quantity (EPQ) is 671 units.

Explanation of Solution

Given information:

Annual Demand (D) = 12,500 units

Number of working days (N) = 250 / year

Holding cost (H) = $2 / unit / year

Ordering cost (S) = 30 / order

Daily production (p) = 300 / day

$\begin{array}{c}\text{Daily demand}\left(\text{d}\right)=\frac{\text{Annual demand}}{\text{Number of days}}\\ =\frac{12,500}{250}\\ =50\text{ days}\end{array}$

Formula to calculate EPQ:

$\text{EPQ}=\sqrt{\frac{\text{2}\times \text{D}\times \text{S}}{\text{H}\left[\text{1}-\frac{\text{d}}{\text{p}}\right]}}$

Calculation of EPQ:

$\begin{array}{c}\text{EPQ}=\sqrt{\frac{2\times 12,500\times 30}{2\left[1-\frac{50}{300}\right]}}\\ =\sqrt{\frac{750,000}{2\left[\frac{250}{300}\right]}}\\ =\sqrt{\frac{750,000}{2\times 0.833}}\end{array}$

$\begin{array}{c}=\sqrt{\frac{750,000}{1.666}}\\ =\sqrt{450,180.07}\\ =670.95\\ =671\text{ units}\end{array}$

Hence, the economic production quantity (EPQ) is 671 units.

b)

Summary Introduction

To calculate: The number of production runs per year.

Introduction:

Production runs:

The production run is the development of similar or associated goods by utilizing a particular approach or processes.

Answer to Problem 18P

The number of production runs per yearis 18.63.

Explanation of Solution

Given information:

Annual Demand (D) = 12,500 units

Number of working days (N) = 250 / year

Holding cost (H) = $2 / unit / year

Ordering cost (S) = 30 / order

Daily production (p) = 300 / day

$\begin{array}{c}\text{Daily demand}\left(\text{d}\right)=\frac{\text{Annual demand}}{\text{Number of days}}\\ =\frac{12,500}{250}\\ =50\text{ days}\end{array}$

Formula to calculate number of production runs:

$\text{Number of production runs}=\frac{\text{D}}{\text{EPQ}}$

Calculation of number of production runs:

$\begin{array}{c}\text{Number of production runs}=\frac{12,500}{671}\\ =18.628\\ =18.63\end{array}$

Hence, the number of production runs per year is 18.63.

c)

Summary Introduction

To calculate: The maximum inventory level.

Introduction:

Maximum inventory level:

The maximum inventory level is the level of inventory in a firm which should not be exceeded at any circumstances. It is to ensure that the cost of capital is not increased.

Answer to Problem 18P

The maximum inventory level is 559 units.

Explanation of Solution

Given information:

Annual Demand (D) = 12,500 units

Number of working days (N) = 250 / year

Holding cost (H) = $2 / unit / year

Ordering cost (S) = 30 / order

Daily production (p) = 300 / day

$\begin{array}{c}\text{Daily demand}\left(\text{d}\right)=\frac{\text{Annual demand}}{\text{Number of days}}\\ =\frac{12,500}{250}\\ =50\text{ days}\end{array}$

Formula to calculate maximum inventory level:

$\text{Maximum inventory level}=\text{EPQ}\times \left(1-\frac{\text{d}}{\text{p}}\right)$

Calculation of maximum inventory level:

$\begin{array}{c}\text{Maximum inventory level}=671\times \left(1-\frac{50}{300}\right)\\ =671\times \frac{250}{300}\\ =559.16\\ =559\text{ units}\end{array}$

Hence, the maximum inventory level is 559 units.

d)

Summary Introduction

To determine: The percentage of time the facility will be producing components.

Answer to Problem 18P

The percentage of time the facility will be producing componentsis 16.7%.

Explanation of Solution

Given information:

Annual Demand (D) = 12,500 units

Number of working days (N) = 250 / year

Holding cost (H) = $2 / unit / year

Ordering cost (S) = 30 / order

Daily production (p) = 300 / day

$\begin{array}{c}\text{Daily demand}\left(\text{d}\right)=\frac{\text{Annual demand}}{\text{Number of days}}\\ =\frac{12,500}{250}\\ =50\text{ days}\end{array}$

Formula to calculate days of demand:

$\text{Days of demand}=\frac{\text{N}}{\text{Number of production runs}}$

Formula to calculate days of production:

$\text{Days in production}=\frac{\text{EPQ}}{\text{p}}$

Calculation of days of demand satisfied by each production run:

$\begin{array}{c}\text{Days of demand}=\frac{\text{N}}{\text{Number of production runs}}\\ =\frac{250}{18.63}\\ =13.419\\ =13.42\text{ days}\end{array}$

Calculation of days in production for each order:

$\begin{array}{c}\text{Days in production}=\frac{\text{EPQ}}{\text{p}}\\ =\frac{671}{300}\\ =2.236\\ =2.24\text{ days}\end{array}$

Calculation of percent time of production:

The percentage of the time the facility is producing components is calculated by dividing the days in production by the days of demand.

$\begin{array}{c}\text{Percent time of production}=\frac{\text{Days in production}}{\text{Days of demand}}\times 100\\ =\frac{2.24}{13.42}\times 100\\ =16.69\\ =16.7\%\end{array}$

Hence, the percentage of time the facility will be producing components is 16.7%.

e)

Summary Introduction

To determine: The annual cost of ordering and holding inventory.

Answer to Problem 18P

The annual cost of ordering and holding inventory is $1,117.90

Explanation of Solution

Given information:

Annual Demand (D) = 12,500 units

Number of working days (N) = 250 / year

Holding cost (H) = $2 / unit / year

Ordering cost (S) = 30 / order

Daily production (p) = 300 / day

$\begin{array}{c}\text{Daily demand}\left(\text{d}\right)=\frac{\text{Annual demand}}{\text{Number of days}}\\ =\frac{12,500}{250}\\ =50\text{ days}\end{array}$

Formula to calculate the annual cost of ordering and holding inventory:

$\text{Annual cost}=\left(\text{Number of production runs}\times \text{S}\right)+\left(\frac{\text{Maximum inventory level}}{2}\times \text{H}\right)$

Calculation of annual cost of ordering and holding inventory:

$\begin{array}{c}\text{Annual cost}=\left(18.63\times 30\right)+\left(\frac{559}{2}\times 2\right)\\ =558.9+559\\ =\$1,117.90\end{array}$

Hence, the annual cost of ordering and holding inventory is $1,117.90.