Chapter 12, Problem 24P

a)

Summary Introduction

To determine: The optimal order quantity.

Introduction: Inventory management is the process of ordering, storing and using inventory of the company such raw material, components and finished goods. It governs the flow of goods from manufacturers to warehouse and to the point of sale. The key function is to maintain record of flow of new or returned products which enters or leaves the company.

Answer to Problem 24P

The optimal order quantity is 16,970.56.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand}=\text{45,000}\text{pieces}\\ \text{Order}\text{cost}=\text{\$200}\text{per}\text{order}\end{array}$

$\begin{array}{c}\text{Price}\text{for}\text{order}\text{less}\text{than}\text{2000}\text{pieces}=\text{\$7}\text{.80/piece}\\ \text{Price}\text{for}\text{order}\text{between2,001}\text{to}\text{5000}\text{pieces}=\text{\$1}\text{.60/piece}\\ \text{Price}\text{for}\text{order}\text{between5,001}\text{to}\text{10,000}\text{pieces}=\text{\$1}\text{.40/piece}\\ \text{Price}\text{for}\text{order}\text{more than}\text{10,001}\text{pieces}=\text{1}\text{.25/piece}\end{array}$

Formula:

$\text{EOQ,Q}=\sqrt{\frac{\text{2DS}}{\text{H}}}$

Where

$\begin{array}{c}\text{D}=\text{Demand}\\ \text{S}=\text{Ordering}\text{cost}\\ \text{H}=\text{Holding}\text{cost}\end{array}$

Calculation of optimal order quantity:

Calculation of EOQ for orders less than 2000 pieces:

$\begin{array}{c}{\text{H}}_{\text{1}}=0.05\times 7.80\\ =0.39\end{array}$

Holding cost is 5% of the purchase price for orders less than 2000 pieces which is 0.05 multiplied by 7.80 which yields 0.39.

$\begin{array}{c}{\text{Q}}_{\text{1}}=\sqrt{\frac{\text{2DS}}{{\text{H}}_1}}\\ =\sqrt{\frac{2\times 45,000\times 200}{0.39}}\\ =6793.66\text{pieces}\end{array}$

EOQ for order less than 2000 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.39 and taking square root which gives 6,793.66 pieces.

Calculation of EOQ for orders between 2,001 to 5,000 pieces:

$\begin{array}{c}{\text{H}}_2=0.05\times 1.60\\ =0.08\end{array}$

Holding cost is 5% of the purchase price for orders between 2001 to 5000 pieces which is 0.05 multiplied by 1.60 which yields 0.08.

$\begin{array}{c}{\text{Q}}_2=\sqrt{\frac{\text{2DS}}{{\text{H}}_2}}\\ =\sqrt{\frac{2\times 45,000\times 200}{0.08}}\\ =15,000\text{pieces}\end{array}$

EOQ for order orders between 2,001 to 5,000 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.08 and taking square root which gives 15,000 pieces.

Calculation of EOQ for orders between 5,001 to 10,000 pieces:

$\begin{array}{c}{\text{H}}_3=0.05\times 1.40\\ =0.07\end{array}$

Holding cost is 5% of the purchase price for orders between 5,001 to 10,000 pieces which is 0.05 multiplied by 1.40 which yields 0.07.

$\begin{array}{c}{\text{Q}}_3=\sqrt{\frac{\text{2DS}}{{\text{H}}_3}}\\ =\sqrt{\frac{2\times 45,000\times 200}{0.07}}\\ =16,035.67\text{pieces}\end{array}$

EOQ for order orders between 5,001 to 10,000 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.07 and taking square root which gives 16,035.67 pieces.

Calculation of EOQ for orders more than 10,001 pieces:

$\begin{array}{c}{\text{H}}_4=0.05\times 1.25\\ =0.0625\end{array}$

Holding cost is 5% of the purchase price for orders more than 10,001 pieces which is 0.05 multiplied by 1.25 which yields 0.0625.

$\begin{array}{c}{\text{Q}}_4=\sqrt{\frac{\text{2DS}}{{\text{H}}_4}}\\ =\sqrt{\frac{2\times 45,000\times 200}{0.0625}}\\ =16,970.56\text{pieces}\end{array}$

EOQ for order orders more than 10,001 pieces is calculated by multiplying 2, 45,000 and 200 and dividing the resultant with 0.0625 and taking square root which gives 16,970.56 pieces.

Based on the above calculations, EOQ for orders more than 10,001 pieces gives optimal order quantity as the EOQ lies within the quantities ordered. Therefore the optimal order quantity is 16,970.56 pieces at $1.25.

Hence, the optimal order quantity is 16,970.56.

b)

Summary Introduction

To determine: The annual holding cost.

Answer to Problem 24P

The annual holding cost is $530.33.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand}=\text{45,000}\text{pieces}\\ \text{Order}\text{cost}=\text{\$200}\text{per}\text{order}\end{array}$

$\begin{array}{c}\text{Price}\text{for}\text{order}\text{less}\text{than}\text{2000}\text{pieces}=\text{\$7}\text{.80/piece}\\ \text{Price}\text{for}\text{order}\text{between2,001}\text{to}\text{5000}\text{pieces}=\text{\$1}\text{.60/piece}\\ \text{Price}\text{for}\text{order}\text{between5,001}\text{to}\text{10,000}\text{pieces}=\text{\$1}\text{.40/piece}\\ \text{Price}\text{for}\text{order}\text{more than}\text{10,001}\text{pieces}=\text{1}\text{.25/piece}\end{array}$

Formula:

$\text{Annual}\text{holdingcost}=\frac{\text{Q}}{\text{2}}\times \text{H}$

Calculation annual holding cost:

$\begin{array}{c}\text{H}=0.05\times 1.25\\ =0.0625\end{array}$

$\begin{array}{c}\text{Annual}\text{holding}\text{cost}=\frac{\text{Q}}{\text{2}}\times \text{H}\\ \text{=}\frac{16,971}{2}\times 0.0625\\ =\$530.33\end{array}$

Annual holding cost is calculated by multiplying half of the economic order quantity which is 16,971 divided by 2 and multiplying with 0.0625 which yields $530.33.

Hence, the annual holding cost is $530.33.

c)

Summary Introduction

To determine: The annual setup cost.

Answer to Problem 24P

The annual setup cost is $530.33.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand}=\text{45,000}\text{pieces}\\ \text{Order}\text{cost}=\text{\$200}\text{per}\text{order}\end{array}$

$\begin{array}{c}\text{Price}\text{for}\text{order}\text{less}\text{than}\text{2000}\text{pieces}=\text{\$7}\text{.80/piece}\\ \text{Price}\text{for}\text{order}\text{between2,001}\text{to}\text{5000}\text{pieces}=\text{\$1}\text{.60/piece}\\ \text{Price}\text{for}\text{order}\text{between5,001}\text{to}\text{10,000}\text{pieces}=\text{\$1}\text{.40/piece}\\ \text{Price}\text{for}\text{order}\text{more than}\text{10,001}\text{pieces}=\text{1}\text{.25/piece}\end{array}$

Formula:

$\text{Annual}\text{setup}\text{cost}=\frac{\text{D}}{\text{Q}}\text{×S}$

Calculation annual ordering cost:

$\begin{array}{c}\text{=}\frac{45,000}{16,971}\times 200\\ =\$530.33\end{array}$

Annual ordering cost is calculated by dividing 45,000 with 16,971 and multiplying the resultant with 200 which yields $530.33.

Hence, the annual ordering cost is $530.33.

d)

Summary Introduction

To determine: The annual cost of silverware with optimal order quantity.

Answer to Problem 24P

The annual cost of silverware with optimal order quantity is $56,250.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand}=\text{45,000}\text{pieces}\\ \text{Order}\text{cost}=\text{\$200}\text{per}\text{order}\end{array}$

$\begin{array}{c}\text{Price}\text{for}\text{order}\text{less}\text{than}\text{2000}\text{pieces}=\text{\$7}\text{.80/piece}\\ \text{Price}\text{for}\text{order}\text{between2,001}\text{to}\text{5000}\text{pieces}=\text{\$1}\text{.60/piece}\\ \text{Price}\text{for}\text{order}\text{between5,001}\text{to}\text{10,000}\text{pieces}=\text{\$1}\text{.40/piece}\\ \text{Price}\text{for}\text{order}\text{more than}\text{10,001}\text{pieces}=\text{1}\text{.25/piece}\end{array}$

Formula:

$\text{Unit}\text{cost}=\text{P}\times \text{D}$

Calculation of annual cost of silverware with optimal order quantity:

$\begin{array}{l}=\text{\$1}\text{.25}\times \text{45,000}\\ =\text{\$56,250}\end{array}$

Annual cost of silverware with optimal order quantity is calculated by multiplying 1.25 with 45,000 which gives $56,250.

Hence, the annual cost of silverware with optimal order quantity is $56,250.

e)

Summary Introduction

To determine: The total annual cost including ordering, holding and purchasing the silverware.

Answer to Problem 24P

The total annual cost including ordering, holding and purchasing the silverware is $57,310.66.

Explanation of Solution

Given information:

$\begin{array}{c}\text{Annual}\text{demand}=\text{45,000}\text{pieces}\\ \text{Order}\text{cost}=\text{\$200}\text{per}\text{order}\end{array}$

$\begin{array}{c}\text{Price}\text{for}\text{order}\text{less}\text{than}\text{2000}\text{pieces}=\text{\$7}\text{.80/piece}\\ \text{Price}\text{for}\text{order}\text{between2,001}\text{to}\text{5000}\text{pieces}=\text{\$1}\text{.60/piece}\\ \text{Price}\text{for}\text{order}\text{between5,001}\text{to}\text{10,000}\text{pieces}=\text{\$1}\text{.40/piece}\\ \text{Price}\text{for}\text{order}\text{more than}\text{10,001}\text{pieces}=\text{1}\text{.25/piece}\end{array}$

Calculation of total annual cost:

$\begin{array}{c}\text{Total}\text{cost}=\text{530}\text{.33}+\text{530}\text{.33}+\text{56,250}\text{.00}\\ =\$\text{57,310}\text{.00}\end{array}$

Total annual cost is calculated by adding holding cost, ordering cost and unit cost which is 530.33, 530.33 and 56,250 is summed up to give 57,310.66.

Hence, the total annual cost including ordering, holding and purchasing the silverware is $57,310.66.