Chapter 11, Problem 9PA

(a)

Summary Introduction

Interpretation:

Economic order quantity (EOQ) and total cost

Concept Introduction:

Economic order quantity refers to the number of unit that an organization added to its inventory in order to minimize inventory cost such as order cost, shortage cost and the holding cost.

Explanation of Solution

Given data, Annual demand =1200

Order cost=$40

Unit cost= $5

Carrying charge rate = 18% = .18

The economic order quantity is calculated by the following formula.

  $\begin{array}{l}\text{Economic order quantity = }\sqrt{\frac{\text{2DS}}{\text{H}}}\\ =\sqrt{\frac{\text{2}\times \text{1200}\times 40}{5\times .18}}\\ =\sqrt{\frac{96,000}{.9}}\\ =\sqrt{106,666.67}\\ =\text{ 326}\text{.6 = 327}\end{array}$

The total order cost is calculated by the following formula.

  $\begin{array}{l}\text{Total cost = Purchase cost+Ordering cost+Holding cost}\\ \text{TC=DC+}\left(\frac{\text{D}}{\text{Q}}\right)\text{S+}\left(\frac{\text{Q}}{\text{2}}\right)\text{H}\\ \end{array}$

Purchase cost

  $\begin{array}{l}=\text{ D}\times \text{C}\\ \text{= 1200}\times \text{5}\\ \text{= 6000}\end{array}$

Thus, the total cost is

  $\begin{array}{l}\text{=DC+}\left(\frac{\text{D}}{\text{Q}}\right)\text{S+}\left(\frac{\text{Q}}{\text{2}}\right)\text{H}\\ \text{= 6000+}\left(\frac{1200}{327}\right)\times 40+\left(\frac{327}{\text{2}}\right)\times .9\\ =\text{6000+}\left(\text{3}\text{.67}\right)\times 40+\left(163.5\right)\times .9\\ =\text{ 6000+ 146}\text{.8+147}\text{.15}\\ \text{= 6293}\text{.95}\end{array}$

Thus, the total cost is 6294.95

(b)

Summary Introduction

Interpretation:

Economic order quantity (EOQ) when disposal cost is incorporated into the model.

Concept Introduction:

Economic order quantity refers to the number of the unit that an organization added to its inventory to minimize inventory costs such as order cost, shortage cost, and the holding cost.

Explanation of Solution

The economic order quantity is calculated by the following formula.

  $\begin{array}{l}\text{Economic order quantity = }\sqrt{\frac{\text{2DS}}{\text{H}}}\\ =\sqrt{\frac{\text{2}\times \text{1200}\times 40}{(5\times .18)+(.75\times .08)}}\\ =\sqrt{\frac{96,000}{.9+0.06}}\\ =\sqrt{\frac{96,000}{0.96}}\\ =\sqrt{100000}\\ =\text{ 316}\text{.2 }\end{array}$

The total order cost is calculated by the following formula.

  $\begin{array}{l}\text{Total cost = Purchase cost+Ordering cost+Holding cost}\\ \text{TC=DC+}\left(\frac{\text{D}}{\text{Q}}\right)\text{S+}\left(\frac{\text{Q}}{\text{2}}\right)\text{H}\\ \end{array}$

Purchase cost

  $\begin{array}{l}=\text{ D}\times \text{C}\\ \text{= 1200}\times \text{5}\\ \text{= 6000}\end{array}$

Thus, the total cost is

  $\begin{array}{l}\text{=DC+}\left(\frac{\text{D}}{\text{Q}}\right)\text{S+}\left(\frac{\text{Q}}{\text{2}}\right)\text{H}\\ \text{= 6000+}\left(\frac{1200}{316}\right)\times 40+\left(\frac{316}{\text{2}}\right)\times .96\\ =\text{6000+}\left(\text{3}\text{.79}\right)\times 40+\left(158\right)\times .96\\ =\text{ 6000+ 151}\text{.6+164}\text{.58}\\ \text{= 6316}\text{.18}\end{array}$

Thus, the total cost is 6294.95

(c)

Summary Introduction

Interpretation:

The outcome of the above calculation on the sustainability practice.

Concept Introduction:

Economic order quantity refers to the number of the unit that an organization added to its inventory to minimize inventory costs such as order cost, shortage cost, and the holding cost.

Explanation of Solution

From the part (a) and (b) it can be concluded that the total cost is a little higher. Thus, by adjusting the economic order quantity, an organization can save the additional cost while protecting the environment.