Chapter 12, Problem 28P

a)

Summary Introduction

To explain: The way (1), (2), and (3) changes as the setup cost ‘k’ decreases by 10%.

Inventory and supply chain models:

The functions of inventory and supply chain are one of the most important business decision areas for an organization. The first important aspect of these concepts is to have adequate inventory on hand. The second important aspect is to carry a little amount of inventory as possible.

Explanation of Solution

The economic order quantity (EOQ) is given by the formula:

$\begin{array}{c}Q=\sqrt{\frac{2\times k\times D}{h}}\\ \text{where:}\\ \text{'k' is the setup cost}\text{.}\\ \text{'D' is the demand}\text{.}\\ \text{'h' is the holding cost}\text{.}\end{array}$                                                                    (1)

The EOQ formula is substituted in the expression for annual holding cost and annual ordering cost to get the following result:

$HC+OC=\sqrt{2\times k\times D\times h}$                                                                         (2)

The time between orders is given by:

$\frac{Q}{D}=\sqrt{\frac{2\times k}{D\times h}}$                                                                                              (3)

The values of (1), (2), and (3) are multiplied by $\sqrt{0.9}$. Hence, the values change in such a way when the setup cost ‘k’ decreases by 10%.

b)

Summary Introduction

To explain: The way (1), (2), and (3) changes if the annual demand doubles.

Explanation of Solution

The economic order quantity (EOQ) is given by the formula:

$\begin{array}{c}Q=\sqrt{\frac{2\times k\times D}{h}}\\ \text{where:}\\ \text{'k' is the setup cost}\text{.}\\ \text{'D' is the demand}\text{.}\\ \text{'h' is the holding cost}\text{.}\end{array}$                                                                     (1)

The EOQ formula is substituted in the expression for annual holding cost and annual ordering cost to get the following result:

$HC+OC=\sqrt{2\times k\times D\times h}$                                                                        (2)

The time between orders is given by:

$\frac{Q}{D}=\sqrt{\frac{2\times k}{D\times h}}$                                                                                              (3)

The values of (1), (2), and (3) are multiplied by $\sqrt{2}$. Hence, the values change in such a way when the annual demand doubles.

c)

Summary Introduction

To explain: The way (1), (2), and (3) changes if the cost of capital increases by 10%.

Explanation of Solution

The economic order quantity (EOQ) is given by the formula:

$\begin{array}{c}Q=\sqrt{\frac{2\times k\times D}{h}}\\ \text{where:}\\ \text{'k' is the setup cost}\text{.}\\ \text{'D' is the demand}\text{.}\\ \text{'h' is the holding cost}\text{.}\end{array}$                                                                    (1)

The EOQ formula is substituted in the expression for annual holding cost and annual ordering cost to get the following result:

$HC+OC=\sqrt{2\times k\times D\times h}$                                                                        (2)

The time between orders is given by:

$\frac{Q}{D}=\sqrt{\frac{2\times k}{D\times h}}$                                                                                              (3)

Since $h=ic$ (1) is multiplied by $\sqrt{\frac{1}{1.1}}$.

Equation (2) is multiplied by $\sqrt{1.1}$.

Equation (3) is multiplied by $\sqrt{\frac{1}{1.1}}$.

Hence, the values change in such a way when the cost of capital increases by 10%.

d)

Summary Introduction

To explain: The way (1), (2), and (3) changes as the changes of setup cost decreasing by 10%, doubling of annual demand, the increase in the cost of capital by 10% happen simultaneously.

Explanation of Solution

The economic order quantity (EOQ) is given by the formula:

$\begin{array}{c}Q=\sqrt{\frac{2\times k\times D}{h}}\\ \text{where:}\\ \text{'k' is the setup cost}\text{.}\\ \text{'D' is the demand}\text{.}\\ \text{'h' is the holding cost}\text{.}\end{array}$                                                                     (1)

The EOQ formula is substituted in the expression for annual holding cost and annual ordering cost to get the following result:

$HC+OC=\sqrt{2\times k\times D\times h}$                                                                         (2)

The time between orders is given by:

$\frac{Q}{D}=\sqrt{\frac{2\times k}{D\times h}}$                                                                                              (3)

Equation (1) is multiplied by $\sqrt{2}$.

Equation (2) is multiplied by $\sqrt{1.98}$.

Equation (3) is multiplied by $\frac{1}{\sqrt{2}}$.

Hence, the above changes happen due to the simultaneous changes in the various values.