Chapter 13, Problem 7P

A manager receives a forecast for next year. Demand is projected to be 600 units for me first half of the year and 900 units for the second half. The monthly holding cost is $2 per unit, and it costs an estimated $55 to process an order.

a. Assuming that monthly demand will be level during each of the six-month periods covered by the forecast (e.g., 100 per month for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods. for each of the first six months), determine an order size that will minimize the sum of ordering and carrying costs for each of the six-month periods.

b. Why is it important to be able to assume that demand will be level during each six-month period?

c. If the vendor is willing to offer a discount of $10 per order for ordering in multiples of 50 units (e.g., 50, 100, 150), would you advise the manager to take advantage of the offer in either period? If so, what order size would you recommend?

Summary Introduction

To determine: The order size that will minimize the sum of ordering and carrying cost.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 7P

The order size that will minimize the sum of ordering and carrying cost is 74 units and 91 units.

Explanation of Solution

Given information:

$\begin{array}{c}\text{D}=600\text{units}\text{(first}\text{half)}\\ =900\text{units}\text{(second}\text{half)}\\ \text{S}=\text{\$55}\\ \text{H}=\text{\$}2/\text{unit}\end{array}$

Formula:

${\text{Q}}_{\text{o}}=\sqrt{\frac{\text{2DS}}{\text{H}}}$

Calculation of order size:

• First half:

$\begin{array}{c}{\text{Q}}_{\text{o}}=\sqrt{\frac{\text{2}\times 100\times 55}{2.00}}\\ =74\text{units}\end{array}$

The order size for first six month period is calculated by dividing the product of 2 and 100 and 55 with 2 and taking square root which gives the resultant value as 74 units.

• Second half:

$\begin{array}{c}{\text{Q}}_{\text{o}}=\sqrt{\frac{\text{2}\times 150\times 55}{2.00}}\\ =91\text{units}\end{array}$

The order size for second six month period is calculated by dividing the product of 2 and 150 and 55 with 2 and taking square root which gives the resultant value as 91 units.

Hence, the order size that will minimize the sum of ordering and carrying cost is 74 units and 91 units.

Summary Introduction

To determine: The importance of assuming that demand will be level during each six-month period.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 7P

Stable demand level is required to use the EOQ.

Explanation of Solution

Given information:

$\begin{array}{c}\text{D}=600\text{units}\text{(first}\text{half)}\\ =900\text{units}\text{(second}\text{half)}\\ \text{S}=\text{\$55}\\ \text{H}=\text{\$}2/\text{unit}\end{array}$

Determine the importance of assuming that demand will be level during each six-month period:

Economic order quantity model is essential to determine the amount of order to be placed at the right time and with right quantity. In order to use the economic quantity model, the demand assumed must be constant and must not vary only then the model gives accurate result.

Hence, stable demand level is required to use the EOQ.

Summary Introduction

To determine: The decision on accepting or rejecting the offer and provide recommendations on order size.

Introduction: Inventory is a stock or store of goods. Every company store lots of goods as inventory which will be used during replenishment periods. Management of inventory is so much essential to manage cost and also to reduce cost.

Answer to Problem 7P

It is advised to the manager to take advantage of the offer.

Explanation of Solution

Given information:

$\begin{array}{c}\text{D}=600\text{units}\text{(first}\text{half)}\\ =900\text{units}\text{(second}\text{half)}\\ \text{S}=\text{\$55}\\ \text{H}=\text{\$}2/\text{unit}\end{array}$

Formula:

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

$\text{TC}=\left(\frac{\text{Q}}{\text{2}}\right)\text{H}+\left(\frac{\text{D}}{\text{Q}}\right)\text{S}+\text{PD}$

Determination on decisions to accept or reject the offer:

Calculation of total cost for first six-month period:

• Q=74 units

$\begin{array}{c}\text{TC}=\left(\frac{74}{\text{2}}\right)2.00+\left(\frac{100}{74}\right)55\\ =\$148.32\end{array}$

With discounts of $10, S=$55-10 = $45.

• Q=50

$\begin{array}{c}\text{TC}=\left(\frac{50}{\text{2}}\right)2.00+\left(\frac{100}{50}\right)45\\ =\$140\end{array}$

• Q=100

$\begin{array}{c}\text{TC}=\left(\frac{100}{\text{2}}\right)2.00+\left(\frac{100}{100}\right)45\\ =\$145\end{array}$

• Q=150

$\begin{array}{c}\text{TC}=\left(\frac{150}{\text{2}}\right)2.00+\left(\frac{100}{150}\right)45\\ =\$180\end{array}$

Recommendation:

From the above calculation it is evident that the offer can be accepted which proves to be cost savings at Q=50 units. So, it is advised to the manager to take advantage of the offer.

Calculation of total cost for second six-month period:

• Q=91 units

$\begin{array}{c}\text{TC}=\left(\frac{91}{\text{2}}\right)2.00+\left(\frac{150}{91}\right)55\\ =\$181.66\end{array}$

With discounts of $10, S=$55-10 = $45.

• Q=50

$\begin{array}{c}\text{TC}=\left(\frac{50}{\text{2}}\right)2.00+\left(\frac{150}{50}\right)45\\ =\$185\end{array}$

• Q=100

$\begin{array}{c}\text{TC}=\left(\frac{100}{\text{2}}\right)2.00+\left(\frac{150}{100}\right)45\\ =\$167.50\end{array}$

• Q=150

$\begin{array}{c}\text{TC}=\left(\frac{150}{\text{2}}\right)2.00+\left(\frac{150}{150}\right)45\\ =\$195\end{array}$

Recommendation:

From the above calculation it is evident that the offer can be accepted which proves to be cost savings at Q=100 units. So, it is advised to the manager to take advantage of the offer.

Hence, it is advised to the manager to take advantage of the offer.