Chapter 16, Problem 12OQ

a.

Summary Introduction

To calculate: The total cost of ownership analysis and select the supplier according to the calculation.

Explanation of Solution

Total cost of ownership analysis and the selection of selection of supplier.

Annual purchase cost can be calculated as follows:

$\begin{array}{c}\text{Annual purchase cost}=\text{Demand }\times \text{Unit price}\\ =12,000\times \$510\\ =\$6,120,000\end{array}$

Tooling cost is $22,000 as given in the question.

Ordering Cost can be calculated as follows:

$\begin{array}{c}\text{Order per year}=\frac{\text{Demand}}{\text{Lot size}}\\ =\frac{12,000}{1,000}\\ =12\text{ orders}\end{array}$

$\begin{array}{c}\text{Order processing cost}=\text{Number of order}\times \text{order processing cost}\\ =12\times 125\\ =\$1,500\end{array}$

The inventory carrying cost can be calculated as follows:

$\text{Inventory carrying cost}=\frac{\text{Lot size}}{2}\times \text{Carrying cost}\times \text{Unit Price}$

$\begin{array}{c}\text{Inventory carrying cost}\left(\text{For A}\right)=\frac{1,000}{2}\times 0.20\times \$510\\ =\$51,000\end{array}$

$\begin{array}{c}\text{Inventory carrying cost}\left(\text{For B}\right)=\frac{1,000}{2}\times 0.20\times \$505\\ =\$50,500\end{array}$

The transportation cost can be calculated as follows:

Weight of annual requirement as per 1,000 units is 22,000 pounds

Now, since 1pound is 0.0005 tons, so 22,000 pounds will have 11 tons.

 Now, for an order quantity of less than the truckload is $1.20 per ton-mile.

Therefore,

$\begin{array}{c}\text{Annual transportation cost for A}=11\text{ tons}\times 125\text{ miles}\times \$1.20\times 12*\\ =\$19,800\end{array}$

$\begin{array}{c}\text{Annual transportation cost for B}=11\text{ tons}\times 100\text{ miles}\times \$1.20\times 12\\ =\$15,840\end{array}$

Note*: 12 is the number of orders per year when 1,000units are ordered in each lot size.

The total cost can be calculated as follows:

Supplier	1	2
Unit price($)	510	505
Annual Purchase cost($)	$6,120,000	$6,060,000
One time tooling cost($)	$22,000	$20,000
Orders Per Year	12	12
Order processing cost ($)	$1,500	$1,500
Inventory Carrying cost ($)	$51,000	$50,500
Distance (Miles)	125	100
Weight per load	22,000	22,000
Transportation (Less than truckload) $1.20 per 2,000 lbs. per mile	$19,800	$15,840
Total Cost	$6,214,300	$6,147,840

Table (1)

So, from the above calculations, supplier 2 should be selected because the total cost of ownership for supplier 2 is $66,460 less than that of supplier 1.

b.

Summary Introduction

To analyze: The situation where truckload quantities are ordered and then select the supplier.

Explanation of Solution

Perform the total cost of ownership analysis using the truckload quantities as follows:

$\begin{array}{c}\text{Required lot size for trucks}=\frac{\text{40,000}}{22}\\ =1,818\text{ approx}\text{.}\end{array}$

 Since the order quantity is under 1,499 units, therefore, the unit price will be calculated as follows:

Number of orders in a year can be calculated as follows:

$\begin{array}{c}\text{Orders per year}=\frac{\text{Demand}}{\text{Lot size}}\\ =\frac{12,000}{1,818}\\ \cong 6.6\text{ orders}\end{array}$

The inventory carrying cost can be calculated as follows:

$\text{Inventory carrying cost}=\frac{\text{Lot size}}{2}\times \text{Carrying cost}\times \text{Unit Price}$

$\begin{array}{c}\text{Inventory carrying cost}\left(\text{For A}\right)=\frac{1,818}{2}\times 0.20\times \$500\\ =\$90,900\end{array}$

$\begin{array}{c}\text{Inventory carrying cost}\left(\text{For B}\right)=\frac{1,818}{2}\times 0.20\times \$505\\ =\$91,809\end{array}$

The transportation cost can be calculated as follows:

Weight of annual requirement as per 1,818 units is 39,996 pounds (assumed as 40,000)

Now, since 1pound is 0.0005 tons, so 40,000 pounds will have 20 tons.

 Now, for an order quantity of the truckload is $0.80 per ton-mile.

Therefore,

$\begin{array}{c}\text{Annual transportation cost for A}=20\text{ tons}\times 125\text{ miles}\times \$0.80\times 6.6\\ =\$13,200\end{array}$

$\begin{array}{c}\text{Annual transportation cost for B}=20\text{ tons}\times 100\text{ miles}\times \$0.80\times 6.6\\ =\$10,560\end{array}$

The total cost can be calculated as follows:

Supplier	1	2
Unit price($)	500	505
Annual Purchase cost($)	$6,000,000	$6,060,000
One time tooling cost($)	$22,000	$20,000
Orders Per Year	6.6	6.6
Order processing cost ($125 for each order)	$825	$825
Inventory Carrying cost ($)	$90,900	$91,809
Distance (Miles)	125	100
Weight per load(in pounds)	40,000	40,000
Transportation (truckload) $0.80 per 2,000 lbs. per mile	$13,200.00	$10,560.00
Total Cost	$6,126,925	$6,183,194

Table (2)

Thus, from the above calculations, it can be observed that the cost of ordering in truckload quantity is $20,915$\left(\$6,147,840-\$6,126,925\right)$ less than the cost of ordering in units.

In this case, the total cost of ownership for supplier 1 is $56,269 less than that of supplier 2. So, the supplier 1 should be selected. Hence, the supplier selection changes after ordering truckload quantities.