Chapter 15, Problem 3P

A manager must make a decision on shipping. There are two shippers, A and B. Both offer a two-day rate: A for $500 and B for $525. In addition, A offers a three-day rate of $460 and a nine-day rate of $400, and B offers a four-day rate of $450 and a seven-day rate of $410. Annual holding costs are 35 percent of unit price. Three hundred boxes are to be shipped, and each box has a price of $ 140. Which shipping alternative would you recommend? Explain.

Summary Introduction

To decide: Which shipping alternative is suitable.

Introduction: Supply chain defined as a sequence of associations, their offices, capacities, and actions that are engaged with manufacturing and conveying a product or administration. The chain starts with essential providers of raw materials and stretches out the distance to the last client.

The supply chain fragment required with getting the completed item from the producer to the purchaser is known as distribution channel. A supply chain is a sequence starts with essential providers or raw materials and stretches out the distance to an item or administration. No business association can exist without the two operations and supply chain.

Answer to Problem 3P

It is recommended that the shipping A and two-day shipping alternatives should be selected.  

Explanation of Solution

Given:

It is given that there are two shippers A and B both offering two-day shipping alternative with A costing $500 and B costing $525. Shipper A offers three-day shipping alternative for $460 and nine-day shipping alternative for $450. Shipper B offers four-day shipping alternative for $450 and seven-date shipping for $410. Annual holding costs are 35% of unit price and each box is priced at $140 per unit. The total units shipped are 300 units.

Calculate the holding cost per year:

It is calculated by multiplying the percentage of annual holding costs with unit price.

$\begin{array}{c}\mathrm{Holding}\mathrm{Cost}\mathrm{per}\mathrm{year}=\left[\mathrm{Unit}\mathrm{Price}\times \mathrm{Annual}\mathrm{Holding}\mathrm{Costs}\right]\\ =\left[\$140\times 30\%\right]\\ =\$49\end{array}$

Calculate the total cost of shipper A with two-days shipping alternative:

It is calculated by multiplying total units with holding cost per year and days of shipping and the result is divided with 365 days and the whole result is added to the shipping cost.

$\begin{array}{c}\mathrm{Total}{\text{Cost}}_{\mathrm{Shipper}\text{A}\mathrm{with}\mathrm{two}-\mathrm{days}}=\left[\mathrm{Shipping}{\text{Cost}}_{\mathrm{Shipper}\text{A}}+\left(\frac{\begin{array}{l}\mathrm{Holding}\mathrm{Cost}\times \mathrm{Total}\mathrm{Units}\times \\ \mathrm{Shipping}\mathrm{Days}\end{array}}{365}\right)\right]\\ =\left[\$500+\left(\frac{\$49\times 300\times 2}{365}\right)\right]\\ =\left[\$500+\left(\frac{\$29,400}{365}\right)\right]\\ =\left[\$500+\$80.5479\right]\\ =\$580.5479\mathrm{or}\$580.55\end{array}$

Calculate the total cost of shipper A with three-days shipping alternative:

It is calculated by multiplying total units with holding cost per year and days of shipping and the result is divided with 365 days and the whole result is added to the shipping cost.

$\begin{array}{c}\mathrm{Total}{\text{Cost}}_{\mathrm{Shipper}\text{A}\mathrm{with}\mathrm{three}-\mathrm{days}}=\left[\mathrm{Shipping}{\text{Cost}}_{\mathrm{Shipper}\text{A}}+\left(\frac{\begin{array}{l}\mathrm{Holding}\mathrm{Cost}\times \mathrm{Total}\mathrm{Units}\times \\ \mathrm{Shipping}\mathrm{Days}\end{array}}{365}\right)\right]\\ =\left[\$460+\left(\frac{\$49\times 300\times 3}{365}\right)\right]\\ =\left[\$460+\left(\frac{\$44,100}{365}\right)\right]\\ =\left[\$460+\$120.8219\right]\\ =\$580.8219\mathrm{or}\$580.82\end{array}$

Calculate the total cost of shipper A with nine-days shipping alternative:

It is calculated by multiplying total units with holding cost per year and days of shipping and the result is divided with 365 days and the whole result is added to the shipping cost.

$\begin{array}{c}\mathrm{Total}{\text{Cost}}_{\mathrm{Shipper}\text{A}\mathrm{with}\mathrm{nine}-\mathrm{days}}=\left[\mathrm{Shipping}{\text{Cost}}_{\mathrm{Shipper}\text{A}}+\left(\frac{\begin{array}{l}\mathrm{Holding}\mathrm{Cost}\times \mathrm{Total}\mathrm{Units}\times \\ \mathrm{Shipping}\mathrm{Days}\end{array}}{365}\right)\right]\\ =\left[\$400+\left(\frac{\$49\times 300\times 9}{365}\right)\right]\\ =\left[\$400+\left(\frac{\$132,300}{365}\right)\right]\\ =\left[\$400+\$362.4658\right]\\ =\$762.4658\mathrm{or}\$762.47\end{array}$

Calculate the total cost of shipper B with two-days shipping alternative:

It is calculated by multiplying total units with holding cost per year and days of shipping and the result is divided with 365 days and the whole result is added to the shipping cost.

$\begin{array}{c}\mathrm{Total}{\text{Cost}}_{\mathrm{Shipper}\text{B}\mathrm{with}\mathrm{two}-\mathrm{days}}=\left[\mathrm{Shipping}{\text{Cost}}_{\mathrm{Shipper}\text{B}}+\left(\frac{\begin{array}{l}\mathrm{Holding}\mathrm{Cost}\times \mathrm{Total}\mathrm{Units}\times \\ \mathrm{Shipping}\mathrm{Days}\end{array}}{365}\right)\right]\\ =\left[\$525+\left(\frac{\$49\times 300\times 2}{365}\right)\right]\\ =\left[\$525+\left(\frac{\$29,400}{365}\right)\right]\\ =\left[\$525+\$80.5479\right]\\ =\$605.5479\mathrm{or}\$605.55\end{array}$

Calculate the total cost of shipper B with four-days shipping alternative:

It is calculated by multiplying total units with holding cost per year and days of shipping and the result is divided with 365 days and the whole result is added to the shipping cost.

$\begin{array}{c}\mathrm{Total}{\text{Cost}}_{\mathrm{Shipper}\text{B}\mathrm{with}\mathrm{four}-\mathrm{days}}=\left[\mathrm{Shipping}{\text{Cost}}_{\mathrm{Shipper}\text{B}}+\left(\frac{\begin{array}{l}\mathrm{Holding}\mathrm{Cost}\times \mathrm{Total}\mathrm{Units}\times \\ \mathrm{Shipping}\mathrm{Days}\end{array}}{365}\right)\right]\\ =\left[\$450+\left(\frac{\$49\times 300\times 4}{365}\right)\right]\\ =\left[\$450+\left(\frac{\$58,800}{365}\right)\right]\\ =\left[\$450+\$161.0959\right]\\ =\$611.0959\mathrm{or}\$611.10\end{array}$

Calculate the total cost of shipper B with seven-days shipping alternative:

It is calculated by multiplying total units with holding cost per year and days of shipping and the result is divided with 365 days and the whole result is added to the shipping cost.

$\begin{array}{c}\mathrm{Total}{\text{Cost}}_{\mathrm{Shipper}\text{B}\mathrm{with}\mathrm{seven}-\mathrm{days}}=\left[\mathrm{Shipping}{\text{Cost}}_{\mathrm{Shipper}\text{B}}+\left(\frac{\begin{array}{l}\mathrm{Holding}\mathrm{Cost}\times \mathrm{Total}\mathrm{Units}\times \\ \mathrm{Shipping}\mathrm{Days}\end{array}}{365}\right)\right]\\ =\left[\$410+\left(\frac{\$49\times 300\times 7}{365}\right)\right]\\ =\left[\$410+\left(\frac{\$102,900}{365}\right)\right]\\ =\left[\$410+\$281.9178\right]\\ =\$691.9178\mathrm{or}\$691.92\end{array}$

From the results obtained Shipper A with offering two-day shipping alternative is low compared to other shipping alternatives.

Hence, it is recommended that the shipping A and two-day shipping alternatives should be selected.