Question

YZ Company is rethinking the way it ships to its 62 customers in another city 220 miles away.

Current Shipping/Delivery Method
They currently hire an LTL (less-than-truckload) carrier to pick up and deliver these shipments. Each customer order shipped via LTL carrier costs $147.
Alternate Shipping/Delivery Method
A 3PL (third-party logistics provider) has approached XYZ Company and suggested that they make full truckload (TL) shipments from their facility to the 3PL's warehouse in the customers' city. The 3PL would then break the bulk shipment (TL or truckload shipment) into individual customer orders to be shipped locally by an LTL carrier. The relative data for this alternate shipping method are as follows:
Full TL shipment cost (220 miles) = $675
Average order weight = 750 lbs.
Warehouse break-bulk fee (per 100 lbs., a.k.a. per "hundred weight") = $13
Local LTL delivery fee = $36
1. What is the total cost of delivering to all customers via LTL carrier (current method
R=_______.
2. How much money would XYZ company save by using the alternate shipping/delivery method?
R=______.
3. At what number of customers would the cost of these two methods be the same?
R=______.

Answer 1

1. Total cost of customer order shipped via LTL carrier is $9,114.

2. XYZ company would save $162 by using the alternate shipping/delivery method.

3. The cost of these two methods would be the same when the number of customers is approximately 6.

Step-by-step explanation:

To ease answering the question, let us first the define as follows:

N = Number of customers = Number of Order

A = Each customer order shipped via LTL carrier costs = $147

B = Average order weight = 750

C = Warehouse break-bulk fee per hundred weight = 13

D = Total cost of weight = ((N * B) / 100) * C

E = Local LTL delivery fee = $36

F = Total Local LTL delivery fee = N * E

G = Full TL shipment cost (220 miles) = 675

H = Total cost of shipping using 3PL = D + F + G

I = Total cost of customer order shipped via LTL carrier = N * A

J = Difference between the cost of the two methods = I - H

1. What is the total cost of delivering to all customers via LTL carrier (current method

This can be calculated using E above as follows:

Total cost of customer order shipped via LTL carrier = E = N * A = 62 * $147 = $9,114

2. How much money would XYZ company save by using the alternate shipping/delivery method?

From the definitions above, we have:

N = Number of orders = 62

D = Total cost of weight = ((N * B) / 100) * C = ((62 * 750) / 100) * 13 = $6,045

F = Total Local LTL delivery fee = N * E = 62 * 36 = $2,232

G = Full TL shipment cost (220 miles) = $675

H = Total cost of shipping using 3PL = D + F + G = $6,045 + $2,232 + $675 = $8,952

I = Total cost of customer order shipped via LTL carrier = $9,114

J = Difference between the cost of the two methods = I - H = $9,114 - $8,952 = $162

Therefore, XYZ company would save $162 by using the alternate shipping/delivery method.

3. At what number of customers would the cost of these two methods be the same?

H = Total cost of shipping using 3PL = D + F + G = (((N * B) / 100) * C) + (N * E) + G ............ (1)

Substituting all the relevant value into equation (1), we have:

H = (((N * 750) / 100) * 13) + (N * 36) + 675

I = N * 147

Equating H and I and solve for N, we have:

(((N * 750) / 100) * 13) + (N * 36) + 675 = N * 147

((N0.01 * 7.50) * 13) + 675 = N147 - N36

(N0.075* 13) + 675 = N111

N0.975 + 675 = N111

675 = N111 - N0.975

N110.025 = 675

N = 675 / 110.025

N = 6.13496932515337.

By approximating to a whole number since we are talking about human being, we have:

N = 6

At what number of customers would

Therefore, the cost of these two methods would be the same when the number of customers is approximately 6.