Problem 11-2 The table below provides shipping rates for packages using UPS next
ID: 349382 • Letter: P
Question
Problem 11-2 The table below provides shipping rates for packages using UPS next day air or ground service options. The rates vary according to both the weight of the package and the distance of the shipment (larger numbered zones are farther away). Note that the zone number also indicates the number of days required to deliver a package using ground service. For example, it would take three days and cost $7.40 to send a 10-pound package to zone 3 using ground service. Table of Nent Day Senvice VWeight Domestic Zones 5 630660 7.10080 s 1345 Suppose you have a package weighing 15 pounds that needs to be shipped to zone 4. The value of the material is $8,500 and the annual inventory holding rate is 35 percent of the product value. a-1. Calculate the total shipping and transit inventory cost using the air and ground transportations. (Use 365 days in a year. Do not round intermediate calculations. Round your answers to 2 decimal places.) a-2. Which transportation mode (air or ground) minimizes the total shipping and transit inventory cost? (Round your answer to 2 decimal places.)Explanation / Answer
Solution:
a1. Given: Value of Material = $8500
Package weight: 15 Lbs
Shipped Zone: 4
So, from the table,
Transportation cost (air) = $63
No.of Days Required for Transit (Air) = 1 day ( as next day delivery)
Transportation cost (Ground) = $9.05
No.of Days Required for Transit (Ground) = 4 days ( as mentioned zone number)
Inventory holding cost : 35 % of Material Value per year
so, Inventory holding cost per day, let denote it by, H = [(35%)* $8500]/365
H = $ (35*85)/365
Now,
Transit Inventory Cost (Air) = Inventory holding cost per day * no. of days required for transit + transportation cost
= H* 1 day + $63
= ${(35*85)/365}*1 + $63
= $8.15 + 63
Transit Inventory Cost (Air) = $71.15
Total cost using Air transportation = Value of Material + Transit Inventory Cost (Air)
= $(8500 + 71.15)
Total cost using Air transportation = $8571.15
Transit Inventory Cost (Ground) = Inventory holding cost per day * no. of days required for transit + transportation cost
=[(35*85)/365]*4 + 9.05
=32.60 + 9.05
= $41.65
Transit Inventory Cost (Ground) = $41.65
Total cost using Ground transportation = Value of Material + Transit Inventory Cost (Ground)
= $(8500 + 41.65)
Total cost using ground transportation = $8541.65
Solution: a2,
Total cost using ground transportation = $8541.65
Total cost using Air transportation = $8571.15
Ground cost minimize total shipping and transit cost by dollar = $8571.15 - $8541.65 = $29.50
Solution: b
To find inventory rate to justify air service we need to balance transit inventory cost using air with total cost with ground.
i.e
Transit Inventory cost (ground transportation) = Transit Inventory cost (Air transportation)
now,
Let Inventory holding rate be X,
value of material = $ 8500
Inventory holding rate per day = (X/365)*8500
Transit Inventory Cost (air) = Inventory holding cost per day * no. of days required for transit + transportation cost
Transit Inventory Cost (air) = (X/365)*8500*1 + 63
similary,
Transit Inventory Cost (Ground) = (X/365)*8500*4 + 9.05
Now again,
Transit Inventory cost (ground transportation) = Transit Inventory cost (Air transportation)
or,
(X/365)*8500*1 + 63 = (X/365)*8500*4 + 9.05
or, 53.95 = (3X/365)*8500
or, X = 0.7722
or, X% = 77.22%
i.e Inventory holding rate should be 77.22% of value of material to justify next day air service.