Question

The Shiny Star Clothing company has launched a new clothing line (SKU number CG736) for export out of the port of Ningbo. You have been tasked with securing the trucking services to handle all of the container freight moves (TEUs) from your four plants to the port of Ningbo. Your plants are located in Chongqing, Beijing, Nanjing, and Shijiazhuang.

The lane information is as follows:

Origin	Distance to Ningbo (Km)	Expected Weekly Demand (TEUs)
Chongqing	1750	19
Beijing	1400	20
Nanjing	450	22
Shijiazhuang	1300	14

Currently Shiny Star Clothing has no contracts of any sort with trucking companies to the Ningbo location. You have decided to run an auction and to only invite your top 3 carriers (Red, Blue, and Green) to participate.

Suppose that the carriers have submitted the following bids in Yuan Renminbi per TEU per km.

Origin	Red	Blue	Green
Chongqing	7.50	9.00	8.60
Beijing	6.40	8.30	8.00
Nanjing	8.80	8.90	9.20
Shijiazhuang	7.80	9.20	8.40

what is the total expected weekly demand?

Part1

Based on this data, how many TEUs will you award to each carrier in order to minimize total expected costs?

Red:

Blue:

Green:

What is the total expected weekly cost for this solution?

Part2

You decide to contact your carriers to make sure they have sufficient capacity to handle your business. The carriers reply with the following capacity in terms of number of TEU loads handled per week in total across all four lanes.

• Red: 15 TEUs per week
• Blue: 25 TEUs per week
• Green: 90 TEUs per week

Based on this new data, how many TEUs will you award to each carrier in order to minimize total expected costs?

Red

Blue

Green

And what is the total expected weekly cost for this?

Part3

You want to ensure that each lane is awarded to one and only one carrier. That is, only one carrier can be awarded volume on a lane -no split assignments. Keep the carrier capacity constraints introduced in Part 2.

Based on this new data, how many lanes will you award to each carrier in order to minimize total expected costs?

Red?

Blue?

Green?

What is the total expected weekly cost for this solution?

Part 4

Your manager has another idea. She wants to ensure that each lane has at least two carriers assigned to it - with at least 5 loads per carrier (per lane).

Based on this new data, how many lanes will you award to each carrier in order to minimize total expected costs?

Red?

Green?

Blue?

What is the total expected weekly cost for this solution?

Answer 1

Total expected weekly demand is

19 + 20 + 22 + 14 = 75 TEU

Part 1

In order to minimize the total cost we need to use the information and solve it as transportation model. However from the vendors table we can see that the Red carrier beats all the others in terms of pricing. Thus if there is no capacity constraint, we will choose the Red carrier. The solution is shown below.

All the TEUs will be awarded to Red carrier

The total expected weekly cost for this will be 657655

Part 2

Now that we have capacity constraints we need to modify the model. The result is shown below.

Based on the new data, the award will be

Red = 15

Blue = 22

Green = 38

The total expected weekly cost for this is 717340

Part 3

If each lane is awarded only one carrier then we need to combine assignment model with the transportation model with binary variables. This is shown below.

The number of lanes assigned to each carrier will be

Red = 0

Blue = 1

Green = 3

The total expected weekly cost is 750940