Question

The Shiny Star Clothing company has launched a new clothing line (SKU number OA694) 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	28
Shijiazhuang	1300	13

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

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

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.

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?

Answer 1

We will use linear programming to solve this problem using Excel -> Solver.

Below screenshot show the step by step approach

How many lanes will you award to each carrier in order to minimize total expected costs?

Red = 1

Blue = 0

Green = 3

What is the total expected weekly cost for this solution? - $757,690.

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