A company wants to expand their business due to success.

They want to set up their own distributions network in the US.

For manufacturing they want 1-2 plants.

Until their own plants are ready another company “X” will do their manufacturing for 2 years, in Baltimore and/or Lincoln (Nebraska). Demand for these 2 years: 50 and 100 million units respectively.

In order to accept this, it require that company “X” are awarded an annual volume of 100 million for the following four years (after the two introductory years).

For their own future manufacturing plants they have 2 possible cities: Seattle and Savannah (Georgia).

For their own future distribution center they have 3 possible cities: Atlanta, Sacramento and Chicago

Demand: volume of 150 million units in year 3, and 200 million units in year 4, and continue of 200 million after that

Data:

Demand (millions of units/year)
Region	West	Midwest	North-east	South-east
Demand	70	25	50	55
Distribution cost from Atlanta (USD/unit)	5	2,5	3	1
Distribution cost from Atlanta (USD/unit)	4	2	2	3
Distribution cost from Atlanta (USD/unit)	1,5	3,5	5	5
From plant to warehouse
Warehouse	Atlanta	Chicago	Sacramento
Distribution cost from Seattle (USD/unit)	5	3,5	1
Distribution cost from Savannah (USD/unit)	1	3	5
Distribution cost from Baltimore(USD/unit)	2,5	2,5	5
Distribution cost from Lincoln (USD/unit)	3,5	1,5	3
Capacities
Facility	Capacity (miilion units/year)		Fixed annual costs (million USD)
Altanta warehouse	100		110
Chicago warehouse	100		100
Sacramento warehouse	100		120
Seattle manufacturing plant	120		540
Savannah manufacturing plant	70		350
Baltimore manufacturing plant	120		Outsourced to company “x”
Lincoln manufacturing plant	100		Outsourced to company “x”

Task:

1. Propose a design for production and distribution network. Any plants shall be able to deliver to any warehouse. The system must be designed for an annual volume of 200 million units, where 100 million units will be manufactured by company “x”
2. Formulate the problem with the goal to minimize costs
   • Include: objective function, constraints
   • DO NOT NEED TO BE SOLVED ONLY FORUMLATED!
3. How will the problem formulation change if the company buy the plants from company “x”
   1. How will that affect the design