This is a conceptual facility location problem. I want advice on how one would approach it.
- We have 20 stands, each plotted on a 2d map. Each stand demands a certain # of apples per year.
- We are trying to place apple factories that can supply every stand’s demand.
A. Factory Constraints:
- a. Any factory must supply between 6,000 and 10,000 apples
- b. The factory cannot supply more than 200km away.
- Minimize the number of factories built.
i have included what i have done so far.
Steps
- First formulate a mathematical approach to find a distance from each factory to each location. (initially begin with 25 factories)
- Fill the demand matrix using the given values.
- Use a indicator variable called yi to calculate the total supply from i th factory. Here yi =1 if we assign the i th factory to any of the location and otherwise yi=0.
- Calculate the respective supplies using equation (2).
- Formulate the mathematical model using relevant constraints.
- Solve it using computer pregame.
i just want to know whether these steps are correct or not. Also i am very appreciate if someone can provide me the mathematical formulation.