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I'm new to modeling mathematical programming problems. I'm trying to solve an exercise about networks optimization with Gurobi solver. This is what the exercise says:

`The graph graph10092015.gml in the attached file contains a set of potential cabinets that a telecom company can connect with an optical fiber network. Each cabinet (node) u has associated a profit and each edge uv has associated a connection cost.

  1. Design a network that maximizes the company profit knowing that the budget for links installation cannot exceed 4000 Euro.
  2. From the previous optimal solution, evaluate the convenience of extending the network to cabinet 19 at a cost of 500 Euro to install a wireless router in the cabinet that connects for free cabinets 4 and 14. `

I formulated the problem as a Prize Collecting Steiner Tree:

formulation of the problem

What do you think about this? To solve this, Should I use the cutting plane approach and therefore define a separation problem?

I think I figured out how to model a problem but I still not feel confident with this type of exercises.

Thanks in advance for the help.

vnzstc
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1 Answers1

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I gave a solution to this problem time ago. I formulated this problem as a PCST. I added a constraint that imposes an upper-bound to costs for designing the network (it model a budget to spend).

Once I have obtained the solution for the first point. I have introduced a binary variable k that when is 1 nullifies the cost of cabinets 4,14 and adds the cost for router installation at 19. Then:

1- I forced the connection of 19 to the arborescence found at point 1. This is equal to: y[19] = 1

2- If cabinet 19 is in the arborescence then even 4 and 14 must be in. This is equal to: (2 * y[19]) <= y[4] + y[14]

3- If 19 is in the arborescence then introduce the cost changes induced by the router. This is equal to: k[1] <= y[19]

vnzstc
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