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3

Following is a possible way of its implementation: First, you define a function that takes an OD matrix, solves the GUROBI model, and returns the optimal locations. FUNCTION OPTIMAL_LOCATION(OD): // This part will prepare the gurobi model and change the parameters related to OD matrix // Solve the model and return locations END FUNCTION ...

1

The question can be understand as determining the truth value of $$(\forall \text{assignments}: \text{relaxation feasible} )\implies \text{problem has integer solution}.$$ However since setting up many LP problems is more expensive then solving a small MILP (or even cheaper 1-in-3 SAT). I instead try to show the opposite: (\forall \text{assignments}: \text{...

2

If I am not mistaken the answer is NO unless $P=NP$. We can reduce Exactly-1 3-satisfiability to your problem. For a proof of 1-IN-3SAT is NP-complete see NP-Completeness of 3SAT, 1-IN-3SAT and MAX 2SAT. Given an instance $I$ of the Exactly-1 3-satisfiability problem. For each variable $x_i$ check whether there is a solution setting it to $1$ and $0$. This ...

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