The vendor location problem

The vendor location problem is the problem of locating a given number of vendors and determining the number of vehicles and the service zones necessary for each vendor to achieve at least a given profit. We consider two versions of the problem with different objectives: maximizing the total profit and maximizing the demand covered. The demand and profit generated by a demand point are functions of the distance to the vendor. We propose integer programming models for both versions of the vendor location problem. We then prove that both are strongly NP‐hard and we derive several families of valid inequalities to strengthen our formulations. We report the outcomes of a computational study where we investigate the effect of valid inequalities in reducing the duality gaps and the solution times for the vendor location problem.