Facility location problems with user cooperation

This paper introduces the concept of cooperative users in facility location problems with a median or a covering objective. Cooperative users can act as intermediate facilities which are more accessible than primary facilities to excentric users. Four versions of location problems with cooperative users are modeled, for all four combinations of median and covering objectives. Several families of valid inequalities are then presented. This is followed by the development of a non-linear model to assess the fair price of cooperation. The results of computational experiments on randomly generated and benchmark instances demonstrate the positive effect of having cooperative users on the solution structure and cost, as well the impact of the valid inequalities on the LP relaxation value and on the CPU time.