Maximum Flow Location (FlowLoc) Modeling without Size Restrictions on Facilities

There are situations when traffic flow is obstructed because of facility placement in the road segments. FlowLoc models deal with such a situation in which a set of facilities with given sizes (capacities) has to be allocated with a given set of arcs of a directed network. The existing models assume that the size of each facility does not exceed the capacity of each of the arc in the given set of arcs and that the number of given facilities does not exceed the total number of available locations on arcs. In this work, we extend the FlowLoc modeling in which facilities can have arbitrary sizes and can have arbitrary numbers. We construct mixed-integer programming models based on static and dynamic network flow modeling. Realizing NP-hardness of problems, we design polynomial time heuristic algorithms to solve the constructed models. The performance of the algorithms is tested in a road network of Bhaktapur city Nepal.