Dynamic location problems with discrete expansion and reduction sizes of available capacities

In this paper a dynamic location problem is formulated that considers the possibility of expanding or reducing the maximum available capacity at any given location during the planning horizon. The expansion (or reduction) of available capacity at a given location is achieved through the opening (or closure) of one or more facilities with different discrete capacities. The mixed–integer linear model developed considers fixed costs for opening the first facility at any location, plus additional fixed costs for every open facility in a location with already existing facilities. It is possible to open, close and reopen any facility at any location more than once during the planning horizon. It is also possible to consider different assignment costs depending on the size of the facility that is assigned to each client. This is important, because, in general, smaller facilities have smaller fixed costs but greater unitary operating costs. A primal–dual heuristic is developed that is able to find primal feasible solutions to the problem here described, and computational results are presented.