Reducing the elastic generalized assignment problem to the standard generalized assignment problem

The elastic generalized assignment problem (eGAP) is a natural extension of the generalized assignment problem (GAP) where the capacities are not fixed but can be adjusted which is expressed by continuous variables. These variables might be un-bounded or restricted by a lower or upper bound, respectively. This paper concerns techniques in order to reduce several variants of eGAP to GAP which enables us to employ Standard approaches for the GAP. This results into an heuristic, which can be customized in order to provide solutions having an objective value arbitrarily close to the optimal one.