Solving the discrete-continuous project scheduling problem via its discretization

In this paper a discrete-continuous project scheduling problem is considere d. In this problem activities simultaneously require discrete and continuou s resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resour ces are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a cl assical (i.e. discrete) project scheduling problem in the multi-mode versio n is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. I n the former case a nonlinear solver is used for solving a corresponding co nvex programming problem. The results are compared with the results obtaine d using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each ite ration. The results of a computational experiment are analyzed and some con clusions are included.