Discrete–continuous project scheduling with discounted cash flows—A tabu search approach

In this paper discrete–continuous project scheduling problems with discounted cash flows are considered. In discrete–continuous project scheduling activities require for their processing discrete and continuous resources. The processing rate of an activity depends on the amount of the continuous resource allotted to this activity at a time. A positive cash flow is associated with each activity. Two common payment models—lump-sum payment and payments at activities’ completion times—are considered. The objective is the maximization of the net present value of all cash flows of the project. Some properties of optimal schedules are discussed, and the formulation of a mathematical programming problem for an optimal continuous resource allocation is presented. Applications of a local search metaheuristic—tabu search, as well as simple search methods—multi-start iterative improvement and random sampling are described. The algorithms are compared on the basis of a computational experiment, the results are analyzed and discussed. Some conclusions as well as directions for further research are given.