---

This paper, we presents a new primary-secondary-criteria scheduling model for resource-constrained project scheduling problem (RCPSP) with uncertain activity durations (UD) and cash flows (UC). The RCPSP-UD-UC approach producing a “robust” resource-feasible schedule immunized against uncertainties in the activity durations and which is on the sampling-based scenarios may be evaluated from a cost-oriented point of view. In the presented approach, it is assumed that each activity-duration and each cash flow value is an uncertain-but-bounded parameter, which is characterized by its optimistic and pessimistic estimations. The evaluation of a given robust schedule is based on the investigation of variability of the makespan as a primary and the net present value (NPV) as secondary criterion on the set of randomly generated scenarios given by a sampling-on-sampling-like process. Theoretically, the robust schedule-searching algorithm is formulated as a mixed integer linear programming problem, which is combined with a cost-oriented sampling-based approximation phase. In order to illustrate the essence of the proposed approach we present detailed computational results for a larger and very challenging project instance. A problem specific fast and efficient harmony search algorithm for large uncertain problems will be presented in a forthcoming paper.

---

In this paper, we present a new idea for robust project scheduling combined with a cost-oriented uncertainty investigation. The result of the new approach is a makespan minimal robust proactive schedule, which is immune against the uncertainties in the activity durations and which can be evaluated from a cost-oriented point of view on the set of the uncertain-but-bounded duration and cost parameters using a sampling-based approximation. In this paper, we assume that the sources of uncertainty are the variability of the activity durations and the cash flow values, and present an appropriate hybrid method, which is a combination of mathematical programming, metaheuristic and sampling-based elements, to cope with this "uncertainty in uncertainty" like real problem.