Despite the dynamic nature of real life scheduling problems, few studies focus on stochastic Resource constrained project scheduling problem and its variants. In this study, we consider stochastic Resource possibilities and propose a new chance constraint, piecewise-linear and mixed integer programming model. Model is tested and verified with known project instances. One of the main strengths of the proposed model is it can be used to construct baseline schedules with a predetermined confidence interval. This gives scheduler an opportunity to construct proactive actions in order to minimize disruptions.

This paper discusses the problem of allocation of constrained renewable Resource to splittable activities of a single project. If the activities of stochastic projects can be split, these projects may be completed in shorter time when the available Resource is constrained. It is assumed that the Resource amount required to accomplish each activity is a discrete quantity and deterministic. The activity duration time is assumed to be a discrete random variable with arbitrary experimental distribution. Solving stochastic mathematical programming model of problem is very hard. So, here some existing methods for deterministic problems have been generalized for stochastic case. Solutions of generalized methods are relatively better than random solutions. However, the authors developed the new algorithm that may improve the solutions of generalized methods and project Completion Time Distribution Function (CTDF). Comparison of solution of a method with random solutions is a common assessment method in literature research. Hence, the efficiency of the proposed algorithm represented using this method.

A project consists of a set of activities with precedence relations. There is also a set of limited Resources with which one can perform the activities. Each activity may be executed in more than one manner, depending on which Resource(s) is (are) assigned to it. The objective of the limited Resource scheduling problem which is known as NP-hard is to find the starting time and the manner in which each activity is performed in order to minimize the project span. In this paper a solution procedure based on genetic algorithm is proposed. Each chromosome is encoded by 9 priority rules. In addition, chromosomes represent best solutions obtained between three cases of: (i) activities are performed at their earliest possible time, (ii) activities are performed at their latest possible time, and (iii) activities are performed at a time randomly selected from their time windows. To describe the solution procedure a numerical example is Presented.

The cumulative Resource constraints of the Resource-constrained project scheduling problem (RCPSP) do not treat the Resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same Resource units over their processing times. In spite of this fact, most papers on Resource-constrained project scheduling mainly in the motivation phase use a strip packing of rectangles (SPR) like visualization to illustrate the Resource allocation. A novice researcher inspired by the "artistic" SPR visualization may think that the "rectangles" are essential elements of the RCPSP, and that the RCPSP is a special counter-intuitive strip packing problem (SPP) which can be solved without explicitly defined strip packing constraints. In this context "artistic" means, that we have to use a "drawing tool" to produce a SPR like visualization, because the standard model of the RCPSP knows nothing about the rectangles. In the RCPSP, the rectangles can be torn vertically and horizontally, which is absurd in the SPP, and the existence of a cumulative solution is only a necessary but not sufficient condition of the existence of the SPR like visualization, as proven by several researchers. Therefore the popular SPR visualization is theoretically wrong and misleading, and hides a real problem, which is connected to the dedicated Resource assignment. In this paper, we prove that replacing the rectangles with a set of strips with unit height we can always generate a theoretically correct strip packing of strips (SPS) like dedicated assignment, where dedicated means that each demand unit is served by exactly one Resource unit over its duration without "hidden" transfer time and cost.