The Stochastic Resource-Constrained Project Scheduling Problem

Resource-constrained project scheduling has been widely investigated in the academic literature, but the issue of the incorporation of uncertainty in project scheduling has received a growing research attention only in the last 15 years. This chapter gives an overview of models and methods for the resource-constrained project scheduling under uncertainty. The case of known deterministic renewable resource requirements and random activity durations with a known probability distribution function is studied in detail. In particular, we show how, through the use of joint probabilistic constraints, a feasible baseline schedule with minimum makespan can be built, which is able to tolerate a certain degree of uncertainty and to absorb dynamic variations in activity durations. The use of joint probabilistic constraints, within the stochastic scheduling problem, represents an innovative element in the literature and enables the relaxation of the common assumption that only one activity at a time disturbs the starting time of a successor activity, rather limiting the joint probability of disruption of the preceding activities to a given probability level. The results obtained with the proposed heuristics are discussed and compared with two well known heuristics taken from the literature on a set of randomly generated project instances. A practical application concerning a real project for construction of students’ apartments at the University of Calabria, Italy, is also illustrated. Based on the analysis of the various researches discussed in this chapter, avenues for future research will be also outlined.