The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling; fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.

In this paper a branch-and-bound procedure is described for scheduling the activities of a project of the PERT/CPM variety subject to precedence and resource constraints where the objective is to minimize project duration. The procedure is based on a depth-first solution strategy in which nodes in the solution tree represent resource and precedence feasible partial schedules. Branches emanating from a parent node correspond to exhaustive and minimal combinations of activities, the delay of which resolves resource conflicts at each parent node. Precedence and resource-based bounds described in the paper are combined with new dominance pruning rules to rapidly fathom major portions of the solution tree. The procedure is programmed in the C language for use on both a mainframe and a personal computer. The procedure has been validated using a standard set of test problems with between 7 and 50 activities requiring up to three resource types each. Computational experience on a personal computer indicates that the procedure is 11.6 times faster than the most rapid solution procedure reported in the literature while requiring less computer storage. Moreover, problems requiring large amounts of computer time using existing approaches for solving this problem type are rapidly solved with our procedure using the dominance rules described, resulting in a significant reduction in the variability in solution times as well.project management, resource constraints, programming, branch-and-bound, networks/graphs, applications

The direct application of the Theory of Constraints (TOC) to project management, known as Critical Chain Scheduling and Buffer Management (CC/BM), has recently emerged as one of the most popular approaches to project management. It is the objective of this paper to highlight the merits and pitfalls of the CC/BM scheduling approach. Following a short overview of the fundamentals of CC/BM, the strengths and weaknesses of the approach are put into perspective, based on a critical analysis of the literature as well as our own experimentation with commercial CC/BM software. The CC/BM scheduling mechanism is tested in a full factorial experiment performed on a set of benchmark problems. It appears that the 50% rule for buffer sizing may lead to a serious overestimation of the required buffer protection. Regularly updating the baseline schedule and the critical chain provides the best intermediate estimates of the final project duration and yields the smallest final project duration. Using clever project scheduling and rescheduling mechanisms such as branch‐and‐bound, has a beneficiary effect on the final makespan.

The majority of resource-constrained project scheduling efforts assumes perfect information about the scheduling problem to be solved and a static deterministic environment within which the precomputed baseline schedule is executed. In reality, project activities are subject to considerable uncertainty, which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects a given baseline schedule against activity duration variability.A branch-and-bound algorithm is developed that solves the proposed resource allocation problem.We report on computational results obtained on a set of benchmark problems.

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