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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During execution, projects may be subject to considerable uncertainty, which may lead to numerous schedule disruptions. Recent research efforts have focused on the generation of robust project baseline schedules that are protected against possible disruptions that may occur during schedule execution. The fundamental research issue we address in this paper is the potential trade-off between the quality robustness (measured in terms of project duration) and solution robustness (stability, measured in terms of the deviation between the planned and realised start times of the projected schedule). We provide an extensive analysis of the results of a simulation experiment set up to investigate whether it is beneficial to concentrate safety time in project and feeding buffers, or whether it is preferable to insert time buffers that are scattered in a clever way throughout the baseline project schedule in order to maximize schedule stability.

The vast majority of the research efforts in project scheduling over the past several years has concentrated on the development of exact and suboptimal procedures for the generation of a baseline schedule assuming complete information and a deterministic environment. During execution, however, projects may be the subject of considerable uncertainty, which may lead to numerous schedule disruptions. Predictive-reactive scheduling refers to the process where a baseline schedule is developed prior to the start of the project and updated if necessary during project execution. It is the objective of this paper to review possible procedures for the generation of proactive (robust) schedules, which are as well as possible protected against schedule disruptions, and for the deployment of reactive scheduling procedures that may be used to revise or re-optimize the baseline schedule when unexpected events occur. We also offer a framework that should allow project management to identify the proper scheduling methodology for different project scheduling environments. Finally, we survey the basics of critical chain scheduling and indicate in which environments it is useful.

This paper reports on new insights derived from computational results obtained with an updated version of the branch-and-bound procedure previously developed by Demeulemeester and Herroelen (Demeulemeester, E., W. Herroelen. 1992. A branch-and-bound procedure for the multiple resource-constrained project scheduling problem. Management Sci. 38 1803--1818.) for solving the resource-constrained project scheduling problem (RCPSP). The new code fully exploits the advantages of 32-bit programming provided by recent compilers running on platforms such as Windows NT ® and OS/2 ® : flat memory, increased addressable memory, and fast program execution. We study the impact of three important variables on the computation time for the RCPSP: addressable computer memory, the search strategy (depth-first, best-first, or hybrid), and the introduction of a stronger lower bound. We compare the results obtained by a truncated branch-and-bound procedure with the results generated by the minimum slack time heuristic and report on the dependency of its solution quality on the allotted CPU time.project scheduling--resource constraints, branch-and-bound, 32-bit programming, computational results