Project scheduling under uncertainty using fuzzy modelling and solving techniques

In the real world, projects are subject to numerous uncertainties at different levels of planning. Fuzzy project scheduling is one of the approaches that deal with uncertainties in project scheduling problem. In this paper, we provide a new technique that keeps uncertainty at all steps of the modelling and solving procedure by considering a fuzzy modelling of the workload inspired from the fuzzy/possibilistic approach. Based on this modelling, two project scheduling techniques, Resource Constrained Scheduling and Resource Leveling, are considered and generalized to handle fuzzy parameters. We refer to these problems as the Fuzzy Resource Constrained Project Scheduling Problem (FRCPSP) and the Fuzzy Resource Leveling Problem (FRLP). A Greedy Algorithm and a Genetic Algorithm are provided to solve FRCPSP and FRLP respectively, and are applied to civil helicopter maintenance within the framework of a French industrial project called Helimaintenance

Proactive and reactive strategies for resource-constrained project scheduling with uncertain resource availabilities.

Research concerning project planning under uncertainty has primarily focused on the stochastic resource-constrained project scheduling problem (stochastic RCPSP), an extension of the basic CPSP, in which the assumption of deterministic activity durations is dropped. In this paper, we introduce a new variant of the RCPSP for which the uncertainty is modeled by means of resource availabilities that are subject to unforeseen breakdowns. Our objective is to build a robust schedule that meets the project due date and minimizes the schedule instability cost, defined as the expected weighted sum of the absolute deviations between the planned and actually realized activity starting times during project execution. We describe how stochastic resource breakdowns can be modeled, which reaction is recommended when are source infeasibility occurs due to a breakdown and how one can protect the initial schedule from the adverse effects of potential breakdowns.

Resource-constrained project scheduling.

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;

The complexity of generating robust resource-constrained baseline schedules.

Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that will change little when variations in the input parameters arise. Robustness can also be achieved by making the schedule makespan insensitive to variability. In this paper, we describe models for the generation of stable and insensitive baseline schedules for resource-constrained scheduling problems and present results on their complexity status. We start from a project scheduling viewpoint and derive results on machine scheduling sub-problems.Complexity; Information; Product scheduling; Robustness; sensitivity; stability;

Project scheduling under undertainty – survey and research potentials.

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.Management; Project management; Robustness; Scheduling; Stability;

A tabu search procedure for developing robust predicitive project schedules.

Proactive scheduling aims at the generation of robust baseline schedules that are as much as possible protected against disruptions that may occur during project execution. In this paper, we focus on disruptions caused by stochastic resource availabilities and aim at generating stable baseline schedules. A schedule’s robustness (stability) is measured by the weighted deviation between the planned and the actually realized activity starting times during project execution. We present a tabu search procedure that operates on a surrogate, free slack based objective function. Its effectiveness is demonstrated by extensive computational results obtained on a set of randomly generated test instances.Project scheduling; Robustness; Proactive; Stability;

A tabu search procedure for generating robust project baseline schedules under stochastic resource availabilities.

The majority of research efforts in project scheduling assume a static and deterministic environment with complete information. In practice, however, these assumptions will hardly, if ever, be satisfied. Proactive scheduling aims at the generation of robust baseline schedules that are as much as possible protected against anticipated disruptions that may occur during project execution. In this paper, we focus on disruptions that may be caused by stochastic resource availabilities and aim at generating stable baseline schedules, where the solution robustness (stability) of the baseline schedule is measured by the weighted deviation between the planned and the actually realized activity starting times during project execution. We present a tabu search procedure that operates on a surrogate free slack based objective function. The effectiveness of the procedure is demonstrated by extensive computational results obtained on a set of randomly generated test instances.

Exact and suboptimal reactive strategies for resource-constrained project scheduling with uncertain resource availabilities.

In order to cope with the uncertainty inherent in practical project management, proactive and/or reactive strategies can be used. Proactive strategies try to anticipate future disruptions by incorporating slack time or excess resource availability into the schedule, whereas reactive strategies react after a disruption happened and try to revert to a feasible schedule. Traditionally, reactive approaches have focused on obtaining a good schedule with respect to the original objective function or a schedule that deviates as little as possible from the baseline schedule. In this paper, we present various approaches, exact as well as heuristic, for optimizing the latter objective and thus encouraging schedule stability. Furthermore, in contrast to traditional rescheduling algorithms, we present a new heuristic that also takes future uncertainty into account when repairing the schedule. We consider a variant of the resource- constrained project scheduling problem in which the uncertainty is modeled by means of unexpected resource breakdowns. The results of an extensive computational experiment are given to compare the performance of the proposed strategies.Schedule stability; Stability; Algorithms; Heuristic; Uncertainty; Project scheduling; Scheduling; Performance; Strategy; Order; Project management; Management; Time;