The Project Scheduling Problem with Non-Deterministic Activities Duration: A Literature Review

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration.Peer Reviewe

Optimal constrained non-renewable resource allocation in PERT networks with discrete activity times

AbstractIn this paper, we develop an approach to optimally allocate a limited nonrenewable resource among the activities of a project, represented by a PERT-Type Network (PTN). The project needs to be completed within some specified due date. The objective is to maximize the probability of project completion on time. The duration of each activity is an arbitrary discrete random variable and also depends on the amount of consumable resource allocated to it. On the basis of the structure of networks, they are categorized as either reducible or irreducible. For each network structure, an analytical algorithm is presented. Through some examples, the algorithms are illustrated

A novel class of scheduling policies for the stochastic resource-constrained project scheduling problem.

We study the resource-constrained project scheduling problem with stochastic activity durations. We introduce a new class of scheduling policies for this problem, which make a number of a-priori sequencing decisions in a pre-processing phase, while the remaining decisions are made dynamically during project execution. The pre-processing decisions entail the addition of precedence constraints to the scheduling instance, hereby resolving some potential resource conflicts. We compare the performance of this new class with existing scheduling policies for the stochastic resource-constrained project scheduling problem, and we observe that the new class is significantly better when the variability in the activity durations is medium to high.Project scheduling; Uncertainty; Stochastic activity durations; Scheduling policies;

Pert using Fuzzy variables and probability distribution function randomly selected

Program Evaluation and Review Technique (PERT) is widely used for project management in real world applications. The aim of this paper is to simulate and analyze a PERT network under conditions of uncertainty though a hybrid model. The basic assumption is that a project under extreme conditions of uncertainty can be satisfactorily modelled by using simple fuzzy linguistic variables to estimate activities durations, and a probability distribution function randomly selected in order to measure the activity times. Fuzzy linguistic expressions are used to estimate the activity time. Activity parameters are calculated by using basic operations between triangular fuzzy numbers and centroid method with classical Beta PERT definition. For each activity time a probability distribution function is randomly selected from a set of four possible distributions commonly cited in the literature. Hypothetical projects with 4, 40, 400 and 4000 activities using the proposed model are analyzed; the project duration is estimated through Monte Carlo Simulation. Finally, results are analyzed and compared with classical Beta PERT technique

Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions

Project managers face difficult decisions with regard to completing projects on time and within the project budget. A successful project manager not only needs to assure that the project is completed, but also desires to make optimal use of resources and maximize the profitability of the project. The goal of this research is to address the time-cost tradeoff problem associated with selecting from among project activity alternatives under uncertainty. Specifically, activities that make up a project may have several alternatives each with an associated cost and stochastic duration. The final project cost is a result of the time and cost required to complete each activity and lateness penalties that may be assessed if the project is not completed by the specified completion time. In an effort to optimize the project time-cost tradeoff, a dynamic, simulation-based optimization method is presented. In particular, the method minimizes the expected project cost due to lateness penalties and the activity alternatives selected. The method is designed to be implemented in two phases. The first phase, referred to as the static phase, is implemented prior to the start of the project. The static phase results in the expected cost for the recommended project configuration including the alternative selected for each activity and the distributions of the project completion and total project cost. The second phase, referred to as the dynamic phase, is implemented as the project progresses. The dynamic phase allows the project manager to reevaluate the remaining project and activity alternatives to dynamically minimize the expected total project cost. The method provides an optimal solution under the assumptions of traditional crashing implementations and a heuristic solution for the generalized problem. An experimental performance evaluation shows the effectiveness of the method for making project management decisions. Finally, the method is fully implemented in computer software and integrated into a commercially available project management tool

Local search methods for the discrete time/resource trade-off problem in project networks.

Abstract: In this paper we consider the discrete time/resource trade-off problem in project networks. Given a project network consisting of nodes (activities) and arcs (technological precedence relations specifying that an activity can only start when al of its predecessors have been completed), in which the duration of the activities is a discrete, on-increasing function of the amount of a single renewable resource committed to it, the discrete time/resource trade-off problem minimizes the project makespan subject to precedence constraints and a single renewable resource constraint. For each activity a work content is specified such that all execution modes (duration-resource pairs) for performing the activity are allowed as long as the product of the duration and the resource requirement is at least as large as the specified work content. We present a tabu search procedure which is based on subdividing the problem into a mode assignment phase and a resource-constrained project scheduling phase with fixed mode assignments. Extensive computational experience, including a comparison with other local search methods, is reported.Scheduling; Methods; Networks; Product; Assignment;

On the optimal resource allocation in projects considering the time value of money

The optimal resource allocation in stochastic activity networks had been previously developed by applying three different approaches: Dynamic Programming (DP), an Electromagnetism Algorithm (EMA) and an Evolutionary Algorithm (EVA). This paper presents an extension to the initial problem considering the value of money over time. This extended problem was implemented using the Java programming language, an Object Oriented Language, following the approaches previously used (DP, EMA and EVA).Fundação para a Ciência e a Tecnologia (FCT