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

Robust optimization models for the dicrete time/cost trade-off problem

Cataloged from PDF version of article.Developing models and algorithms to generate robust project schedules that are less sensitive to disturbances are essential in today’s highly competitive uncertain project environments. This paper addresses robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). We formulate the robust DTCTP with three alternative optimization models in which interval uncertainty is assumed for the unknown cost parameters. We develop exact and heuristic algorithms to solve these robust optimization models. Furthermore, we compare the schedules that have been generated with these models on the basis of schedule robustness. & 2010 Elsevier B.V. All rights reserved

Algorithmic Developments in Two-Stage Robust Scheduling

This thesis considers the modelling and solving of a range of scheduling problems, with a particular focus on the use of robust optimisation for scheduling in two-stage decision-making contexts. One key contribution of this thesis is the development of a new compact robust counterpart for the resource-constrained project scheduling problem with uncertain activity durations. Resource conflicts must be resolved under the assumption of budgeted uncertainty, but start times can be determined once the activity durations become known. This formulation is also applied to the multi-mode version of this problem. In both cases, computational results show the clear dominance of the new formulation over the prior decomposition-based state-of-the-art methods. This thesis also demonstrates the first application of the recoverable robust framework to single machine scheduling. Two variants of this problem are considered, in which a first-stage schedule is constructed subject to uncertain job processing times, but can be amended in some limited way following the realisation of these processing times. The first of these problems is considered under general polyhedral uncertainty. Key results concerning the second-stage subproblem are derived, resulting in three formulations to the full problem which are compared computationally. The second of these problems considers interval uncertainty but allows for a more general recovery action. A 2-approximation is derived and the performance of a proposed greedy algorithm is examined in a series of computational experiments. In addition to these results on two-stage robust scheduling problems, a new deterministic resource-constrained project scheduling model is developed which, for the first time, combines both generalised precedence constraints and flexible resource allocation. This model is introduced specifically for the application of scheduling the decommissioning of the Sellafield nuclear site. A genetic algorithm is proposed to solve this model, and its performance is compared against a mixedinteger programming formulation

A Selective Scheduling Problem with Sequence-dependent Setup Times: A Risk-averse Approach

This paper addresses a scheduling problem with parallel identical machines and sequence-dependent setup times in which the setup and the processing times are random parameters. The model aims at minimizing the total completion time while the total revenue gained by the processed jobs satisfies the manufacturer’s threshold. To handle the uncertainty of random parameters, we adopt a risk-averse distributionally robust approach developed based on the Conditional Value-at-Risk measure hedging against the worst-case performance. The proposed model is tested via extensive experimental results performed on a set of benchmark instances. We also show the efficiency of the deterministic counterpart of our model, in comparison with the state-of-the-art model proposed for a similar problem in a deterministic context

A compact reformulation of the two-stage robust resource-constrained project scheduling problem

This paper considers the resource-constrained project scheduling problem with uncertain activity durations. We assume that activity durations lie in a budgeted uncertainty set, and follow a robust two-stage approach, where a decision maker must resolve resource conflicts subject to the problem uncertainty, but can determine activity start times after the uncertain activity durations become known. We introduce a new reformulation of the second-stage problem, which enables us to derive a compact robust counterpart to the full two-stage adjustable robust optimisation problem. Computational experiments show that this compact robust counterpart can be solved using standard optimisation software significantly faster than the current state-of-the-art algorithm for solving this problem, reaching optimality for almost 50% more instances on the same benchmark set

Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems

Models and algorithms for deterministic and robust discrete time/cost trade-off problems

Ankara : The Department of Management, Bilkent University, 2008.Thesis (Ph.D.) -- Bilkent University, 2008.Includes bibliographical references leaves 136-145Projects are subject to various sources of uncertainties that often negatively impact activity durations and costs. Therefore, it is of crucial importance to develop effective approaches to generate robust project schedules that are less vulnerable to disruptions caused by uncontrollable factors. This dissertation concentrates on robust scheduling in project environments; specifically, we address the discrete time/cost trade-off problem (DTCTP). Firstly, Benders Decomposition based exact algorithms to solve the deadline and the budget versions of the deterministic DTCTP of realistic sizes are proposed. We have included several features to accelerate the convergence and solve large instances to optimality. Secondly, we incorporate uncertainty in activity costs. We formulate robust DTCTP using three alternative models. We develop exact and heuristic algorithms to solve the robust models in which uncertainty is modeled via interval costs. The main contribution is the incorporation of uncertainty into a practically relevant project scheduling problem and developing problem specific solution approaches. To the best of our knowledge, this research is the first application of robust optimization to DTCTP. Finally, we introduce some surrogate measures that aim at providing an accurate estimate of the schedule robustness. The pertinence of proposed measures is assessed through computational experiments. Using the insight revealed by the computational study, we propose a two-stage robust scheduling algorithm. Furthermore, we provide evidence that the proposed approach can be extended to solve a scheduling problem with tardiness penalties and earliness rewards.Hazır, ÖncüPh.D

Robust Execution Strategy for Scheduling Under Uncertainity

VARAKANTHAM, Pradeep; CHENG, Shih-Fen ; LIM, Yun Fong</p