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

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;

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;

A modied branch and cut procedure for resource portfolio problem under relaxed resource dedication policy

Multi-project scheduling problems are characterized by the way resources are managed in the problem environment. The general approach in multi-project scheduling literature is to consider resource capacities as a common pool that can be shared among all projects without any restrictions or costs. The way the resources are used in a multi-project environment is called resource management policy and the aforementioned assumption is called Resource Sharing Policy in this study. The resource sharing policy is not a generalization for multi-project scheduling environments and different resource management policies maybe defined to identify characteristics of different problem environments. In this study, we present a resource management policy which prevents sharing of resources among projects but allows resource transfers when a project starts after the completion of another one. This policy is called the Relaxed Resource Dedication (RRD) Policy in this study. The general resource capacities might or might not be decision variables. We will treat here the case where the general available amounts of resources are decision variables to be determined subject to a limited budget. We call this problem as the Resource Portfolio Problem (RPP). In this study, RPP is investigated under RRD policy and a modified Branch and Cut (B&C)procedure based on CPLEX is proposed. The B&C procedure of CPLEX is modified with different branching strategies, heuristic solution approaches and valid inequalities. The computational studies presented demonstrate the effectiveness of the proposed solution approaches

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 biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm

Railway scheduling reduces the expected project makespan.

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.Railway scheduling; Roadrunner scheduling; Feeding buffer; Priority list; Resource availability;

MPS - Decision Support System for Multiobjective Project Scheduling

The report presents a decision support system (DSS) for multiobjective project scheduling under multiple-category resource constraints. It handles quite a general class of nonpreemptive scheduling problems with renewable, nonrenewable and doubly-constrained resources, multiple performing modes of activities, precedence constraints in the form of an activity network and multiple project performance criteria of time and cost type. The DSS has been implemented on a microcomputer compatible with IBM PC, and called MPS. It is based on three kinds of heuristics: parallel priority rules, simulated annealing and branch-and-bound. The last algorithm can even yield exact solutions when sufficient processing time is available. Some parts of the MPS are interactive, in particular, the search for a best compromise schedule. Graphical facilities enable a thorough evaluation of feasible schedules. The report starts with a methodological guide presenting the problem formulation and the three heuristics. Then, the general scheme of the MPS is given together with an executive guide. An expanding menu and all its options are described and illustrated with a simple example. The last part presents a real problem solving consisting in scheduling 40 farm activities