Algebraic Solutions to Scheduling Problems in Project Management
نویسنده
چکیده
An approach to schedule development in project management is proposed based on models and methods of idempotent algebra. The approach offers a way to represent various types of precedence relationships among activities in projects as linear vector equations in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempotent algebra setting, like linear equations and the eigenvalue problem. The solutions to the problems are given in a compact vector form that provides the basis for the development of efficient computation procedures and related software applications. Key-Words: idempotent semiring, linear equation, eigenvalue and eigenvector, project scheduling, activity precedence relations, activity flow time
منابع مشابه
A multi-objective resource-constrained optimization of time-cost trade-off problems in scheduling project
This paper presents a multi-objective resource-constrained project scheduling problem with positive and negative cash flows. The net present value (NPV) maximization and making span minimization are this study objectives. And since this problem is considered as complex optimization in NP-Hard context, we present a mathematical model for the given problem and solve three evolutionary algorithms;...
متن کاملAn Energy-efficient Mathematical Model for the Resource-constrained Project Scheduling Problem: An Evolutionary Algorithm
In this paper, we propose an energy-efficient mathematical model for the resource-constrained project scheduling problem to optimize makespan and consumption of energy, simultaneously. In the proposed model, resources are speed-scaling machines. The problem is NP-hard in the strong sense. Therefore, a multi-objective fruit fly optimization algorithm (MOFOA) is developed. The MOFOA uses the VIKO...
متن کاملAn Optimization via Simulation approach for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problems
In this paper a novel modelling and solving method has been developed to address the so-called resource constrained project scheduling problem (RCPSP) where project tasks have multiple modes and also the preemption of activities are allowed. To solve this NP-hard problem, a new general optimization via simulation (OvS) approach has been developed which is the main contribution of the current re...
متن کاملProject resource investment problem under progress payment model
As a general branch of project scheduling problems, resource investment problem (RIP) considers resource availabilities as decision variables to determine a level of employed resources minimizing the costs of the project. In addition to costs (cash outflows), researchers in the later extensions of the RIP took payments (cash inflows) received from clients into account and used the net present v...
متن کاملAn Evolutionary Algorithm Based on a Hybrid Multi-Attribute Decision Making Method for the Multi-Mode Multi-Skilled Resource-constrained Project Scheduling Problem
This paper addresses the multi-mode multi-skilled resource-constrained project scheduling problem. Activities of real world projects often require more than one skill to be accomplished. Besides, in many real-world situations, the resources are multi-skilled workforces. In presence of multi-skilled resources, it is required to determine the combination of workforces assigned to each activity. H...
متن کامل