Resource Tardiness Weighted Cost Minimization in Project Scheduling

In this paper, we study a project scheduling problem that is called resource constrained project scheduling problem under minimization of total weighted resource tardiness penalty cost (RCPSP-TWRTPC). In this problem, the project is subject to renewable resources, each renewable resource is available for limited time periods during the project life cycle, and keeping the resource for each extra period results in some tardiness penalty cost. We introduce a branch and bound algorithm to solve the problem exactly and use several bounding, fathoming, and dominance rules in our algorithm to shorten the enumeration process. We point out parameters affecting the RCPSP-TWRTPC degree of difficulty, generate extensive sets of sample instances for the problem, and perform comprehensive experimental analysis using the customized algorithm and also CPLEX solver. We analyze the algorithm behavior with respect to the changes in instances degree of difficulty and compare its performance for different cases with the CPLEX solver. The results reveal algorithm efficiency

Dynamic resource constrained multi-project scheduling problem with weighted earliness/tardiness costs

In this study, a conceptual framework is given for the dynamic multi-project scheduling problem with weighted earliness/tardiness costs (DRCMPSPWET) and a mathematical programming formulation of the problem is provided. In DRCMPSPWET, a project arrives on top of an existing project portfolio and a due date has to be quoted for the new project while minimizing the costs of schedule changes. The objective function consists of the weighted earliness tardiness costs of the activities of the existing projects in the current baseline schedule plus a term that increases linearly with the anticipated completion time of the new project. An iterated local search based approach is developed for large instances of this problem. In order to analyze the performance and behavior of the proposed method, a new multi-project data set is created by controlling the total number of activities, the due date tightness, the due date range, the number of resource types, and the completion time factor in an instance. A series of computational experiments are carried out to test the performance of the local search approach. Exact solutions are provided for the small instances. The results indicate that the local search heuristic performs well in terms of both solution quality and solution time

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem.

In this paper we study the resource-constrained project scheduling problem with weighted earliness-tardiness penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness-tardiness penalty cost of the project subject to the finish)start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in -time environments.We introduce e depth-first branch-and-bound algorithm for the unconstrained weighted earliness-tardiness problem to compute lower bounds. The procedure has been coded in Visual C++, version 4.0 under Windows NT and has been validated on a randomly generated problem set.Studies; Scheduling; Costs; Requirements; Just-in-time;

An exact procedure for the unconstrained weighed earliness-tardiness project scheduling problem.

In this paper we study the unconstrained project scheduling problem with weighted earliness-tardiness penalty costs subject to zero-lag finish-start precedence constraints. Each activity of this unconstrained project scheduling problem has a known deterministic due date, a unit earliness penalty cost and a unit tardiness penalty cost. The objective is to schedule the activities in order to minimize the weighted earliness-tardiness penalty cost of the project, in the absence of constraints on the use of resources. With these features the problem setting become highly attractive in just-in-time environments.We introduce a two-step recursive algorithm. The first step consists of a forward pass procedure which schedules the activities such that they finish at their due date or later. The second step applies a recursive search in which the activities are eventually shifted backwards (topwards time zero) in order to minimize the weighted earliness-tardiness cost of the project. The procedure has been coded in Visual C++, version 4.0 under Windows NT 4.0 and has been validated on a randomly generated data set.Scheduling;

Resource dedication problem in a multi-project environment

There can be different approaches to the management of resources within the context of multi-project scheduling problems. In general, approaches to multiproject scheduling problems consider the resources as a pool shared by all projects. On the other hand, when projects are distributed geographically or sharing resources between projects is not preferred, then this resource sharing policy may not be feasible. In such cases, the resources must be dedicated to individual projects throughout the project durations. This multi-project problem environment is defined here as the resource dedication problem (RDP). RDP is defined as the optimal dedication of resource capacities to different projects within the overall limits of the resources and with the objective of minimizing a predetermined objective function. The projects involved are multi-mode resource constrained project scheduling problems with finish to start zero time lag and non-preemptive activities and limited renewable and nonrenewable resources. Here, the characterization of RDP, its mathematical formulation and two different solution methodologies are presented. The first solution approach is a genetic algorithm employing a new improvement move called combinatorial auction for RDP, which is based on preferences of projects for resources. Two different methods for calculating the projects’ preferences based on linear and Lagrangian relaxation are proposed. The second solution approach is a Lagrangian relaxation based heuristic employing subgradient optimization. Numerical studies demonstrate that the proposed approaches are powerful methods for solving this problem

Resource dedication problem in a multi-project environment

There can be different approaches to the management of resources within the context of multi-project scheduling problems. In general, approaches to multiproject scheduling problems consider the resources as a pool shared by all projects. On the other hand, when projects are distributed geographically or sharing resources between projects is not preferred, then this resource sharing policy may not be feasible. In such cases, the resources must be dedicated to individual projects throughout the project durations. This multi-project problem environment is defined here as the resource dedication problem (RDP). RDP is defined as the optimal dedication of resource capacities to different projects within the overall limits of the resources and with the objective of minimizing a predetermined objective function. The projects involved are multi-mode resource constrained project scheduling problems with finish to start zero time lag and non-preemptive activities and limited renewable and nonrenewable resources. Here, the characterization of RDP, its mathematical formulation and two different solution methodologies are presented. The first solution approach is a genetic algorithm employing a new improvement move called combinatorial auction for RDP, which is based on preferences of projects for resources. Two different methods for calculating the projects’ preferences based on linear and Lagrangian relaxation are proposed. The second solution approach is a Lagrangian relaxation based heuristic employing subgradient optimization. Numerical studies demonstrate that the proposed approaches are powerful methods for solving this problem

An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem.

In this paper we study the resource-constrained project scheduling problem with weighted earliness-tardinesss penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness-tardinesss penalty cost of the project subject to the finish-start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in-time environments.resource-constrained project scheduling; weighted earliness-tardiness costs; branch-and-bound; discounted cash flows; bound procedure;

A combination of different resource management policies in a multi-project environment

Multi-project problem environments are defined according to the way resources are managed in the problem environment, which is called the resource management policy (RMP) in this study. Different resource management policies can be defined according to the characteristics of the projects and/or resources in the problem environment. The most common RMP encountered in the multi-project scheduling literature is the resource sharing policy (RSP), where resources can be shared among projects without any costs or limitations. This policy can be seen as an extreme case since there is a strong assumption of unconstrained resource sharing. Another RMP can be defined as the other extreme such that resources cannot be shared among projects, which is called the resource dedication policy (RDP). The last RMP considered in this study is between these two policies where resources are dedicated but can be transferred among projects when a project finishes, the dedicated resources to this project can be transferred to another one starting after the finish of the corresponding project. This RPM is called the resource transfer policy (RTP). In this study we investigate a problem environment where all these three types of RPM are present. Additionally, the general resource capacities are taken as decision variables that are constrained by a given general budget. We call this multi-project environment as the Generalized Resource Portfolio Problem (GRPP). We have investigated this problem and proposed an iterative solution approach based on exact solution methods which determines the general resource capacities from the budget, resource dedications, resource sharing and resource transfer decisions and schedules the individual projects. Computational results for over forty test problems are reported