Project Scheduling Model Research Articles

Packing Problems and Project Scheduling Models: An Integrating Perspective

Packing Problems and Project Scheduling Models: An Integrating Perspective

A zero-one model for project portfolio selection and scheduling

A zero-one integer linear programming model is proposed for selecting and scheduling an optimal project portfolio, based on the organisation's objectives and constraints such as resource limitations and interdependence among projects. The model handles some of the issues that frequently arise in real world applications but are not addressed by previously suggested models, such as situations in which the amount of available and consumed resources varies in different periods. It also allows for interactive adjustment following the optimisation process, to provide decision makers a method for controlling portfolio selection, based on criteria that may be difficult to elicit directly. It is critical for such a system to provide fast evaluation of alternatives the decision makers may want to examine, and this requirement is addressed. The proposed model not only suggests projects that should be incorporated in the optimal portfolio, but it also determines the starting period for each project. Scheduling considerations can have a major impact on the combination of projects that can be incorporated in the portfolio, and may allow the addition of certain projects to the portfolio that could not have been selected otherwise. An example problem is described and solved with the proposed model, and some areas for future research are discussed.

A Zero-One Model for Project Portfolio Selection and Scheduling

A Zero-One Model for Project Portfolio Selection and Scheduling

A genetic algorithm approach to a general category project scheduling problem

A genetic algorithm (GA) approach is proposed for the general resource-constrained project scheduling model, in which activities may be executed in more than one operating mode, and renewable as well as nonrenewable resource constraints exist. Each activity's operation mode has a different duration and requires different amounts of renewable and nonrenewable resources. The objective is the minimization of the project duration or makespan. The problem under consideration is known to be one of the most difficult scheduling problems, and it is hard to find a feasible solution for such a problem, let alone the optimal one. The GA approach described in this paper incorporates problem-specific scheduling knowledge by an indirect chromosome encoding that consists of selected activity operating modes and an ordered set of scheduling rules. The scheduling rules in the chromosome are used in an iterative scheduling algorithm that constructs the schedule resulting from the chromosome. The proposed GA is denoted a hybrid GA (HGA) approach, since it is integrated with traditional scheduling tools and expertise specifically developed for the general resource-constrained project scheduling problem. The results demonstrate that HGA approach produces near-optimal solutions within a reasonable amount of computation time.

Project scheduling using a genetic algorithm with adaptable changing genetic operators

Genetic algorithms (GA) have been widely used to solve planning problems. However, they require one to determine the optimal values of many genetic parameters, such as population sizes, crossover probability, mutation probability, and so on. To make matters worse, the most suitable combination of parameters for one problem is not always optimal for others. Therefore, these parameters should be tuned whenever the problem changes. In this paper, we propose an adaptable GA mechanism that has autonomic parameter tuning for the composition of generic operators. This mechanism raises questions concerning the probability of genetic operators that acted effectively, that is, the probability that one operator created better individuals than the other operators. It also successively adjusts the combinations of genetic parameters suitable for the target problem. We applied the adaptable GA mechanism to a project scheduling model (PSM) and evaluated it with manual tuning methods. © 1998 Scripta Technica, Electr Eng Jpn, 124(2): 36–42, 1998

A heuristic for network project scheduling with random activity durations depending on the resource allocation

This paper presents a heuristic for resource-constrained network project scheduling. A PERT-type project, where activities require resources of various types with variable capacities, is considered. Each activity is of random duration depending on the resource amounts assigned to that activity. The problem is to minimize the expected project duration by determining for each activity its starting time and the assigned resource capacities. The resource project scheduling model is an NP-complete knapsack resource reallocation problem. To obtain a precise solution, a lookover algorithm has been developed. For the case when a lookover requires mmuch computational time, an approximate heuristic algorithm is suggested. The problem has to be solved at each decision point, when at least more than one activities are ready to be operated but the available amount of resources is limited. The heuristic model is illustrated by a numerical example.

Study on Development of Available Tool for System Approach to Multi-Project Planning of Construction Project

In this study effective simulation tool for multi-construction-project planning is developed from the planning and managemental viewpoint as follows: At the first stage concept of integrated system approach for urban development is studied according to the planning process of integrated urban planning. At the second stage multi-construction-projecpt lanning and scheduling model located at system model of the system approach considered in the first stage is formulated from theviewpoint of cooperation is supply and demand relation considering balance of soil among multiple project. At the final stage hybrid model concept is studied through combining multi-project planning and scheduling model which had been already developed and multi-construction project planning and scheduling model formulated in the second stage.

Project segmentation—a tool for project management

Since the late 1950s network-based techniques are commonly used for project management. The critical path method (CPM) and programme evaluation and review technique ( pert) are standard tools for scheduling. Related techniques such as pert-COST are used for budgeting and control. In this paper, a new tool for project management is suggested. This tool is designed for projects in which the work content (of the project) can be divided into several subprojects or segments so that the same set of activities is performed on each segment. The proposed tool is the basis of a project scheduling model and a project control model designed to support project management in cases where CPM and pert are not suitable.

動的遺伝操作切替を用いた遺伝的アルゴリズムによるプロジェクトスケジューリング

Genetic Algorithm (GA) has been widely used to solve planning problems. However, it requires to determine the optimal values of many genetic parameters, such as population sizes, crossover probability, mutation probability and so on. To make matter worse, the mostt suitable combination of parameters for one problem is not always optimal for others. Therefore, these parameters should be tuned up whenever the problem changes.In this paper, we propose an adaptable GA mechanism which has an autonomic parameter tuning for the composition of generic operators. This mechanism raises the probability of the genetic operators which acted effectively, that is, the operator created better individuals than the other operators. And, it adjusts the combinations of genetic parameters as the suitable one for the target problem successively. We applied the adaptable GA mechanism to a project scheduling model (PSM) acrd evaluated with the manual tuning methods.

FUZZY PROJECT SCHEDULING MODELS UNDER INFLATION CONDITION

The paper defines four fuzzy project scheduling models under inflation condition without or with budget limit. The activity time is described by fuzzy relation or fuzzy variables. The models can be solved in the forms of crisp LP or NLP after using the concept of α-cut.

Threshold reliability of networks with small failure sets

AbstractThis paper addresses two classes of reliability analysis models: a network flow model and a project scheduling model. In each model, the arcs randomly and independently take on two possible states–an “operating” state and a “failed” state–corresponding to two different capacity/task‐time values, and the network is required to maintain a specified “threshold” max‐flow/project‐completion‐time value. In general, this problem is NP‐hard. We address the special case in which the difference between the lower and higher arc lengths is constant for every arc in the network. For these special cases, we show that if the underlying system is 1‐critical, i.e., minimally able to withstand a single component failure, then the probability that the system can maintain the required threshold for the flow and planar project scheduling model is computable in polynomial time. Both solutions are obtained by reducing the problems to the problem of determining the probability that the failed arcs in a directed acyclic graph lie on a single path or, equivalently, that the set of failed elements in a given partial order comprises a chain in that order. We also show how the basic approach can be used to generate bounds for systems that are “almost critical”.

Scheduling of projects under the condition of inflation

This paper (see also [4]) develops a linear programming (LP) model for an efficient scheduling and management of big projects. The model has an inflation factor as one of its major features and incorporates an extensive modification of existing project scheduling models. The paper includes numerical examples to demonstrate the usefulness of the model and the consequences of excluding inflation factor during project cost-estimation, planning and scheduling in an environment of high inflation. By transforming the variables of the LP model, a new model with fewer constraints is obtained, thereby reducing the amount of effort required to find an optimal solution.

Resource constrained project scheduling: Modelling with multiple alternatives

A generalized resource constrained project scheduling model is developed. In addition to incorporating common generalizations to the resource constrained project scheduling problem, this model can also handle any of the major scheduling objectives, alternative activity completion modes, and the simultaneous scheduling of multiple projects. Furthermore, this approach makes the general project scheduling problem amenable to solution by commercially available mixed integer/linear programming software. The central concept is the split of activities and the allocation of different resource usage rates. Numerical examples are given to illustrate the approach and its advantages.

A multi-stage non-deterministic model for project scheduling under resources constraints

Nowadays the general purpose of project scheduling is the development of decision-aids to help managers improving the planning, the programming and the control of their projects. This target is hard to be achieved because projects have complex descriptions and because such decisions include multiple choices about the allocation of resources and the project calendar, which have to be improved in terms of several criteria such as total duration, net present value, risk of failing to meet the planned durations for important fractions of the project, etc. A review of the major approaches adopted to describe projects in terms of time and resources is presented in this paper showing that, unfortunately, too large deterministic models are usually obtained for projects with a realistic size. A new formulation of the general problem of project scheduling under resources constraints is proposed in this paper considering the project as a sequence of stages. According to this approach, the project can be studied as a sequence of decisions on resources allocation where each time interval between successive decisions (stage duration) is explicitly formulated as a decision variable. This formulation is very powerful and flexible as it avoids large amounts of binary variables and it allows progressive levels of detail concerning the discretization of the project schedule. Also, non-deterministic attributes can be introduced and the optimization problem can be easily solved for most common objective functions. Analytical solutions can also be deduced using the proposed model if specific hypotheses about the restrictions on durations and resources are assumed.

A multiple objective programming framework for tradeoffs in project scheduling

This paper presents a multiple objective linear programming (MOLP) model for project scheduling. The MOLP approach allows potentially conflicting objectives to be considered without the necessity of creating specific rankings or weights for the objectives, although such factors can be considered if they are desired. An efficient set of solutions is developed from which a final schedule may be selected by the project manager utilizing non-quantifiable criterion and factors. The approach can be implemented using computer algorithms readily available in the public domain.

Resource constrained project crashing

The resource constrained project crashing problem is reviewed. Models for two specific cases are developed by extending traditional project scheduling models. The development of the model for the resource critical crashing case is based on the Pritsker, Watters, and Wolfe model [16]. The model developed for the activity duration crashing case is based on Bowman's model [2]. The paper concludes with several suggestions for future research.

Project scheduling via stochastic programming

If for a project (described by a non-empty set of activities, a relation on this set of activities the transitive closure of which is a strict order, and activity-completion-times assigned to the single activities) the activity-completion-times are assumed to be random variables a two-stage stochastic programming approach can be used for a cost-oriented project scheduling model. Completion-time estimates for the activity-completion-times are computed in such a way that, in order to meet a prescribed time-constraint for the project-completion-time, the expected costs for performing the activities according to the computed time-schedule are minimized. An example is included for illustration.

A Probabilistic Model for Optimal Project Scheduling

This paper formulates a model for the scheduling and control of a multiphase project that consists of a given sequence of jobs to be completed by a specified due date. The duration of each job is the sum of a known fixed time and a random delay; and, while the former may be shortened within given limits, there is no control over the latter. The decision variables are the level of activity in each job and the starting time of the first in the sequence. An optimal decision policy for this model is obtained assuming a simple cost structure. It is shown that, if this policy is followed, a minimum a priori probability of meeting the due date is guaranteed.