Generalized Precedence Relations Research Articles

On the concept of criticality on GPRs project network with variable activity durations

Temporal analysis of project networks has been widely studied in the literature; basically, it consists of determining the starting and finishing times of activities respecting a set of precedence constraints among them. The main output of the temporal analysis is twofold: on the one hand, it provides information on the minimum completion time of the project and, on the other hand, it determines which activity may be considered critical. Defining and determining activity criticalities on its own is a problem that has attracted the attention of many researchers over the last decades. In this paper, in an attempt to further pursue these studies, we focus on project scheduling with generalized precedence relationships where durations are not fixed in advance, but are variable within given ranges and have to be determined to minimize the makespan of the project. Analyzing activity criticalities for the same problem where activity durations are fixed has been tackled within the literature; what happens when durations are assumed variables, to the best of our knowledge, has not been investigated. We show that, in this scenario, the current knowledge on activity criticalities is no longer valid and we give new definitions of criticality together with the rules for its identification. An extensive experimental campaign on benchmark instances is presented to show that our findings are meaningful for quantitative project management.

Energy-efficient resource-constrained multi-project scheduling problem with generalized precedence relations and multi-skilled resources

Energy-efficient resource-constrained multi-project scheduling problem with generalized precedence relations and multi-skilled resources

A chance-constrained programming method with credibility measure for solving the multi-skill multi-mode resource-constrained project scheduling problem

This paper addresses a multi-skilled extension of the multi-mode resource-constrained project scheduling problem (MRCPSP) with preemption of activities and generalized precedence relations under uncertainty. The problem is formulated mathematically as a single objective optimization model to minimize the project makespan. Concerning real-world circumstances, amount of non-renewable resources and availability are considered as interval type-2 fuzzy numbers. Therefore, a type-2 fuzzy chance-constrained programming (TFCP) method is developed to tackle the problem. Four unique characteristics are taken into account in this paper concurrently: (i) multi-skilled resources; (ii) renewable and non-renewable resources; (iii) preemptable activities; and (iv) interval type-2 fuzzy parameters. The existence of these practical contributions causes projects schedule, especially construction projects, to be closer to the real-world conditions. The proposed mathematical model is validated and tested on instances from PSPLIB (j12, j16 and j18) and MMLIB (MM50 and MM100) datasets. In this study, the computational results for the first time demonstrate that the number of preemption points depend heavily on fluctuations of non-renewable resources and number of skills. It is also shown that considering multi-skill renewable resources is an effective factor in project makespan. In J20, there were both a four-unit reduction and increase in the number of preemption points achieving by increasing the average amount of available non-renewable resources by 23 units and decreasing it by 22 units, respectively. Additionally, when seven skills of renewable resources were reduced, the number of preemption points increased by seven units. In this problem instance, project is completed within 28 days considering multi-skill renewable resources, whereas the project makespan is reported 33 days without considering them. Various sensitivity analyses are presented to evaluate the proposed mathematical model and the overall solution approach. Comparative analysis is conducted to compare the schedule in crisp and uncertain conditions. Eventually, the importance of considering multi-skill resources in project scheduling is illustrated compared to not considering them.

Optimization-based Scheduling of Construction Projects with Generalized Precedence Relationships: A Real-Life Case Study

Optimization-based Scheduling of Construction Projects with Generalized Precedence Relationships: A Real-Life Case Study

Simultaneous scheduling of multiple construction projects considering supplier selection and material transportation routing

In a construction supply chain, supply-related decisions can affect project scheduling because the project activities require essential resources to start. This study wants to show how the integration of project scheduling with supplier selection and transportation routing creates value in the entire project supply chain. Therefore, an integrated problem including the three mentioned concepts is considered in an organization managing multiple construction projects. Moreover, the following conditions are assumed in the problem to make it closer to the real situations of construction projects: (1) the quality of all projects is inspected by a single committee; (2) suppliers sell the resources with incremental discounts; (3) generalized precedence relations are considered between the project activities. In order to address the research problem, a mathematical model is proposed based on mixed-integer linear programming. The model is hard to solve because it simultaneously involves multi-project scheduling and vehicle routing. Therefore, a solution method based on the tabu search (TS) algorithm is suggested, validated with small-scale and big-scale examples. This method is used to compare the suggested model with two related models. The comparisons show that the proposed model creates a better balance between costs of different sectors in the project supply chain. Achieving this balance decreases the total cost associated with the problem and increases customer satisfaction. As a result of these findings, project managers and related researchers should pay more attention to supply chain integration in their problems.

Project scheduling with generalized precedence relations: A new method to analyze criticalities and flexibilities

In this paper, we illustrate a new method to overcome the failures of the theory proposed by Elmaghraby and Kamburowski (1992) and De Reyck (1998) for the analysis of activity criticalities and flexibilities in non-preemptive project scheduling with generalized precedence relations under unlimited resources. These failures, discussed in detail in this paper, call for a new approach to study this problem. We provide new definitions of criticalities and consequently new tools for their identification within a more general framework without ambiguities.

Modified Pareto archived evolution strategy for the multi-skill project scheduling problem with generalized precedence relations

In this research, we study the multi-skill resource-constrained project scheduling problem, where there are generalized precedence relations between project activities. Workforces are able to perform one or several skills, and their efficiency improves by repeating their skills. For this problem, a mathematical formulation has been proposed that aims to optimize project completion time, reworking risks of activities, and costs of processing the activities, simultaneously. A modified version of the Pareto Archived Evolution Strategy (MV-PAES) is developed to solve the problem. Contrary to the basic PAES, this algorithm operates based on a population of solutions. For the proposed method, we devised crossover and mutation operators, which strengthen this algorithm in exploring solution space. Comprehensive numerical tests have been conducted to evaluate the performance of the MV-PAES in comparison with two other meta-heuristics. The outputs show the excellence of the MV-PAES in comparison with other methods. A real-world software development project has been studied to demonstrate the practicality of the proposed model for real-world environment. The influence of competency evolution has been investigated in this case study. The results imply that the competency evolution has a considerable impact on the objective function values.

Preprocessing the Discrete Time-Cost Tradeoff Problem with Generalized Precedence Relations

This study investigates the deadline of the discrete time-cost tradeoff problem (DTCTP-D) with generalized precedence relations (GPRs). This problem requires modes to be assigned to the activities of a project such that the total cost is minimized and the total completion time and the precedence constraints are satisfied. Anomalies under GPRs are irreconcilable with many current theories and methods. We propose a preprocessing technology, an equivalent simplification approach, which is an effective method for solving large-scale complex problems. We first study a way to deal with the anomalies under GPRs, such as the reduce (increase) in project completion as a consequence of prolonging (shortening) an activity, and discover relationships between time floats and path lengths. Then, based on the theories, we transform the simplification into a time float problem and design a polynomial algorithm. We perform the simplification and improve the efficiency of the solution by deleting redundant calculation objects.

Multi-mode Resource Constrained Project Scheduling with Alternative Prerequisites: New Models and Computational Studies

We study the multi-mode resource constrained project scheduling problem (MRCPSP), which we generalize to account for the case of alternative prerequisite activities (MRCPSP-AP). The MRCPSP-AP arises in many real-world applications when two or more activities can serve as the required precursor to some subsequent activity, and it aims to determine not only the optimal schedule but also the optimal activity network. We propose a total of seven discrete-time models and compare their numerical tractability through comprehensive computational studies on literature benchmarks. We also extend the well-known critical path method to handle the existence of alternative prerequisites, allowing us to precalculate tight time windows for each activity. Our computational study reveals that a formulation implementing the generalized precedence relationships in a time-aggregated fashion dominates the rest, in terms of solution quality and runtime.

Zero-One Formulation for a Partial Resource-Constrained Project Scheduling Problem with Generalized Precedence Relations

AbstractThe resource-constrained project scheduling problem (RCPSP) aims to arrange activities to meet resource restrictions. In real life, not all resource types are constrained, nor do all activi...

Invisible consumptions and enlargements of activity floats under generalized precedence relations

Generalized precedence relations (GPRs) between activities widely exist in modern construction projects. Time floats of activities (activity floats) are indispensable to arrange the activities to cope with unstable external conditions. This paper discovers that the GPRs result in new singularities of activity floats—time floats of an activity can be consumed and enlarged imperceptibly even if the activity has not started and all activities don’t consume their time floats. The singularities are called invisible consumptions and enlargements of activity floats. This paper analyzes the singularities and presents algorithms to identify and quantize them. The new singular characteristics of activity floats may weaken current optimization approaches for project scheduling. Inspired by the characteristics, this paper develops an emergency resource leveling with GPRs that focuses on emergency actions for the dynamic and uncertain environment. An illustration demonstrates that the correct solution relies on the invisible consumptions and enlargements of activity floats.

New Quantization Approach for the Anomaly: The Increase in Time Float following Consumption

Anomalous scenarios in projects with generalized precedence relations (GPRs) have been arousing widely interest. A recent relevant discovery of anomaly under GPRs is that an activity’s time float increases following its consumption. The scenario is contrary to a common idea for plan management, and it also changes relationships between time floats and maximum prolongations of activity durations. Classic computations may be invalid to time parameters under GPRs. This study tests the fact that the current analysis on the anomaly has limitations so that it may provide improper guidelines for project scheduling and lead to undesirable effects. A new quantization algorithm is presented for the anomaly that overcomes the limitations of the current works. In particular, the algorithm confirms accurate time parameters and maximum duration prolongations of activities under constraints that retain project duration. The accuracy of quantization for the anomaly is particularly important for project scheduling with GPRs. Moreover, an application of the anomaly is developed in the resource-constrained project scheduling with activity splitting and GPRs, and an illustration is provided to test the fact that the new quantization result of the anomaly is an essential guarantee to achieve optimal solutions.

Multi-mode resource leveling in projects with mode-dependent generalized precedence relations

In real-life project management, resource leveling is an important technique to ensure the effective use of resources, in which activities (a) can often be executed in alternative modes and (b) are constrained by precedence relations with minimum and maximum time lags that can be modeled using generalized precedence relations (GPRs). In addition, the values of the time lags tend to depend on activity modes. The resource leveling problem with multiple modes and mode-dependent GPRs (MRLP-GPR) is a generalization of the classic NP-hard resource leveling problem. To our knowledge, no literature exists regarding the MRLP-GPR.We propose several heuristics for the MRLP-GPR built upon two solution approaches: (a) a steepest descent algorithm and a fast descent algorithm that are based on a decomposition approach and (b) a hybrid estimation of distribution algorithm (EDA), which is based on an integration approach. Extensive computational experiments on a large number of benchmark instances are conducted to evaluate the proposed heuristics. A comparison of the results shows that our EDA outperforms or is competitive with three baseline heuristics (a random search algorithm and two variants of a genetic algorithm that is the best-performing metaheuristic for the single-mode resource leveling problem with GPRs). Our results can serve as a benchmark for future research. Our model and solution algorithms provide an automatic tool for the project manager's multi-mode resource leveling decision-making.

A New Stochastic Time-Cost-Quality Trade-Off Project Scheduling Problem Considering Multiple-Execution Modes, Preemption, and Generalized Precedence Relations

Project managers always try to make the best decisions in order to complete their projects in the shortest period of time, with the least amount of costs, and with the highest degree of quality. Therefore, the process of decision-making is conducted in a triangle of time, costs, and quality. This triangle is a crucial part of management process throughout the execution of the project. However, in all problems, some unpredictable situations may be faced. In such situations, some or all parameters of the problem are expressed by uncertain variables. In this paper, a stochastic time-costquality trade off project scheduling problem (STCQTP) considering multiple-execution modes, preemption, and generalized precedence relations is developed. In order to solve the STCQTP, a hybrid solution approach based on Stochastic Chance Constraint Programming (SCCP) and Goal Programming (GP) is proposed. SCCP and GP are used to handle the uncertain nature and multiple-objectives of STCQTP, respectively. Numerical example is solved in order to illustrate the applicability of proposed model and solution approach.

Theory and application of reciprocal transformation of “path problem” and “time float problem”

The concept of analytic geometry, i.e. , the reciprocal transformation of geometry and algebra, hints a prospect for the reciprocal transformation of the “path problem” and the “time float problem”. A reciprocal transformation can be used to solve a complex problem in one field by translating it into a simpler one in another field. In this case, owing to the generalized concept of length, various types of non-path problems such as the optimum allocation problem and equipment replacement problem can be represented as “path problems”. A “length network”, which is generalized in nature, is translated into a “time network” by changing the meanings of arcs and lengths. Furthermore, “path problems” can be represented as “time float problems” by discovering the relationships of paths in the length network and time floats in the time network. Base on the relationships, “time float problems” also can be represented as “path problems”. The relationships are keys to updating the mutual correspondence of path problems and time float problems. The relationships mirror the uniform qualities of networks in various disciplines and fields. We apply such relationships to solve optimum allocation problems, equipment replacement problems, and path problems with required lengths and to analyze anomalies in projects under generalized precedence relations. These applications test the effectiveness of our proposed approach to theoretical and applied researches in various disciplines and fields.

Lower bounds for the Event Scheduling Problem with Consumption and Production of Resources

The Event Scheduling Problem with Consumption and Production of Resources (ESPCPR) is a general scheduling problem where the availability of a resource is depleted and replenished at the occurrence times of a set of events. This problem is an extension of the Resource Constrained Project Scheduling Problem (RCPSP) where activities are replaced by events, which have to be scheduled subject to generalized precedence relations. The aim of this paper is to show the connections between ESPCPR and classical scheduling problems in order to bring new lower bounds for ESPCPR. We start by recalling some similar models in literature such as the Project Scheduling with Inventory Constraints and the Financing Problem. Subsequently, we describe how to model classical scheduling problems using ESPCPR. Finally, we propose four lower bounds for this problem. The obtained computational results confirm their effectiveness.

Resource levelling in project scheduling with generalized precedence relationships and variable execution intensities

We study the problem of levelling resources in a project with generalized precedence relationships, given a deadline for the completion of all the activities and variable execution intensities and flexible durations of the activities. Variable execution intensities have been taken into account firstly by Kis (Math Program 103(3):515---539, 2005) applied to a real world scenario in which, due to the physical characteristics of some manufacturing processes, the effort associated with a certain activity for its execution may vary over time. Generalized precedence relationships and variable intensity execution and duration have not been dealt with together to the best of our knowledge. For this novel problem we propose a mixed-integer linear programming formulation, a lower bound based on Lagrangian relaxation, and a branch and bound algorithm. Computational results on known benchmarks are provided.

Minimizing the Project Cost with Generalized Precedence Relations

Minimizing the Project Cost with Generalized Precedence Relations

On the efficient modeling and solution of the multi-mode resource-constrained project scheduling problem with generalized precedence relations

For variants of the single-mode resource-constrained project scheduling problem, state-of-the-art exact algorithms combine a Branch and Bound algorithm with principles from Constraint Programming and Boolean Satisfiability Solving. In our paper, we propose new exact approaches extending the above principles to the multi-mode RCPSP (MRCPSP) with generalized precedence relations (GPRs). More precisely, we implemented two constraint handlers cumulativemm and gprecedencemm for the optimization framework SCIP. With the latter, one can model renewable resource constraints and GPRs in the context of multi-mode activities, respectively. Moreover, they integrate domain propagation and explanation generation techniques for the above problem characteristics. We formulate three SCIP-models for the MRCPSP with GPRs, two without and one with our constraint handler gprecedencemm. Our computational results on instances from the literature with 30, 50 and 100 activities show that the addition of this constraint handler significantly strengthens the SCIP-model. Moreover, we outperform the state-of-the-art exact approach on instances with 50 activities when imposing time limits of 27 s. In addition, we close (find the optimal solution and prove its optimality for) 289 open instances and improve the best known makespan for 271 instances from the literature.

The Fuzzy Project Scheduling Problem with Minimal Generalized Precedence Relations

AbstractIn scheduling, estimations are affected by the imprecision of limited information on future events, and the reduction in the number and level of detail of activities. Overlapping of processes and activities requires the study of their continuity, along with analysis of the risks associated with imprecision. In this line, this article proposes a fuzzy heuristic model for the Project Scheduling Problem with flows and minimal feeding, time and work Generalized Precedence Relations with a realistic approach to overlapping, in which the continuity of processes and activities is allowed in a discretionary way. This fuzzy algorithm handles the balance of process flows, and computes the optimal fragmentation of tasks, avoiding the interruption of the critical path and reverse criticality. The goodness of this approach is tested on several problems found in the literature; furthermore, an example of a 15‐story building was used to compare the better performance of the algorithm implemented in Visual Basic for Applications (Excel) over that same example input in Primavera© P6 Professional V8.2.0, using five different scenarios.