Resource Constrained Project Scheduling Problem Research Articles

Proposing new clustering-based algorithms for the multi-skilled resource-constrained multi-project scheduling problem with resource leveling adjustments

PurposeThe target of this research is to develop a mathematical model which combines the Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) and the Multi-Skilled Resource-Constrained Project Scheduling Problem (MSRCPSP). Due to the importance of resource management, the proposed formulation comprises resource leveling considerations as well. The model aims to simultaneously optimize: (1) the total time to accomplish all projects and (2) the total deviation of resource consumptions from the uniform utilization levels.Design/methodology/approachThe K-Means (KM) and Fuzzy C-Means (FCM) clustering methods have been separately applied to discover the clusters of activities which have the most similar resource demands. The discovered clusters are given to the scheduling process as priori knowledge. Consequently, the execution times of the activities with the most common resource requests will not overlap. The intricacy of the problem led us to incorporate the KM and FCM techniques into a meta-heuristic called the Bi-objective Symbiosis Organisms Search (BSOS) algorithm so that the real-life samples of this problem could be solved. Therefore, two clustering-based algorithms, namely, the BSOS-KM and BSOS-FCM have been developed.FindingsComparisons between the BSOS-KM, BSOS-FCM and the BSOS method without any clustering approach show that the clustering techniques could enhance the optimization process. Another hybrid clustering-based methodology called the NSGA-II-SPE has been added to the comparisons to evaluate the developed resource leveling framework.Practical implicationsThe practical importance of the model and the clustering-based algorithms have been demonstrated in planning several construction projects, where multiple water supply systems are concurrently constructed.Originality/valueReviewing the literature revealed that there was a need for a hybrid formulation that embraces the characteristics of the RCMPSP and MSRCPSP with resource leveling considerations. Moreover, the application of clustering algorithms as resource leveling techniques was not studied sufficiently in the literature.

A Risk Minimization Model for a Multi-Skilled, Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off

A novel model called Multi-Skilled, Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off (MS-MRCPSP-DTCQRTP) was formulated, focusing primarily on minimizing project risks. This integer programming-based model generates various schedules that aim to optimize time, cost, quality, and risk, either individually or by achieving a balanced combination of these factors. By allocating accessible resources to the tasks of the project and adhering to precedence and resource constraints dictated by availability and skills, a collection of viable schedules was generated. Using a uniform distribution for time, cost, quality, and risk, three project case studies were derived from existing literature and expanded upon. These case studies were then employed to showcase the model. To generate optimal solutions, an open-source Python-MIP package employing the branch-and-cut methodology was employed. It was found that time is not a factor in minimizing the risk of a project, except for large-scale projects. Meanwhile, cost is a factor in all sizes of the project. Quality has no significant impact on risk. Project managers must strike a balance between resources that contain skills set with short to medium duration, moderate to high cost, and moderate to high-quality level to minimize project risk.

Project scheduling to minimize the makespan under flexible resource profiles and marginal diminishing returns of the resource

A standard approach to project scheduling that tackles the problem of minimizing the makespan under variable resource profiles is the Flexible Resource-Constrained Project Scheduling Problem (FRCPSP). This approach traditionally considers constant marginal returns from increasing the allocation of a particular resource, whereas in practice, project and operational managers are often faced with diminishing marginal returns. This work is the first to integrate these two interrelated aspects of resource allocation (flexible profiles and diminishing marginal returns) in order to determine the optimal resource allocation and project scheduling that will minimize the project makespan. This paper develops a mixed-integer linear programming model to obtain an optimal solution of the FRCPSP assuming diminishing marginal returns as the resource allocations are increased. In addition, to solve medium-sized instances of the problem, a heuristic algorithm based on relaxation of this mixed-integer programming model is presented. Through a series of computational tests, we further show that the average deviation in the makespan between the two strategies (optimal vs. heuristic solution) does not exceed 5%.

Multi-skill resource-constrained project scheduling problem considering overlapping: fuzzy multi-objective programming approach to a case study

Resource-constrained project scheduling problem (RCPSP) is a broadly researched issue in the literature. The purpose of the classic form of the problem is scheduling a set of activities considering resource and precedence constraints for minimizing the project completion time. Companies mostly deal with the issue of properly assigning multi-skilled workforces and maintaining the needed skill levels while implementing projects. In this study, a novel MILP model with three objectives is presented to tackle multi-skill RCPSP (MS-RCPSP). This study concentrates on minimizing project makespan, minimizing resource costs as well as tardiness costs, and maximizing quality under uncertainty. However, the standard MS-RCPSP is not able to consider several practical engineering requirements owing to its narrow assumptions. Therefore, key assumptions including overlap between activities, tardiness penalties of activities and the rework duration concept for activities in this model are considered. Due to the complexity of the real world, interval valued fuzzy numbers are taken into account for some of the problem’s parameters. The efficiency of the proposed mathematical framework is represented using both a real case study to construct a railway bridge with 34 activities and large-size problem instances from MMLIB (MM50 and MM100). Since this model is multi-objective, a new extended IVF-ABS approach is presented in this study. Finally, the proposed approach is compared with two methods, namely SO and ABS, from the literature.

An integrated hybrid metaheuristic model for the constrained scheduling problem

Several problems in the domains of project management (PM) and operations research (OP) can be classified as optimization problems which are classically NP-Hard. One such highly important problem is the resource constrained project scheduling problem (RCPSP). The main aim of this problem is to find a schedule of the lowest and optimum makespan to complete a project, which involves resource as well as precedence constraints. But, being classically NP-Hard, the RCPSP requires exponential computational resources as the problem complexity increases. Thus, approximate techniques like computational intelligence (CI) based approaches provide better chances of finding near optimal solutions. This paper presents the usage of a hybrid technique using the phases of teaching learning-based optimization (TLBO) metaheuristic integrated with operators like crossover and mutation from the genetic algorithm (GA). An integrated hybrid using TLBO and 2-point crossover is applied in the teacher and learner phases to the discrete RCPSP problem. Further, to diversify the population, and enhance global search, the mutation operator is applied. The proposed model is extensively tested on well-known benchmark test instances and has been compared with other seminal works. The encouraging results make evident the efficiency of the provided solution for the RCPSP problem of varying magnitudes.

A novel swarm intelligence approach for the constrained scheduling problem

ABSTRACT The Resource Constrained Project Scheduling Problem (RCPSP) is a prevalent problem in the domains of Project Management and Operations Research. This problem demands a huge number of computational resources as the project’s complexity increases. Hence, approximate methods using heuristics and metaheuristics have proven to provide feasible solutions to the problem in acceptable time. This research adapts a prominent Swarm Intelligence (SI) metaheuristic, the Firefly Algorithm (FA), to solve the RCPSP with some modifications. By applying a 2-point crossover for the intensity-based firefly movement, a discrete framework has been provided. Further, to reduce the occurrence of the solution being stuck in the local optima, a swap-based mutation is introduced. The performance of the proposed research has been thoroughly evaluated through extensive experiments conducted on widely recognized benchmark instances. Comparison with seminal works demonstrated the competitiveness of the approach.

Automated design of priority rules for resource-constrained project scheduling problem using surrogate-assisted genetic programming

In the past few years, the genetic programming approach (GP) has been successfully used by researchers to design priority rules for the resource-constrained project scheduling problem (RCPSP) thanks to its high generalization ability and superior performance. However, one of the main drawbacks of the GP is that the fitness evaluation in the training process often requires a very high computational effort. In order to reduce the runtime of the training process, this research proposed four different surrogate models for the RCPSP. The experiment results have verified the effectiveness and the performance of the proposed surrogate models. It is shown that they achieve similar performance as the original model with the same number of evaluations and better performance with the same runtime. We have also tested the performance of one of our surrogate models with seven different population sizes to show that the selected surrogate model achieves similar performance for each population size as the original model, even when the searching space is sufficiently explored. Furthermore, we have investigated the accuracy of our proposed surrogate models and the size of the rules they designed. The result reveals that all the proposed surrogate models have high accuracy, and sometimes the rules found by them have a smaller size compared with the original model.

A GA-Based Scheduling Method for Civil Aircraft Distributed Production with Material Inventory Replenishment Consideration

The production of civil aircrafts is confronted with a significant demand for the interconnectivity of production resources among distributed factories, while the complex coupling relationships among various production resources might restrict the improvement of production efficiency. Therefore, researching scheduling methods for civil aircraft distributed production is necessary, but previous studies have not taken material inventory into account sufficiently. This article proposes a scheduling method for civil aircraft distributed production that aims to minimize the production time to complete all the jobs in a large production station under the condition of material inventory replenishment. Firstly, we analyze the factors constraining civil aircraft production efficiency, and formulize the production scheduling problem into the Resource-Constrained Project Scheduling Problem model with Inventory Replenishment (RCPSP-IR). Precedence constraints and resource constraints, especially the inventory constraints, are mainly considered in RCPSP-IR. To solve the corresponding scheduling problem, the Genetic Algorithm (GA) is applied and multiple approaches are introduced to handle the complex constraints and avoid local optimum. Finally, we applied the proposed scheduling method to a case study of a jet twin-engine civil aircraft production of COMAC. The results of the case study show that the proposed method can give a nearly optimal scheduling strategy to be applied to actual civil aircraft production.

Fast and Robust Resource-Constrained Scheduling with Graph Neural Networks

Resource-Constrained Project Scheduling Problems (RCPSPs) are NP-complete, which makes it challenging to efficiently solve large instances and robustify solutions in the presence of uncertainty. To remedy this, we learn to efficiently mimic the solutions produced by Constraint Programming (CP) solver, using a Graph Neural Network (GNN) architecture designed to capture the structure of RCPSPs. Since the GNN solution may violate constraints, we ensure schedule feasibility at inference time by extracting the task ordering from the GNN schedule and post-processing it with the well-known Schedule Generation Scheme (SGS). We find that SIREN, the resulting algorithm, produces schedules that are of higher quality than those produced by the CP solver within the same computation time budget. The speed and solution quality of SIREN make it suitable as a component of an on-line scenario-based optimisation procedure for RCPSPs with stochastic durations. This leads to the SERENE system, which robustly selects, in real-time, the best next tasks to start in order to minimise the average makespan over the scenarios. Empirically, SERENE achieves better average makespan over different realisations of uncertainty than deterministic algorithms that continuously reschedule on the basis of either the worst, best or average task durations.

MIMEM: A Hybrid Metaheuristic Method Solving the Resource Constrained Scheduling Problem

The Multi-Skill Resource-Constrained Project Scheduling Problem(MS-RCPSP) is an NP-Hard problem that involves scheduling activities whileaccounting for resource and technical constraints. This paper aims to present anovel hybrid algorithm called MIMEM, which combines the Memetic algorithm with the Inverse method to tackle the MS-RCPSP problem. The proposedalgorithm utilizes the inverse method to identify local extremes and then relocates the population to explore new solution spaces for further evolution. TheMIMEM algorithm is evaluated on the iMOPSE benchmark dataset, and the results demonstrate that it outperforms. The solution of the MS-RCPSP problemusing the MIMEM algorithm is a schedule that can be used for intelligent production planning in various industrial production fields instead of manual planning.

A problem-specific parallel pareto local search for the reactive decision support of a special RCPSP extension

The disaster information collection mission should be executed after the disaster occurs to provide details for the decision-makers. During the execution of the information collection mission, some disruptions may occur and prevent the resource used for information collection from completing the mission as planned. It is difficult for decision-makers to make reactive resource scheduling plan that optimize the mission’s execution time, quality, and cost at the same time under such circumstances. This article focuses on designing the reactive decision support algorithm for the disaster information collection resource scheduling, which aims to provide multi high-quality scheduling plans for decision-makers to choose. The problem studied in this article is modeled as an extension of Resource-Constrained Project Scheduling Problem (RCPSP). First, the basic problem formulation for a normal schedule and two disruption recovery models are presented. Second, a novel framework of a parallel pareto local search based on decomposition is designed to repair the schedule within the time limit. Third, two solution acceptance criteria based on constraint handling and negative correlation are specially designed to maintain high-quality population with diversity. The experiments show that the proposed method outperforms the other competitors with respect to Inverted Generational Distance, Spacing, and Hypervolume, which means that the proposed method can help decision-makers to make better decisions.

A late-mover genetic algorithm for resource-constrained project-scheduling problems

The Resource-Constrained Project Scheduling Problem (RCPSP) plays a critical role in various management applications. Despite its importance, research efforts are still ongoing to improve lower bounds and reduce deviation values. This study aims to develop an innovative and straightforward algorithm for RCPSPs by integrating the “1+1” evolution strategy into a genetic algorithm framework. Unlike most existing studies, the proposed algorithm eliminates the need for parameter tuning and utilizes real-valued numbers and path representation as chromosomes. Consequently, it does not require priority rules to construct a feasible schedule. The algorithm's performance is evaluated using the RCPSP benchmark and compared to alternative algorithms, such as cWSA, Hybrid PSO, and EESHHO. The experimental results demonstrate that the proposed algorithm is competitive, while the exploration capability remains a challenge for further investigation.

A holistic analysis of maritime logistics process in fuzzy environment in terms of business process management

PurposeThe aim of this study is to provide a holistic analysis of all possible maritime business logistics processes related to import and export shipments in a fuzzy environment through a case study of a maritime logistics company based on the as-is and to-be models within business process management (BPM).Design/methodology/approachThe analyses considered the following perspectives: (i) in the stage of the process identification, the definition of the problem was carried out; (ii) in the stage of the process discovery, ocean department was divided into ocean export/import operation departments; ocean export/import operation were divided into freight collect/prepaid operation processes; ocean export/import logistics activity groups were broken down into sub-activities for freight collect/prepaid operation; the logistics activity groups and their sub-activities were defined; each sub-activity as either operation or documentation process group was classified; the durations of sub-activities were evaluated by decision-makers (DMs) as fuzzy sets (FSs); the monthly total jobs activities were estimated by DMs as FSs; the applied to monthly jobs activities of total shipments were estimated by DMs as FSs; the durations of each sub-activities were aggregated; the duration of the logistics activity groups and the sub-activities for per job were calculated; the cumulative workload of logistics activity groups and sub-activities were calculated; the duration of sub-activities for per job as operation or documentation departments were calculated, (iii) in the stage of the process analysis, cumulative ocean export/import workload as operation or documentation for freight collect/prepaid were calculated; duration of activity groups and sub-activities for per job as operation or documentation were calculated; cumulative workload activity groups and sub-activities as operation or documentation were calculated, (iv) in the stage of the process redesign, cumulative workload, process cycle time as operation and documentation group and required labor force were calculated; the process cycle time of the theoretical, the as-is model and the to-be model were calculated: (i) the theoretical minimum process cycle time without resource were calculated by the critical path method (CPM), (ii) the process cycle time of the as-is model perspective with the 1 person resource constraint and (iii) the process cycle time of the to-be model perspective with the 2-person resource constraint were calculated by the resource constrained project scheduling problem (RCPSP) method.FindingsThe methodology for analyzing the ocean department operation process was successfully implemented in a real-life case study. It is observed that the results of the to-be model can be applicable for the company. The BPM-proposed methodology is applicable for the maritime logistics industry in the present study; however, it can be applied to other companies in maritime logistics as well as other industries.Originality/valueThis study contributes to research using BPM methodology in maritime logistics. This is the first study the logistics process analyses were carried out in terms of including all operation processes for a company. All processes were analyzed by using BPM methodology in maritime logistics. This study demonstrated the application of the BPM as-is and to-be models to maritime logistics. The as-is and the to-be models of the BPM methodology were applied in maritime logistics.Research implicationsThis methodology applied in this study can enable organizations operating in the time-urgent maritime logistics sector to manage their logistics processes more efficiently, increase customer satisfaction, reduce the risks of customer loss due to poor operational performance and increase profits in the long term. Through the use of these methodologies utilizing FSs, the CPM and the RCPSP methods, this study is expected to make contributions to the BPM literature and provide original insights into the field. Furthermore, this study will undertake a comprehensive analysis of maritime logistics with respect to BPM to deliver noteworthy contributions to the maritime logistics literature and provide original perspectives into the field.

On Propeties of the LIP Model in the Class of RCPSPs

The Resource-Constrained Project Scheduling Problem (RCPSP) is a significant and important issue in the field of project management. It arises during project planning when resources must be allocated among tasks with specific time constraints. Solving this problem enables the optimization of project execution time, minimization of resource costs, and increased efficiency of the entire team’s work. Due to the increasing complexity of projects, the development of new methods and algorithms to solve RCPSP is relevant nowadays. The existing methods for obtaining approximate solutions with guaranteed accuracy are characterized by high computational complexity and are often ineffective in considering the specific constraints of the problem. Fast heuristic approaches also have several drawbacks related to fine-tuning algorithm parameters and strong dependence on the quality of the initial solution. This paper investigates the features of the linear integer programming (LIP) model to solve RCPSP. The proposed LIP model is universal and scalable, enabling it to fully consider all specific aspects of the problem. The paper provides a construction algorithm of a functional space of the model and discusses the estimation of complexity. From the estimation of the mentioned algorithm’s complexity, it is observed that the general complexity of the proposed approach is proportional to a controlled parameter of the LIP. Increasing this controlled parameter can significantly reduce the dimensionality of the initial problem, thus leading to the effectiveness of the LIP model-based approach in terms of computational resources. An upper bound for the value of this parameter is obtained for a special case of the RCPSP. Using the obtained balanced value, a numerical experiment was carried out on real-world samples.

Complicated Time-Constrained Project Scheduling Problems in Water Conservancy Construction

Water conservancy project scheduling is an extension to the classic resource-constrained project scheduling problem (RCPSP). It is limited by special time constraints called “forbidden time windows” during which certain activities cannot be executed. To address this issue, a specific RCPSP model is proposed, and an approach is designated for it which incorporates both a priority rule-based heuristic algorithm to obtain an acceptable solution, and a hybrid genetic algorithm to further improve the quality of the solution. In the genetic algorithm, we introduce a new crossover operator for the forbidden time window and adopt double justification and elitism strategies. Finally, we conduct simulated experiments on a project scheduling problem library to compare the proposed algorithm with other priority-rule based heuristics, and the results demonstrate the superiority of our algorithm.

Solving resource-constrained project scheduling problems under different activity assumptions

Much research has focused on Resource-Constrained Project Scheduling Problems (RCPSP(A)), where the focus has been on limited or even inadequate resources as a type of risk to implement project activities and decrease completion time. Activity interruption assumptions are considered in this paper. The RCPSP(B) is the RCPSP(A) when the non-preemption assumption is relaxed but the RCPSP(D) is the RCPSP(A) when both the non-preemption and the fixed resources are relaxed. A fundamental assertion of this paper is that the A, B, and D scheduling interruption categories can be interchanged with sufficient managerial effort. Effectively, this becomes a constraint relaxation problem. Because the capacity to manage scheduling interruptions is limited, the issue is which category A activities should be relaxed to type B and D, and which category B activities should be relaxed to type D. This paper introduces the interruptible and flexible planning project activity concept and presents a heuristic method to accomplish the reassessment of category types from A to B and D. First, the heuristic changes the interruptible activities (IAs) under categories A, B, and D. Secondly, critical interruptible activities (CIAs) that have significant impacts in reducing the project makespan are identified. This increases the manager's decision choices with respect to scheduling activities as category type A, B, or D. The methodology facilitates an understanding of how A, B, and D interpretability assumptions affect the project makespan and helps project manager to selectively choose how specific activities in a project should be managed.

New resource-constrained project scheduling instances for testing (meta-)heuristic scheduling algorithms

The resource-constrained project scheduling problem (RCPSP) is a well-known scheduling problem that has attracted attention since several decades. Despite the rapid progress of exact and (meta-)heuristic procedures, the problem can still not be solved to optimality for many problem instances of relatively small size. Due to the known complexity, many researchers have proposed fast and efficient meta-heuristic solution procedures that can solve the problem to near optimality. Despite the excellent results obtained in the last decades, little is known why some heuristics perform better than others. However, if researchers better understood why some meta-heuristic procedures generate good solutions for some project instances while still falling short for others, this could lead to insights to improve these meta-heuristics, ultimately leading to stronger algorithms and better overall solution quality.In this study, a new hardness indicator is proposed to measure the difficulty of providing near-optimal solutions for meta-heuristic procedures. The new indicator is based on a new concept that uses the σ distance metric to describe the solution space of the problem instance, and relies on current knowledge for lower and upper bound calculations for problem instances from five known datasets in the literature.This new indicator, which will be called the σD indicator, will be used not only to measure the hardness of existing project datasets, but also to generate a new benchmark dataset that can be used for future research purposes. The new dataset contains project instances with different values for the σD indicator, and it will be shown that the value of the σ distance metric actually describes the difficulty of the project instances through two fast and efficient meta-heuristic procedures from the literature.

A Formulation for the Stochastic Multi-Mode Resource-Constrained Project Scheduling Problem Solved with a Multi-Start Iterated Local Search Metaheuristic

This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version of the problem. For its deterministic version, the MRCPSP is an NP-hard optimization problem that has been widely studied. The problem deals with a trade-off between the amount of resources that each project activity requires and its duration. In the case of the proposed stochastic formulation, the execution times of the activities are uncertain. Benchmark instances of projects with 10, 20, 30, and 50 activities from well-known public libraries were adapted to create test instances. The adapted algorithm proved to be capable and efficient for solving the proposed stochastic problem.

New pseudo polynomial algorithms for a partial resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) aims to arrange activities to be processed by limit renewable resources. In real life, not all resources are constrained, nor do all activities face resource restrictions in a project. The RCPSP may emerge in parts of the project, which could be named as the partial RCPSP. In this paper, we consider a typical partial RCPSP that arranging $ K $ renewable resources to execute $ H $ parallel activities in a project for minimum makespan. In particular, we consider the problem under hypotheses that $ N=2 $ and $ N<H\le 2N $. We study the problem from the perspective of 'resource-unconstrained$ \rightarrow $resource-constrained', and discover the relationships between 'scheduling the $ H $ activities' and 'project makespan'. Based on the relationships, we redescribe the problem as new formats, which include only the $ H $ considered activities instead of all activities and emphasize the positions of theses activities on the activity-chains, and then present pseudo polynomial time algorithms for the problem under the hypotheses of $ N=2 $. We evaluate the performance of our algorithms, and present detailed computational results of instances that evaluate the efficiency and competitiveness of our procedure. For example, computational experiments test that about 0.008 seconds average is required for exactly disposing 300 parallel activities using our algorithms, while about 432 seconds average is required using general exact approaches. The proposed theories and methodologies can be extended to general partial RCPSP and some important types of RCPSP (such as reactive RCPSP). Furthermore, the obtained results may enlighten ideas and more effective theoretical tools for general RCPSP/MS-RCPSP.

A convolutional neural network for the resource-constrained project scheduling problem (RCPSP): A new approach

All projects require a structure to meet project requirements and achieve established goals. This framework is called project management. Therefore, project management plays an important role in national development and economic growth. Project management includes various knowledge areas such as project integration management, project scope management, project schedule management, etc. The article focuses on the resource-constrained project scheduling known as problem so- called the resource-constrained project scheduling problem (RCPSP). The RCPSP is a part of schedule management. The standard RCPSP has two important constraints, resource constraints and precedence relationships of activities during project scheduling. The objective of the problem is to optimize and minimize the project duration, subject to the above constraints. In this paper, we develop a convolutional neural network approach to solve the standard single mode RCPSP. The advantage of this algorithm over conventional methods such as metaheuristics is that it does not need to generate many solutions or populations. In this paper, the serial schedule generation scheme (SSGS) is used to schedule the project activities using an evolved convolutional neural network (CNN) as a tool to select an appropriate priority rule to filter out a candidate activity. The evolved CNN learns according to the eight project parameters, namely network complexity, resource factor, resource strength, average work per activity, etc. The above parameters are the inputs of the network and are recalculated at each step of the project planning. Moreover, the developed network has priority rules which are the outputs of the developed neural network. Therefore, after the learning process, the network can automatically select an appropriate priority rule to filter an activity from the eligible activities. In this way, the algorithm is able to schedule all project activities according to the given project constraints. Finally, the performance of the Convolutional Neural Network (CNN) approach is investigated using standard benchmark problems from PSPLIB in comparison to the MLFNN approach and standard metaheuristics.