Multi-mode Resource-constrained Project Scheduling Problem Research Articles

Bi-objective optimization of a multi-mode, multi-site resource-constrained project scheduling problem

PurposeThis study aims to deal with the multi-mode resource-constrained project scheduling problem (MRCPSP) with the ability to transport resources among multiple sites, aiming to minimize the total completion time and the total cost of the project simultaneously.Design/methodology/approachTo deal with the problem under consideration, a bi-objective optimization model is developed. All activities are interconnected by finish-start precedence relations, and pre-emption is not allowed. Then, the ɛ-constraint optimization method is used to solve 24 different-sized instances, ranging from 5 to 120 activities, and report the makespan, total cost and CPU time. A set of Pareto-optimal solutions are determined for some instances, and sensitivity analyses are performed to find the impact of changing parameters on objective values.FindingsResults highlight the importance of resource transportability assumption on project completion time and cost, providing useful insights for decision makers and practitioners.Originality/valueA novel bi-objective optimization model is proposed to deal with the multi-site MRCPSP, considering both the cost and time of resource transportation between multiple sites. To the best of the authors’ knowledge, none of the studies in the project scheduling area has yet addressed this problem.

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.

A robust chance-constrained programming approach for a bi-objective pre-emptive multi-mode resource-constrained project scheduling problem with time crashing

The presented study proposes a novel bi-objective mixed integer linear programming (MILP) framework for the multi-mode resource-constrained project scheduling problem (MRCPSP) with pre-emptive and non-preemptive activities splitting under uncertain conditions. Minimising the project makespan and resource costs are the considered objectives. Renewable and non-renewable resources along with different modes are taken into account for activities implementation. Additionally, some activities can be crashed by consuming additional renewable and non-renewable resources. Model uncertainty is efficiently addressed by utilising a fuzzy chance constrained programming (CPP) method as well as extending two robust possibilistic programming models. The capability of the presented mathematical framework is validated using problem instances from PSPLIB (j10, j14, j20, and j30) and MMLIB (MM50 and MM100). Finally, a detailed computational comparison is presented to assess the performance of the two robust possibilistic programming models.

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.

An integrated chance-constrained stochastic model for a preemptive multi-skilled multi-mode resource-constrained project scheduling problem: A case study of building a sports center

A multi-mode resource-constrained project scheduling problem (MRCPSP) with multiple skills is investigated in this paper. Unlike the traditional form of this problem, and considering the real-world project circumstances, project activities can be preempted. In this paper, a new multi-objective mixed-integer linear programming (MILP) model with three objective functions is extended. These objectives are: (1) minimizing the project makespan, (2) minimizing the total resource costs, and (3) minimizing the total project risk. Based on real-life projects, non-renewable resources are represented as an uncertain stochastic parameter. To cope with the uncertain environment, chance-constrained programming with a confidence level is considered. A real-world construction project of a sports center in Tehran is utilized to demonstrate the applicability of the presented formulation. A well-known lexicographic optimization method, namely AUGMECON2, is applied to solve the proposed formulation with three objectives. Ultimately, for the case study and two datasets J30 and MM50, the proposed lexicographic optimization algorithm is compared with an efficient multi-objective mathematical programming technique known as the AUGMECON method. The comparison is based on performance metrics (i.e., IGD and HV) commonly used in multi-objective optimization. The results show the relative dominance of the proposed lexicographic optimization algorithm over the AUGMECON method in all sizes of the problem instances.

A data-driven meta-learning recommendation model for multi-mode resource constrained project scheduling problem

Meta-heuristics widely proposed in addressing multi-mode resource constrained project scheduling problem (MRCPSP) are problem-dependent. This paper first proposes an adaptive data-driven meta-learning Meta-heuristic Recommendation Model (MRM) to solve MRCPSP intelligently and efficiently. By learning the association between problem meta-features and algorithm performance, MRM can identify the most appropriate algorithm for different MRCPSPs. Multiclass Support Vector Machine (MCSVM) are integrated to train the classifiers for predicting the performance of the candidate meta-heuristics. To validate the proposed MRM, the performance is evaluated and compared in terms of accuracy, precision, sensitivity, and comprehensive evaluation index. In the experiments of 4 scenarios with 2 strategies, the average optimization and prediction accuracies are higher than 90% without increase in computational complexity. Comprehensive experiments and numerical results demonstrate the outperforming performance of the proposed MRM across various MRCPSP.

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.

A Constraint Programming Formulation of the Multi-Mode Resource-Constrained Project Scheduling Problem for the Flexible Job Shop Scheduling Problem

A Constraint Programming Formulation of the Multi-Mode Resource-Constrained Project Scheduling Problem for the Flexible Job Shop Scheduling Problem

Pro-Reactive Approach for Project Scheduling Under Unpredictable Disruptions.

Existing solution approaches for handling disruptions in project scheduling use either proactive or reactive methods. However, both techniques suffer from some drawbacks that affect the performance of the optimization process in obtaining good quality schedules. Therefore, in this article, we develop an auto-configured multioperator evolutionary approach, with a novel pro-reactive scheme for handling disruptions in multimode resource-constrained project scheduling problems (MM-RCPSPs). In this article, our primary objective is to minimize the makespan of a project. However, we also have secondary objectives, such as maximizing the free resources (FRs) and minimizing the deviation of activity finishing time. As the existence of FR may lead to a suboptimal solution, we propose a new operator for the evolutionary approach and two new heuristics to enhance the algorithm's performance. The proposed methodology is tested and analyzed by solving a set of benchmark problems, with its results showing its superiority with respect to state-of-the-art algorithms in terms of the quality of the solutions obtained.

A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply

In a resource-constrained project scheduling problem, most studies ignore that resource supply is a separate optimization problem, which is not in line with the actual situation. In this study, the project scheduling problem and the resource supply problem are regarded as a dynamic game system, with interactive influences and constraints. This study proposes a Stackelberg dynamic game model based on the engineering supply chain perspective. In this model, the inherent conflicts and complex interactions between the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP) and the Multi-Period Supply Chain Problem (MPSCP) are studied to determine the optimal equilibrium strategy. A two-level multi-objective programming method is used to solve the problem. The MRCPSP is the upper-level planning used to optimize project scheduling and activity mode selection to minimize project cost and duration; MPSCP is a lower-level planning method that seeks to make resource transportation decisions at a lower cost. A two-layer hybrid algorithm, consisting of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), is proposed to determine the optimal equilibrium strategy. Finally, the applicability and effectiveness of the proposed optimization method are evaluated through a case study of a large hydropower construction project, and management suggestions for related departments are provided.

A Binary Integer Linear Programming Approach for Risk Minimization of a Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off

The multi-mode resource-constrained project scheduling problem (MRCPSP) allows project managers to assign schedules and limited resources to project activities while minimizing total duration. This time objective has been extended to include the trade-offs of cost and quality called the discrete time-cost-quality trade-off problem (DTCQTP) to provide project managers an overview of indicators affecting project performance. However, the impacts of the COVID-19 pandemic have led project managers and consultants to assess their projects’ risks regarding scheduling and resource assignment decisions. Hence, this paper aims to extend the MRCPSP and the DTCQTP to include risk at the resource level to highlight the importance of hiring the proper resources in project scheduling. A binary integer linear programming model named the multi-mode resource-constrained project scheduling with discrete time-cost-quality-risk trade-off (MRCPSP-DTCQRT) was developed with risk minimization as the objective function. A case study from prior literature was used to illustrate the model using the open-sourced Python-MIP package, which uses the branch-and-cut methodology for generating optimal solutions. A set of schedules that either prioritize time, cost, quality, risk, or a balance among the four was generated for the use of the project manager to make decisions based on the current situation. Future research may extend the model further to include resource skills, test large-scale case studies, and use other methodologies such as metaheuristics and machine learning to arrive at optimal solutions within reasonable computing time.

Multi‐start iterated local search metaheuristic for the multi‐mode resource‐constrained project scheduling problem

AbstractIn this paper a multi‐start iterated local search (MS‐ILS) algorithm is presented as a new and effective approach to solve the multi‐mode resource‐constrained project scheduling problem (MRCPSP). The MRCPSP is a well‐known project scheduling NP‐Hard optimization problem, in which there is a trade‐off between the duration of each project activity and the amount of resources they require to be completed. The proposed algorithm generates an initial solution, performs a local search to obtain a local optimum, subsequently, for a certain number of iterations, makes a perturbation to that local optimum and performs a new local search on the perturbed solution. This whole process then restarts with a different initial solution for a certain number of restarts. The algorithm was tested on benchmark instances of projects with 30, 50 and 100 activities from well‐known libraries. The obtained results were compared to recent benchmark results from the literature. The proposed algorithm outperforms other solution methods found in related literature for the largest tested instances (100 activities), while for smaller instances it shows to be quite competitive, in terms of the average deviation against known lower bounds.

A matheuristic approach to the multi-mode resource constrained project scheduling problem

This article addresses the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP). It is an NP-Hard problem and consists of scheduling all activities of a project, respecting the precedence order of these activities, which, once initiated, cannot be interrupted. Jobs have combinations of execution modes, in the form of different combinations of processing time and resource consumption. The objective is to minimize the duration of the project, finding start times for each project activity. This article proposes a Local Branching matheuristic strategy for solving MRCPSP. The influence of the parameters of the based local search method is verified, as well as the characterization of neighborhood structures that define a subproblem during the enumeration of the LB matheuristic. Two characterizations to define the subproblems are proposed, and one of them surpasses the characterization discussed in the literature. Computational tests were performed using sets of instances from the PSPLIB and MMLIB libraries. The best-known results for these instances in relation to the state-of-the-art are presented as a reference to validate the results obtained by the approach proposed in this article.

An adaptative bacterial foraging optimization algorithm for solving the MRCPSP with discounted cash flows

In this paper, a metaheuristic solution algorithm for solving the multi-mode resource-constrained project scheduling problem (MRCPSP) with discounted cash flows (MRCPSPDC) is proposed. This problem consists of determining a schedule such that the project is completed, maximizing the project’s net present value (NPV) while complying with the delivery deadline. The adaptative bacterial foraging optimization (ABFO) algorithm is a variation of the original bacterial foraging optimization (BFO), which is a nature-inspired metaheuristic optimization algorithm. We implement a version of the chemotactic operator based on a double justification of the activities given the cash flow. This metaheuristic has been tested in the PSPLIB and MMLIB benchmark datasets available in the literature with promising results. Our ABFO algorithm shows excellent performance in all tested instances and provides suitable solutions for the MRCPSP maximizing the NPV.

Developing a multi-mode doubly resource constrained project scheduling problem using meta-heuristic approaches

In real-life projects, a multi-mode resource-constrained project scheduling problem (MRCPSP) is one of the most crucial problems. Multi-mode resource requirements significantly increase the difficulty and increase the solution spaces. The purpose of this paper is to maximise the project profit by considering the real situation of a project in which the constraint of the predecessor relationships between the activities and doubly-resources in the multi-mode state is implemented. In this study, a problem with 16 activities is solved which includes two renewables, two non-renewable resources, a doubly-resource, and three performance modes for each activity. To evaluate the designed algorithms problem samples of different sizes are considered. Both doubly-constraint and the profit of activities are defined in this study. Since the type of the model is complicated, mega-heuristic approaches including the genetic algorithm (GA) and simulated-annealing (SA) are proposed as the research methods and their results are compared.

A Multi-Objective Scheduling Algorithm for Multi-Mode Resource Constrained Projects in the Presence of Uncertain Resource Availability

Goal: The issue of resource allocation is a major concern for project engineers in the scheduling process of a project. Resources over-allocation are often seen in practice after the scheduling of a project, which makes scheduling unhelpful. Modifying an over-allocated schedule is very complicated and requires a lot of effort and time. Besides, during the scheduling process of resource-constrained projects in the constructing companies, managers should concern more than one objective at the same time. This research aims to propose a new heuristic algorithm for minimizing project completion time, cost or maximizing quality of execution of activities simultaneously while multi-mode activities are taken into consideration.
 Design / Methodology / Approach: In this research, a new heuristic method is proposed for solving multi-objective scheduling problem for multi-mode resource constrained project scheduling problems (MRCPSPs) where the aim is maximizing the net present value (NPV) of project, minimize completion time and maximize the quality of executing activities simultaneously and along with emerging the uncertainty of resources availability and activity durations. The proposed method is then coded by Matlab® 2016.
 Results: The outcomes of solving small, medium and large scale case studies, the following results achieved: (i) the algorithm could solve all problems in different circumstances with no difficulties; (ii) the large scale problems (with 200 activities, 20 resources and 3 execution modes for each activity) could be solved in 4.43 seconds. (iii) in none of the studied cases over-allocation problem. The proposed method can be considered among the fastest scheduling algorithms found in the literature. In addition, it is found that makespan, NPV and quality have co-relation must be taken into consideration during the scheduling process.
 Limitations of the investigation: The main limitations of this research is that it only covers resource constrained project scheduling. Moreover, risk factors associated with the objectives of this research have yet to be addressed in future research studies.
 Practical implications: The performance of the algorithm is validated by using 24 series of dataset that are found in the literature. In order to verify its performance in real practice, it has been applied for a part of a construction project in Malaysia. The outcomes indicated that the algorithm scheduled the problem with 23 activities, 5 constrained resources and 2 execution modes in less than a second and with no over-allocations. The proposed multi-objective algorithm allows the project managers to consider NPV, completion time and quality of activities while scheduling a multi-mode project. In practice, this algorithm can provide a better atmosphere for managers while they aim to consider more than one objective during the scheduling process.
 Originality / Value: The proposed algorithm is original and can be of great value for future studies and managers in preventing resource over-allocation during the scheduling of multi-objective multi-mode resource constraint project scheduling. Moreover, it can help project managers to find near optimum solutions for complex multi-objective resource constraint projects faster and also with more accuracy.

Reactive heuristics for disrupted multi-mode resource-constrained project scheduling problem

This paper accounts for the mode change disruption in the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP). In fact, during its execution, the project may face some unexpected events, which can lead to the schedule deterioration or even unfeasibility. A reactive mathematical modeling is proposed. Moreover, three heuristics with several variants are suggested to repair the initial disrupted schedule. These heuristics aim to perform a very quick response to provide the project manager with, hopefully, a feasible schedule. An extensive computational study is performed on PSPLIB benchmark instances with complementary generated data. Finally, the experimental results have shown that the three heuristics outperform Cplex in terms of the CPU running time. Moreover, Lexicographic Regret-Based Heuristic (LRBH) outranks the other heuristics in finding feasible solutions and in terms of the makespan deviation.

Selection of Multimode Resource-Constrained Project Scheduling Scheme Based on DEA Method

A multimode resource-constrained project scheduling problem (MRCPSP) may have multifeasible solutions, due to its nature of targeting multiobjectives. Given the NP-hard MRCPSP and intricate multiobjective algorithms, finding the optimized result among those solutions seems impossible. This paper adopts data envelopment analysis (DEA) to evaluate a series of solutions of an MRCPSP and to find an appropriate choice in an objective way. Our approach is applied to a typical MRCPSP in practice, and the results validate that DEA is an effective and objective method for MRCPSP solution selection.

Multi-mode resource constrained project scheduling problem along with contractor selection

In real-world environments, selecting the right contractor is an important issue which considerably influences completion time, total cost and quality of performing the project. This paper deals with the multi-mode resource constrained project scheduling problem (MRCPSP) and contractor selection (CS) in an integrated manner. In fact, each activity is assigned to a contractor, an execution mode is selected for each activity, and the start/finish times of activities are determined. This paper presents a bi-objective optimization model to deal with MRCPSP-CS, aiming to minimize the total cost and completion time of the project, simultaneously. Then, four multi-objective decision making (MODM) techniques are used to solve the proposed model. Since none of MODM techniques dominates other ones, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used to assess the performance of MODM techniques, confirming that MCGP-U outranks other ones. Finally, the augmented -Constraint method is used to solve some test problems, and perform sensitivity analysis on the number of contractors. Sensitivity analyses show that by increasing the number of available contractors, the Pareto front is significantly improved, and the Number of Pareto-optimal Solutions (NPS) increases. This helps decision maker(s) make appropriate decisions in a more flexible manner.

Hybrid evolutionary algorithm for large-scale project scheduling problems

The Multi-Mode Resource Constrained Project Scheduling Problem (MMRCPSP) is a challenging NP-hard optimization problem, that schedules activities under a set of resource constraints. Although, over the last few decades, different solution approaches have been proposed, no single algorithm has consistently been the best for a wide range of MMRCPSPs. In this paper, we have proposed an effective hybrid algorithm, in which two multi-operator evolutionary algorithms perform sequentially under two sub-populations, with their sizes dynamically adapted based on their performance during the evolutionary process. In addition, two heuristics are proposed, the first one is based on a linear programming approach with an aim to obtain feasible modes, while the second one is based on a modified forward and backward justification approach with an aim of obtaining feasible schedules. Also, a classification technique is used to determine the complexity of a given problem, based on its resource’s availability. The proposed approach is tested by solving a wide-range of multi-mode resource-constrained project scheduling problems, including available larger test problems, with the results revealing that the proposed method outperforms well-known algorithms.