Multi-mode Resource-constrained Project Research Articles

Developing a Robust Multi-Skill, Multi-Mode Resource-Constrained Project Scheduling Model with Partial Preemption, Resource Leveling, and Time Windows

Real-world projects encounter numerous issues, challenges, and assumptions that lead to changes in scheduling. This exposure has prompted researchers to develop new scheduling models, such as those addressing constrained resources, multi-skill resources, and activity pre-emption. Constrained resources arise from competition among projects for limited access to renewable resources. This research presents a scheduling model with constrained multi-skill and multi-mode resources, where activity durations vary under different scenarios and allow for partial pre-emption due to resource shortages. The main innovation is the pre-emption of activities when resources are unavailable, with defined minimum and maximum delivery time windows. For this purpose, a multi-objective mathematical programming model is developed that considers Bertsimas and Sim’s robust model in uncertain conditions. The model aims to minimize resource consumption, idleness, and project duration. The proposed model was solved using a multi-objective genetic algorithm and finally, its validation was completed and confirmed. Analysis shows that limited renewable resources can lead to increased activity pre-emption and extended project timelines. Additionally, higher demand raises resource consumption, reducing availability and prolonging project duration. Increasing the upper time window extends project time while decreasing the lower bound pressures resources, leading to higher consumption and resource scarcity.

Multi-mode resource-constrained project scheduling problem with multiple shifts and dynamic energy prices

Considering the characteristics of time-of-use tariffs and multi-shifts in real-life project execution scenarios, we present a multi-mode resource-constrained project scheduling problem with multi-shift and time-of-use tariffs (MRCPSP-MS-TOU). The MRCPSP-MS-TOU is a bi-objective scheduling problem that aims to simultaneously minimise both project duration and energy costs. In this problem, renewable resources are the critical equipment that consumes the most energy and can work continuously for multiple shifts. Activities that require critical equipment with high energy consumption are given priority for shifts with lower electricity prices under time-of-use tariffs. We construct a mixed integer linear programming model for the MRCPSP-MS-TOU. For small-scale projects, the ε-constraint method is implemented to solve the MRCPSP-MS-TOU using the Gurobi optimiser. For large-scale projects, this paper develops meta-heuristic algorithms in the framework of the two non-dominated sorting genetic algorithm versions. The MRCPSP-MS-TOU enables manufacturers and the construction industry to schedule projects using time-of-use tariffs and multi-shifts in a more efficient manner since it can control the intensity of energy consumption, reduce project costs, make full use of energy-intensive equipment, and effectively reduce order delivery time.

Preemptive and non-preemptive multi-skill multi-mode resource-constrained project scheduling problems considering sustainability and energy consumption: A comprehensive mathematical model

Modern project managers cope with significant challenges to schedule and control projects considering dynamic environments, frequent uncertainties, strict project deadlines, and stricter sustainable requirements above all. Sustainability taking into account resource utilization has been recently associated with project management. Hence, this paper presents a new mixed-integer linear programming (MILP) model with two objectives for a resource-constrained project scheduling problem (RCPSP) with multiple skills and multiple modes, assuming preemptive and non-preemptive activities in an uncertain environment. Given the importance of sustainable developments in projects, the considered objectives are to maximize job opportunities and minimize project duration, resource costs, and total energy consumption. To deal with the model, an AUGNMECON2VIKOR algorithm is utilized to create Pareto solutions. In this model, project activities can be crashed by allocating extra resources. Furthermore, multi-skill resources are used to perform project activities. This study also investigates the impact of these resources on project scheduling. To deal with uncertain circumstances, a fuzzy chance-constrained programming method is employed to develop a robust possibilistic programming model. With respect to the increasing significance of sustainability in project management, this study pioneers the examination of the impact of sustainable factors on project scheduling. Finally, the proposed formulation is validated using instances from the well-known PSPLIB and MMLIB test sets. Finally, a comparison is drawn between the presented solution method considering AUGMECON2VIKOR and AUGMECON2.

A new low-carbon project scheduling problem with renewable and traditional energy: A comprehensive analysis and its solution

Employing multi-energy complementarity in project energy supply proves to be an efficient strategy for accomplishing low-carbon project scheduling. However, current project scheduling problems primarily concentrate on traditional single-energy models. They optimize schedules to reduce energy emissions but often neglect the potential of renewable energy. This paper integrates project scheduling and renewable energy as interrelated aspects. Based on a renewable energy supply model grounded in the generation characteristics of renewable energy sources, a model for MC-MRCPSPM (multi-mode resource-constrained project scheduling problem with multiple complementary energies in the manufacturing context) is constructed and a memetic algorithm is employed for its resolution. The research findings conclusively demonstrate that using renewable energy as a power source during project execution leads to an average reduction of approximately 58.8% in carbon emissions, with a justifiable 14.73% increase in energy costs. Employing a multi-energy complementarity approach in project scheduling effectively reduces carbon emissions while maintaining reasonable energy costs and offers project managers greater decision-making flexibility.

A matheuristic-oriented iterated greedy algorithm for multi-mode resource-constrained project scheduling problem under uncertainty

Multi-mode resource-constrained project scheduling problem is one of the most important branches of combinatorial optimization problems. The aim is to find a feasible solution consisting of activity start time and execution mode so that the project makespan is minimized. However, there are a lot of uncertain events, that bring great challenges to project scheduling. We first propose a mixed integer linear programming model where the activity duration is uncertain. Then two uncertain parameters are introduced to describe the disturbance degree of uncertain activity duration and the allowable violation degree of constraints respectively, and the MILP model with uncertain activity duration is converted to its deterministic robust counterpart model. A matheuristic local optimization approach is proposed to balance computational time with the optimization of the computational result. A matheuristic-oriented iterated greedy algorithm that combines a matheuristic local optimization approach and an iterated greedy algorithm is proposed to solve this problem in this paper. Experimental results indicate that the robust counterpart model can obtain robust optimal solutions for small-scale instances in accepted computational time. Meanwhile, the proposed matheuristic-oriented iterated greedy algorithm can obtain robust near-optimal solutions for large-scale instances and is superior to other compared algorithms.

Scheduling optimization model for linear projects with resource transfer in diverse construction scenarios

Studies on linear engineering projects often overlook complex construction scenarios, neglecting global resource quantities, transfer time and cost during resource deliberation. This study addresses these gaps by employing a linear scheduling method and a multi-mode resource-constrained project model. The decision variables of the model include the construction mode, construction direction, activity priority and global resource amounts, considering linear, bar and block construction scenarios. A hybrid algorithm combining the non-dominated sorting genetic algorithm-III with differential evolution is proposed for model resolution, featuring hierarchical, multi-strategy, adaptive crossover and mutation operators. Sensitivity analysis and case studies demonstrate the effectiveness and superiority of the model and algorithm. According to the study, the unit cost of resource transfer significantly influences the optimization result more than the unit time; the optimizing cost has an upper bound; and linear projects scheduling optimization with resource transfer are more realistic and provide a better trade-off between time and cost.

Simulation-based hybrid genetic algorithms for the stochastic multi-mode resource-constrained project scheduling problem with minimized financial risk

Projects face uncertainties during implementation, and these uncertainties often lead to risk factors that disrupt successful project execution and cause a loss of profit. The stochastic project scheduling technique has been an effective avenue for reducing the risks in project management. Nevertheless, previous studies often neglected resource limits for minimizing the financial risks of projects in stochastic project scheduling problems. This study aims to optimize the conditional net present value at risk (CNPVaR), which measures a project’s expected loss of net present value (NPV) in a stochastic multi-mode resource-constrained project scheduling problem (SMRCPSP). Accordingly, considering the stochastic activity duration and cash flow, we construct a scenario-based optimization model for the SMRCPSP, where the solution (strategy) of the SMRCPSP is represented by a policy that includes an activity list and execution mode list; a scheduling policy is then employed to map the start times of activities at each decision time based on the solution. Three simulation-based hybrid genetic algorithms embedded with different iteration alternatives according to activity-based (AB) or resource-based (RB) scheduling policies are used. Furthermore, computational experiments are conducted to evaluate the proposed procedures through 480 instances. With respect to the CNPVaR, expected NPV, and algorithm stability metrics, the results of the experiments demonstrate that the genetic algorithm (GA) with local search based on the RB scheduling policy performed best compared with two other hybrids of the GA, the existing vibration damping optimization (VDO) method and a pure GA for large-sized projects. However, the VDO outperforms the other approaches according to the AB scheduling policy for small-scale projects. Additionally, a case study is conducted; the findings demonstrate that the risk attitude (confidence level) of project managers and the discount factor have impacts on the CNPVaR and expected NPV, but the CNPVaR is insensitive to the number of simulations.

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.

Continuous-time formulations for multi-mode project scheduling

This paper reviews compact continuous-time formulations for the multi-mode resource-constrained project scheduling problem. Specifically, we first point out a serious flaw in an existing start-end-event-based formulation owing to inconsistent mode choices. We propose two options to formulate the missing constraints and consider an equivalent reformulation with sparser constraint matrix. Second, we formulate an aggregate variant of an existing model that relies on on-off-events, and we clarify the role of mode consistency issues in such models. Third, we suggest two variants of an existing network flow formulation. We enhance our models by adapting several techniques that have been used previously, e.g., in cases with only a single mode. A large set of benchmark instances from the literature provides the basis for an up-to-date and fair computational study with an out-of-the-box solver package. We compare our models against two models from the literature. Our experiments assert confidently that network flow formulations prevail in the test bed, and they provide a hint on why event-based models become less competitive in multi-mode settings.

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 faster exact method for solving the robust multi-mode resource-constrained project scheduling problem

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions that minimise the worst-case project makespan, whilst assuming that activity durations lie in a budgeted uncertainty set. Computational experiments show that this easy-to-implement formulation is many times faster than the current state-of-the-art solution approach for this problem, whilst solving over 40% more instances to optimality over the same benchmarking set.

Credibility-based chance-constrained multimode resource-constrained project scheduling problem under fuzzy uncertainty

This paper investigates a multimode resource-constrained project scheduling problem under hybrid uncertain environment. With the activity durations are fuzzy variables, the resource requests change with the durations. The goal is to minimize the project duration and the cost associated with the required resources. Considering the stochastic duration and resource demand, a chance constrained programming model based on credibility is established. In order to solve the model, the chance constraints and fuzziness are treated by introducing the credibility distribution function and its inverse function. And, a hybrid algorithm combining particle swarm optimization (PSO) and genetic algorithm (GA) is proposed. It has shown fine performance in solving problems with 30, 60, and 120 activities. We also analyze the sensitivity of confidence, fuzziness, number of activities, number of modes, and resource unit cost. Meanwhile, fuzzy value-at-risk is used as a risk measure, and a model based on it is constructed. These numerical results show that the developed algorithm can obtain the near optimal solution of large-scale projects in a reasonable calculation time.

A comparative study of modeling and solution approaches for the multi-mode resource-constrained discrete time–cost trade-off problem: Case study of an ERP implementation project

Most knowledge-intensive industries, especially companies developing software engineering projects such as Enterprise Resource Planning (ERP) implementation projects, generally necessitate finding the optimal trade-off between the project duration and total usage cost of the renewable resource costs (e.g., human resource expertise costs). Therefore, the MRC-DTCTP, which integrates classical multi-mode resource-constrained project scheduling (MRCPSP) and discrete time–cost trade-off problems (DTCTP), can be seen as a more applicable problem since it better reflects the objectives and requirements of today’s real-life software project applications. The MRC-DTCTP is a much more complex variant of the MRCPSP since it aims to minimize total direct/indirect costs of the resources simultaneously under a pre-specified project deadline. Based on this motivation, a new explicit integer-linear programming (ILP) model of the MRC-DTCTP was first developed based on the implicit non-linear programming model of Wuliang and Chengen (2009). Due to its NP-hard nature, we also proposed a constraint programming (CP) model that includes several search strategies to solve large-sized problem instances within reasonable computation time. In addition, a genetic algorithm (GA) approach in combination with a Modified Serial Schedule Generation scheme (SSGS) is implemented to make further comparisons on several benchmark instances, which are generated based on the existing MRCPSP data sets taken from the project scheduling problem library (PSPLIB) by considering additional problem characteristics. A comprehensive experimental study has shown that the proposed CP model and GA approach can provide superior results in shorter run times for large-sized benchmark instances. Finally, an international Enterprise Resource Planning (ERP) Software Company’s real-life application is presented. The ERP projects generally necessitate finding the optimal trade-off between project makespan and human resource costs, making the MRC-DTCTP much more difficult than classical MRCPSPs & DTCTPs. For further analysis, time–cost trade-off curves under different human resource availabilities and project deadlines are drawn to provide managerial insights to ERP project managers.