Resource Constrained Project Scheduling Problem Research Articles

Comparison of Heuristic Priority Rules in the Solution of the Resource-Constrained Project Scheduling Problem

Resource-constrained project scheduling (RCPS) aims to minimize project duration under limited resource availabilities. The heuristic methods that are often used to solve the RCPS problem make use of different priority rules. The comparative merits of different priority rules have not been discussed in the literature in sufficient detail. This study is a response to this research gap. It compares 17 heuristic priority rules and seeks the best performing heuristic priority rule. This is the first study ever that compares heuristic priority rules by considering combinations of variations in (1) resource allocation procedures, (2) number of activities, (3) number of resource constraints, and (4) resource supply levels. The objective is to understand the relative merits of heuristic rules used in solving the RCPS problem. The findings indicate that the “minimum late finish time” rule generates the shortest predicted project duration when used in parallel resource allocation, whereas the “minimum late start time”, “minimum late finish time”, and the “highest rank of positional weight 2” rules perform best in serial resource allocation. It was also found that parallel resource allocation is slightly superior to serial resource allocation in most instances.

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.

A multi-objective multi-agent optimization algorithm for the multi-skill resource-constrained project scheduling problem with transfer times

This paper addresses the Multi-Skill Resource-Constrained Project Scheduling Problem with Transfer Times (MSRCPSP-TT). A new model has been developed that incorporates the presence of transfer times within the multi-skill RCPSP. The proposed model aims to minimize project’s duration and cost, concurrently. The MSRCPSP-TT is an NP-hard problem; therefore, a Multi-Objective Multi-Agent Optimization Algorithm (MOMAOA) is proposed to acquire feasible schedules. In the proposed algorithm, each agent represents a feasible solution that works with other agents in a grouped environment. The agents evolve due to their social, autonomous, and self-learning behaviors. Moreover, the adjustment of environment helps the evolution of agents as well. Since the MSRCPSP-TT is a multi-objective optimization problem, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is used in different procedures of the MOMAOA. Another novelty of this paper is the application of TOPSIS in different procedures of the MOMAOA. These procedures are utilized for: (1) detecting the leader agent in each group, (2) detecting the global best leader agent, and (3) the global social behavior of the MOMAOA. The performance of the MOMAOA has been analyzed by solving several benchmark problems. The results of the MOMAOA have been validated through comparisons with three other meta-heuristics. The parameters of algorithms are determined by the Response Surface Methodology (RSM). The Kruskal–Wallis test is implemented to statistically analyze the efficiency of methods. Computational results reveal that the MOMAOA can beat the other three methods according to several testing metrics. Furthermore, the impact of transfer times on project’s duration and cost has been assessed. The investigations indicate that resource transfer times have significant impact on both objectives of the proposed model.

Airline ground operations: Schedule recovery optimization approach with constrained resources

Most airlines have established integrated hub and operations control centers for the monitoring and adjustment of tactical operations. However, decisions in such a control center are still elaborated manually on the basis of expert knowledge held by several agents representing the interests of different airline departments and local stakeholders. This article studies a concept which incorporates the situational awareness gained by airport-collaborative decision making into an airline-internal decision support system, such that it integrates all available schedule recovery options during aircraft ground operations. The developed mathematical optimization model is an adaptation of the Resource-Constrained Project Scheduling Problem (RCPSP) and incorporates key features from turnaround target time prediction, passenger connection management, tactical stand allocation and ground service vehicle routing into the airline hub control problem. The model is applied in a case study consisting of 20 turnarounds during a morning peak at Frankfurt airport. Schedule recovery performance (resilience) is analyzed for a set of key performance indicators within multiple scenario instances which contain different resource availability and aim at solving various arrival delay situations. Results highlight that a minimization of tactical cost concurrently reduces average departure delay for flight and passengers while recovery performance is substantially affected when some options are not included in the evaluation process. Thus, our concept provides airlines with an optimization approach for constrained airport resources so that total cost and delay resulting from schedule deviations are reduced, which may benefit strategic schedule planning and improve predictability of operations for local collaborators, such as airport, ground handlers and ATM performance.

Towards Finding Robust Execution Strategies for RCPSP/max with Durational Uncertainty

Resource Constrained Project Scheduling Problems with minimum and maximum time lags (RCPSP/max) have been studied extensively in the literature. However, the more realistic RCPSP/max problems — ones where durations of activities are not known with certainty – have received scant interest and hence are the main focus of the paper. Towards addressing the significant computational complexity involved in tackling RCPSP/max with durational uncertainty, we employ a local search mechanism to generate robust schedules. In this regard, we make two key contributions: (a) Introducing and studying the key properties of a new decision rule to specify start times of activities with respect to dynamic realizations of the duration uncertainty; and (b) Deriving the fitness function that is used to guide the local search towards robust schedules. Experimental results show that the performance of local search is improved with the new fitness evaluation over the best known existing approach.

Constraint Logic Programming for Real-World Test Laboratory Scheduling

The Test Laboratory Scheduling Problem (TLSP) and its subproblem TLSP-S are real-world industrial scheduling problems that are extensions of the Resource-Constrained Project Scheduling Problem (RCPSP). Besides several additional constraints, TLSP includes a grouping phase where the jobs to be scheduled have to be assembled from smaller tasks and derive their properties from this grouping. For TLSP-S such a grouping is already part of the input. In this work, we show how TLSP-S can be solved by Answer-set Programming extended with ideas from other constraint solving paradigms. We propose a novel and efficient encoding and apply an answer-set solver for constraint logic programs called clingcon. Additionally, we utilize our encoding in a Very Large Neighborhood Search framework and compare our methods with the state of the art approaches. Our approach provides new upper bounds and optimality proofs for several existing benchmark instances in the literature.

Scheduling project with stochastic durations and time-varying resource requests: A metaheuristic approach

This paper studies a resource constrained project scheduling problem (RCPSP) under dynamic environments. Along with stochastic activity-durations, resource requests and resource availabilities are also prone to vary with time (i.e., that is, dynamic). To account for stochastic activity durations and the resource dynamic, a chance constrained based mathematical model is proposed. To solve the developed model, an efficient genetic algorithm (GA) based memetic algorithm (MA) is proposed. The proposed algorithm has shown excellent performance for solving 2880 30-activity and 3600 120-activity instances for RCPSP with predefined but time-varying resource requests and availabilities (i.e., RCPSP/t setting). The proposed algorithm has also demonstrated an excellent performance for the extended RCPSP/t setting with stochastic activity durations (i.e., RCPSP/td). Due to the unavailability of any real benchmark instances for this extended RCPSP, this work proposes a pragmatic approach to generate simulated benchmark instances. Numerous time-dependent benchmark instances from the project scheduling library (PSPLIB) are solved to validate the proposed MA. Rigorous experimental analysis with a standard set of 2448 newly generated problem instances for 30, 60, 90, and 120 activities indicates that the proposed meta-heuristic can solve large projects with a reasonable computational burden.

Problem-specific multi-objective invasive weed optimization algorithm for reconnaissance mission scheduling problem

With the progress of technology, the multi-agent system is successfully applied in many applications. In this paper, we investigate the problem of multi-agent system reconnaissance mission scheduling, which is the core of the reconnaissance decision support system and can be modeled as an extension of Multi-Mode Multi-Skill Resource-Constrained Project Scheduling Problem. Three objectives are considered in this paper: (1) minimizing the reconnaissance mission’s makespan, (2) minimizing the total cost of allocating reconnaissance agents, and (3) maximizing the total quality of all reconnaissance tasks. An effective problem-specific multi-objective invasive weed optimization algorithm (PS-MOIWO) is proposed for solving the problem. Firstly, a new chromosome structure guaranteeing the feasibility of solutions and an initialization method are proposed. Secondly, we propose a self-adaptive penalty-based constraint handling technique to describe the fitness of each individual and adopt a novel non-dominated sorting method to rank the population. Thirdly, by using the problem-specific knowledge, a local search procedure is developed and incorporated into the PS-MOIWO framework to enhance the exploitation ability. Based on the Taguchi method, algorithm’s suitable parameter combinations are determined. Simulation results based on a set of newly generated reconnaissance instances and the comparisons with some existing algorithms demonstrate the proposed algorithm’s effectiveness.

Pattern mining‐based pruning strategies in stochastic local searches for scheduling problems

AbstractScheduling problems are a subclass of combinatorial problems consisting of a set of tasks/activities/jobs to be processed by a set of resources usually to minimize a time criterion. Some optimization methods used to solve these problems are hybridized with knowledge discovery techniques to extract information during the optimization process and enhance it. However, most of these hybrid techniques are custom‐designed and lack generalization. In this paper, a module for knowledge extraction in Stochastic Local Searches is designed, aiming to be problem independent and plugged into optimization methods that relies on multiple Stochastic Local Search replications. The objective is to prune parts of the search space for which the exploration is likely to lead to poor solutions. This is performed through the extraction of high‐quality patterns occurring in locally optimal solutions. Benchmarked on two well‐known scheduling problems, the Job‐shop Problem and the Resource Constrained Project Scheduling Problem, the results show both a speed up in the convergence and the reaching of better local optima solutions.

Multi-objective multi-mode resource-constrained project scheduling with fuzzy activity durations in prefabricated building construction

Different from traditional project management, the prefabricated building (PB) construction project has a complex distributed supply chain model, and the overall project is completed by multi-stage cooperation. Therefore, the implementation process will be restricted by many constraints, and various uncertain factors will also interfere with the smooth implementation of the project. In order to improve the stability and reliability of the PB construction project implementation process, it is very important to study an effective robust project scheduling method considering resource constraints in an uncertain environment. In this paper, we formulate a PB construction resource-constrained project scheduling with multi-objective multi-mode, focus on the uncertainty of the execution time of the execution activity, and constructs the interval value of the execution time to express it through fuzzy theory; also considers the multiple objectives of PB construction project, including time-based profit, and cost-based profit. Secondly, we propose a hybrid cooperative co-evolution algorithm (HCOEA) to obtain the highly robust project scheduling, reduce the impact of the uncertainty of the execution time of the activity on the overall project. Resource-constrained project scheduling problem (RCPSP) is an NP-hard combinatorial optimization problem. This paper also needs to consider the complex combination of time-resource and/or time–cost constraints. At the same time, it is necessary to consider the impact of time changes in different mode combinations. Therefore, how to design an effective multi-objective optimization algorithm is very difficult. This paper design a Hybrid Cooperative Co-evolution Algorithm (HCOEA) with multi-stage representation for the activity sequencing and the resource allocation, further improve the search efficiency. We improve the cooperative co-evolution framework with a self-adaptive mechanism and a self-adaptive selection process. Finally, benchmarks and extended datasets with fuzzy processing time are adopted to test our HCOEA. Computational results show that the HCOEA performs better than the existing state-of-the-art methods.

Bi-objective robust project scheduling with resource constraints and flexible activity execution lists

This paper analyses a type of extension of the resource-constrained project scheduling problem (RCPSP) whose activities have multiple execution lists. This sort of problem is titled resource-constrained project scheduling problem with flexible activity execution lists (abbreviated as RCPSP-FAL). The goal is to minimize makespan and maximize robustness simultaneously to improve the ability of the project to handle emergencies within the design completion time. Six robustness measures are proposed depending on the free slack determined by start time and renewable resource surplus per unit time. Moreover, a bi-objective mixed-integer programming model is developed to solve the considered problem. Besides, a simple data structure, namely selection-tree, is designed to detect available activity execution lists. Two algorithms are proposed, whose names are variant-genetic algorithm (VGA) and variant-simulated-annealing algorithm (VSA), to solve the developed model. Also, an aggregation function is established for assessing the fitness consisting of makespan and robustness. Several computation experiments are designed to evaluate the proposed algorithms and the six robustness measures. Results show the characteristics of different robust measures. Meanwhile, they also show the effectiveness of VSA and VGA, as well as the relations among robustness, makespan, and resource-usage.

Enhanced method to plan the operations of vertical supply systems of high-rise projects

Logistics planning and management are integral to the successful management of construction projects. Although on-site logistics are critical to efficient project delivery, they receive less attention in terms of research. This research introduces a new method for planning on-site logistics operations utilizing vertical supply systems (VSS) in high-rise projects. This method challenges the limitations of using critical path method and Resource Constrained Project Scheduling Problem in scheduling high-rise projects. The presented method treats lifting operations as activities with durations. The method presents a new classification of lifting activities based on their relation to other works, and it prioritizes the assignment of VSS to lifting activities based on the flexibility of VSS choice for each task. These two novel contributions allow planning construction works to match the capacity of available VSS, and it allows an efficient distribution of lifting tasks among available VSS. This method was applied to two towers in an ongoing project. The application to the first tower was during construction which allowed measuring tangible improvements on site and the other applied during the planning stage. The application of this method resulted in shorter floor cycles by 20% to 30%, less idle workers and more efficient cost control.

An analysis of network and resource indicators for resource-constrained project scheduling problem instances

In the past decades, the resource on the resource-constrained project scheduling problem (RCPSP) has grown rapidly, resulting in an overwhelming amount of solution procedures that provide (near)-optimal solutions in a reasonable time. Despite the rapid progress, little is still known what makes a project instance hard to solve. Inspired by a previous research study that has shown that even small instances with only up to 30 activities is sometimes hard to solve, the current study provides an analysis of the project data used in the academic literature. More precisely, it investigates the ability of four well-known resource indicators to predict the hardness of an RCPSP instance.The study introduces a new instance equivalence concept to show that instances might have very different values for their resource indicators without changing any possible solution for this instance. The concept is based on four theorems and a search algorithm that transforms existing instances into new equivalent instances with more compact resources. This algorithm illustrates that the use of resource indicators to predict the hardness of an instance is sometimes misleading.In a set of computational experiment on more than 10,000 instances, it is shown that the newly constructed equivalent instances have values for the resource indicators that are not only different than the values of the original instances, but also often are better in predicting the hardness the project instances. It is suggested that the new equivalent instances are used for further research to compare results on the new instances with results obtained from the original dataset.

Dynamic Optimization for Analyzing Effects of Multiple Resource Failures on Project Schedule Robustness

This study develops hybrid modeling and algorithmic frameworks for analyzing the mutual effects of multiple sources of uncertainty on the quality and the robustness of construction schedules. To cope with multiple sources of disruptions, i.e., random resource failures and severe weather conditions, this paper develops a simulation-optimization model that aims to generate delay resistant project schedules. The Variable Neighborhood Search (VNS) is hybridized with an event-driven simulation framework to generate efficient and robust solutions for computationally expensive resource-constrained project scheduling problems (RCPSP). The simulation experiments have been carried out by a flexible modeling framework that can be adopted by project experts to design construction schedules subject to the uncertainty associated with the multiple resource failure. The problem is mathematically formulated as a bi-objective optimization model aiming to minimize the project makespan and maximize a novel surrogate robustness function simultaneously. The computational results of the proposed VNS method have been compared with those obtained from the commercial optimization solvers. The simulation-optimization model’s application is demonstrated through a case study of the hydropower plant construction project with multiple renewable and non-renewable resources. Based on an extensive statistical analysis of real-life scenarios, this study contributes to a trade-off analysis of project makespan and robustness in construction projects. The t-test statistical analysis results indicate the significance of the project’s average delay reduction by implementing the robust project schedule. The outcomes confirm that the designed framework can generate a more efficient project schedule with a higher rate of protection compared with the existing robust approaches.

A local search framework for industrial test laboratory scheduling

In this paper we introduce a complex scheduling problem that arises in a real-world industrial test laboratory, where a large number of activities has to be performed using qualified personnel and specialized equipment, subject to time windows and several other constraints. The problem is an extension of the well-known Resource-Constrained Project Scheduling Problem and features multiple heterogeneous resources with very general availability restrictions, as well as a grouping phase, where the jobs have to be assembled from smaller units. We describe an instance generator for this problem and publicly available instance sets, both randomly generated and real-world data. Finally, we present and evaluate different metaheuristic approaches to solve the scheduling subproblem, where the assembled jobs are already provided. Our results show that Simulated Annealing can be used to achieve very good results, in particular for large instances, where it is able to consistently find better solutions than a state-of-the-art constraint programming solver within reasonable time.

Optimization Model for the Pavement Pothole Repair Problem Considering Consumable Resources

When heavy rain strikes Taiwan, it always results in cracks in road pavement, and damages arising from potholes. Tremendously compromising road safety, road users may have fatal accidents caused by untimely repair actions. The road maintenance department needs to take the responsibilities for road sections in the form of inspections and faces the decision about how to properly allocate available resources to repair pavement damages immediately. When performing pavement repair works, we need to consider the resource consumption behavior and explore the mechanism of replenishing resources and calculating the return time. Therefore, in order to help maintenance units to deal with consumable resource issues, this study proposes a novel approach to offer the mechanism of consumable resource calculation, which is difficult to solve through the traditional vehicle routing problem (VRP) approach. This proposed model treats the pothole repair problem as a resource-constrained project scheduling problem (RCPSP), which is capable of resolving such consumable resource considerations. The proposed model was developed by adopting constraint programming (CP) techniques. Research results showed that the proposed model is capable of providing the optimal decisions of pavement pothole repair tasks and also meets practical requirements to make appropriate adjustment, and helps the maintenance unit to shorten total repair duration and optimize resource assignment decisions of pavement maintenance objectives.

Energy-cost-aware resource-constrained project scheduling for complex product system with activity splitting and recombining

Energy-cost-aware scheduling in manufacturing process has recently been considered as an effective way to use energy. In addition, applying time-of-use is regarded as one of the optimal uses of energy which the governments extend to control energy consumption. Complex product system (CoPS) has more complex and huge amounts of multiple manufacturing activities with higher energy sensibility in project scheduling than commodity products. This paper presents a new variant of resource-constrained project scheduling problem (RCPSP), which is named energy-cost-aware resource-constrained project scheduling problem with activity splitting and recombining (eRCPSP-AS&R) for CoPS. In the proposed model, a dynamic activity splitting and recombining strategy for CoPS is used by considering energy consumption. Also, a bi-objective (project delay and energy consumption cost) mathematical model is established. The solution framework of eRCPSP-AS&R model consists of two parts: activity splitting and recombining, project scheduling. The dynamic strategy of activity splitting and recombining is used to perform energy-cost-aware based on hybrid intuitionistic fuzzy information entropy, TOPSIS and fuzzy clustering method. Moreover, an improved NSGA-II algorithm is employed to solve the Pareto-optimal solutions for the proposed bi-objective optimization problem. Series of computational experiments are conducted and verified the overall performance of proposed eRCPSP-AS&R model and approaches.

Emergency Repair Scheduling Model for Road Network Integrating Rescheduling Feature

When a natural disaster occurs, road maintenance departments always face the challenge of how to assign repair resources properly to recover damaged road segments as soon as possible. From the literature review, most studies treat such problems as a vehicle routing problem (VRP). In those studies, repair resources are always dispatched as complete crews, and cannot be divided into smaller scales. Furthermore, each disaster point is only allowed one group of resources to recover it, without considering the possibility of accelerating the production rate subjected to specific objectives. Such limitation restricts required resources in an inflexible manner. Therefore, this study defines all repair works as an emergency repair project and adopts the framework of the Resource-Constrained Project Scheduling Problem (RCPSP), which can resolve such complicated resource assignment issue. A novel emergency repair scheduling model for the road network is proposed based on Constraint Programming (CP) as the searching algorithm to facilitate model formulation. According to the RCPSP concepts, disaster points are set as repair activities and resource travel routes between disaster points are set as transit activities. All the repair activities are linked by transit activities and the required resources are assigned accordingly. In order to consider the second-wave hazard events of where new disaster points may occur, and new resources may be added into emergency repair projects, a rescheduling feature is integrated into the proposed model. Through two case studies, research findings show that this model can be easily modulated to adapt to different situations satisfying practical disaster management goals and solving emergency repair scheduling problems for road networks efficiently.

Cooperative self-configuring nature-inspired algorithm for a scheduling problem

One of the crucial challenges related to operational manufacturing planning is an optimal plan search in the current situation using a workflow model. The problem solving is greatly hindered by the rapid growth of the search space with an increase in dimension or the so-called combinatorial explosion. This paper uses two different approaches to solving a hierarchical scheduling problem based on different solution representations. The first approach assumes a search of an optimal project order and then solving of resource-constrained project scheduling problem (RCPSP) for each of the projects using a model based on the greedy principle. In the second approach we are searching for priorities of all actions of all projects and then use them in the process of building a schedule if there are any conflicts when choosing the next action. To solve the problem with both approaches, the paper considers some nature-inspired algorithms such as the intelligent water drops algorithm (IWDs), a genetic algorithm (GA) and ant colony optimization (ACO) as well as a self-configuring version of the last two. The paper shows the efficiency of the application of the coevolution algorithm using IWDs, self-configuring GA and ACO.

Underground mine scheduling under uncertainty

Underground mine schedules seek to determine start dates for activities related to the extraction of ore, often with an objective of maximizing net present value; constraints enforce geotechnical precedence between activities, and restrict resource consumption on a per-time-period basis, e.g., development footage and extracted tons. Strategic schedules address these start dates at a coarse level, whereas tactical schedules must account for the day-to-day variability of underground mine operations, such as unanticipated equipment breakdowns and ground conditions, both of which might slow production. At the time of this writing, the underground mine scheduling literature is dominated by a deterministic treatment of the problem, usually modeled as a Resource Constrained Project Scheduling Problem (RCPSP), which precludes mine operators from reacting to unforeseen circumstances. Therefore, we propose a stochastic integer programming framework that: (i) characterizes uncertainty in duration and economic value for each underground mining activity; (ii) formulates a new stochastic variant of the RCPSP; (iii) suggests an optimization-based heuristic; and, (iv) produces implementable, tactical schedules in a practical amount of time and provides corresponding managerial insights.