Resource Constrained Project Scheduling Problem Research Articles

A Genetic Algorithm with a New Local Search Method for Solving the Multimode Resource-constrained Project Scheduling Problem

The existence of limited resources and precedence relations between activities makes project scheduling a difficult task. In this paper, the multimode resource-constrained project scheduling problem (MRCPSP) as one of the important project scheduling problems is focused. In this regard, a genetic algorithm (GA) is proposed for solving the multimode resource-constrained project scheduling problem (MRCPSP) improved by a new local search method. The Activity Mode List (AML) is used as encoding and the multimode serial schedule generation scheme (MSSGS) is employed as the decoding procedure. The aim of the suggested local search is maximum use of existed nonrenewable resources of the project such that its makespan is decreased. For this purpose, the local search procedure allocates the unused nonrenewable resources of each feasible solution to the activities with lower total float. Comparing results of the proposed method with other ones using the set J20 in Project Scheduling Problem Library (PSPLIB) validates the effectiveness of the proposed algorithm to solve the MRCPSP.

A satisfiability and workload-based exact method for the resource constrained project scheduling problem with generalized precedence constraints

This paper deals with the resource constrained project scheduling problem (RCPSP) with generalized precedence constraints (RCPSP/Max). We propose an exact method that tackles a relaxed version of the original problem by modeling it as a satisfiability problem (SAT). Several SAT formulations are introduced, as well as workload-based procedures that were developed in order to reduce the domain of the decision variables, and custom propagators that were implemented with a view of improving the efficiency of the SAT solver. Extensive computational experiments involving different configurations of the method were carried out on 2430 RCPSP/Max benchmark instances ranging from 10 to 500 activities and with 5 resources, and on 2040 RCPSP benchmark instances ranging from 30 to 120 activities and with 4 resources. The results obtained suggest that the proposed method is extremely competitive as almost all known optima were found and 86 instances were solved to optimality for the first time. Moreover, a number of bounds were improved for those instances that still remain open.

Weighted superposition attraction algorithm for combinatorial optimization

Weighted Superposition Attraction (WSA) is a swarm based metaheuristic algorithm that is lately proposed for solving continuous optimization problems. Performance of the WSA was comprehensively tested with numerous unconstrained/constrained optimization problems. Due to its reasonable performance on continuous optimization problems we were motivated to develop a combinatorial version of WSA. A new method is devised to handle combinatorial problems without requiring an indirect representation mechanism like random keys. A random walk procedure is integrated into the combinatoric WSA (cWSA) so as to improve its diversification capability. Additionally, opposition based learning is also integrated into cWSA to increase its performance further. Performance of cWSA is tested on two well-known combinatorial optimization problems, namely the Resource Constrained Project Scheduling Problem (RCPSP) and the Permutation Flow Shop Scheduling Problem (PFSP). The results of the extensive computational study point out the efficiency of the proposed cWSA.

A Memetic Algorithm for Multiskill Resource-Constrained Project Scheduling Problem under Linear Deterioration

This paper proposes a general variable neighborhood search-based memetic algorithm (GVNS-MA) for solving the multiskill resource-constrained project scheduling problem under linear deterioration. Integrating a solution recombination operator and a local optimization procedure, the proposed GVNS-MA is assessed on two sets of instances and achieves highly competitive results. One set of benchmark instances is commonly used in the literature where the capability of the proposed algorithm to find high quality solutions is demonstrated, compared with the state-of-the-art algorithms in the literature. The other set revises the former through incorporating the linear deterioration effect. Two key components of the proposed algorithm are investigated to confirm their critical role to the success of the proposed method.

A Modified Variable Neighbourhood Search Heuristic for the Multi‐Mode Resource Constrained Project Scheduling Problem with A Case Study

AbstractThis paper provides a fast near‐optimum solution to the Multi‐Mode Resource Constrained Project Scheduling Problem (MRCPSP), for projects with activities that have known deterministic renewable and non‐renewable resource requirements. Multi‐modes allows any activity to execute one of many alternative combinations of resource usages and durations, while each activity needs to pick the most feasible one. This type of setting is more prevalent for real‐life project schedules, which necessitates systematic methodologies and advanced solution approaches in harmony with real‐world implementations. This study proposes a Modified Variable Neighbourhood Search Heuristic (MVNSH) algorithm as an advanced optimization technique for scheduling projects. To validate our approach, exhaustive computational tests were carried out by using relevant benchmark instances. The MVNSH algorithm has been shown to be faster and more accurate than many existing heuristic methods. This research also contributes to developing a practical decision support system for resolving real‐life constraints in multi‐mode resource‐constrained projects.

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.

Discrete Optimization for Dynamic Systems of Operations Management in Data-Driven Society

Society is being reshaped by large volumes of data generated from various operations, and research in handling dynamic issues related to data-driven systems has greatly increased in the past decades, where most rely upon discrete optimization models for handling dynamic features contained in operations management (OM) activities. With the rapid growth in computational technologies, including data mining technologies, discrete event simulation techniques, and intelligence algorithms, OM relies more and more on optimal solutions (or their approximates) based on high-performance models and algorithms. This special issue collects 32 original research contributions that present recent advances in models and algorithms concerning discrete optimizations on dynamic OM systems relevant to the data-driven society. In particular, the papers address the topics related to discrete optimization methodologies for stochastic OM problems, dynamic programming based exact methods for stochastic OM problems, system dynamics in behavior OM for E-commerce, data-driven risk analysis and modeling for OM decisions in dynamic contexts, data-driven models for dynamic supply chain management, etc. It is hoped that this special issue will help the integration of the latest research achievements in the relevant field. The paper by S. Li et al. entitled “Probability Mechanism Based Particle Swarm Optimization Algorithm and Its Application in Resource-Constrained Project Scheduling Problems” proposes a new probability mechanism based particle swarm optimization (PMPSO) algorithm to solve combinatorial optimization problems by introducing new particles based on the optimal particles in the population and the historical optimal particles in the individual changes. This method is applied to solve resource-constrained project scheduling problems and the experimental results are quite encouraging.

Resource-constrained project scheduling with activity splitting and setup times

This paper presents a new solution algorithm to solve the resource-constrained project scheduling problem with activity splitting and setup times. The option of splitting activities, known as activity preemption, has been studied in literature from various angles, and an overview of the main contributions will be given.The solution algorithm makes use of a meta-heuristic search for the resource-constrained project scheduling problem (RCPSP) using network transformations to split activities in subparts. More precisely, the project network is split up such that all possible preemptive parts are incorporated into an extended network as so-called activity segments, and setup times are incorporated between the different activity segments. Due to the inherent complexity to solve the problem for such huge project networks, a solution approach is proposed that selects the appropriate activity segments and ignores the remaining segments using a boolean satisfiability problem solver, and afterwards schedules these projects to near-optimality with the renewable resource constraints.The algorithm has been tested using a large computational experiment with five types of setup times. Moreover, an extension to the problem with overlaps between preemptive parts of activities has been proposed and it is shown that our algorithm can easily cope with this extension without changing it. Computational experiments show that activity preemption sometimes leads to makespan reductions without requiring a lot of splits in the activities. Moreover, is shown that the degree of these makespan reductions depends on the network and resource indicators of the project instance.

Multipurpose linear programming optimization model for repetitive activities scheduling in construction projects

Repetitiveness in project's activities has gained an important role in the construction industry. Multiple linear scheduling methods have been proposed in order to fully take advantage of the spatial and temporal information these type of project can provide to practitioners. Besides the advances in the optimization models in these fields, to the extent of the authors knowledge, there is still pending a complete and flexible mathematical linear programming formulation that allow practitioners to easily and jointly solve the Resource allocation, Resource-Constrained Project Scheduling and Time-Cost Tradeoff problem, taking into account as many scheduling properties, benefits and challenges that linear scheduling of repetitive activities imply. This paper shows a complete guide and computational experimentation, of a novel mathematical model that can be easily used by practitioners to optimize construction schedules considering to the largest extent the time and space conditions repetitive projects offer. Particularly, it contributes to the repetitive activities scheduling body of knowledge by successfully implementing a robust linear programing optimization model in a real construction project, while considering as much linear scheduling characteristics as possible. It proves that relationships in the sub-activity level, continuity conditions, multiple modes of execution, controlled acceleration routines and execution mode shifts, and multiple crews can be easily and jointly integrated to a linear optimization model by adding simple linear restrictions to the model.

Chaotic Vibrating Particles System for Resource-Constrained Project Scheduling Problem

Project scheduling in the resource-constrained situation is one of the key issues of project-oriented organizations. The aim of resource-constrained project scheduling problem (RCPSP) is finding a schedule with minimum makespan by considering precedence and resource constraints. RCPSP is a combinatorial optimization problem and belongs to the class of NP-hard problems. The exact methods search the entire search space and are unable to solve large-sized project networks. Thus metaheuristics are used to solve this problem with less computational time. Due to the probabilistic nature of metaheuristics, it is a challenging problem to balance between exploitation and exploration phases. The literature review shows that embedding with chaos improves both the convergence speed and the local optima avoidance of metaheuristics. This paper presents a Chaotic Vibrating Particles System (CVPS) optimization algorithm for solving the RCPSP. Vibrating Particles System (VPS) is a physic inspired metaheuristic which mimics the free vibration of single degree of freedom systems with viscous damping. The performance and applicability of the CVPS is compared with the standard VPS, and five well known algorithms on three benchmark instances of the RCPSPs Experimental studies reveals that the proposed optimization method is a promising alternative to assist project managers in dealing with RCPSP.

A new mixed-integer linear programming formulation and particle swarm optimization based hybrid heuristic for the problem of resource investment and balancing of the assembly line with multi-manned workstations

Resource investment and balancing problem of an assembly line with parallel multi-manned workstations can be defined as the assignment of tasks to reduce the cost of the line, which includes the cost of opened workstations and required renewable resources. Although mentioned problem has been commonly occurred in industrial environment that produce large scale products in high volumes, there have been restricted number of studies in the literature about this field. This article proposes a new mixed-integer linear programming approach that can be used in solving small size instances of the problem. In addition, a new hybrid method has been developed to solve larger scale instances by combining particle swarm optimization algorithm with a special constructive heuristic. In the constructive heuristic, serial schedule generation scheme widely used in solving resource constrained project scheduling problems has been adapted to resource investment problem with some modifications. Proposed metaheuristic has been compared against a tabu search and cuckoo search algorithm taken from the assembly line balancing literature. Many precedence diagrams commonly used in solving various assembly line balancing problems in the literature, have been used to generate test instances for the considered problem type. After solving these test instances using each solution methods, it has been observed that the proposed hybrid metaheuristic yielded the solutions, which have acceptable deviations from the lower bounds.

Probability Mechanism Based Particle Swarm Optimization Algorithm and Its Application in Resource-Constrained Project Scheduling Problems

In this paper, a new probability mechanism based particle swarm optimization (PMPSO) algorithm is proposed to solve combinatorial optimization problems. Based on the idea of traditional PSO, the algorithm generates new particles based on the optimal particles in the population and the historical optimal particles in the individual changes. In our algorithm, new particles are generated by a specially designed probability selection mechanism. We adjust the probability of each child element in the new particle generation based on the difference between the best particles and the elements of each particle. To this end, we redefine the speed, position, and arithmetic symbols in the PMPSO algorithm. To test the performance of PMPSO, we used PMPSO to solve resource-constrained project scheduling problems. Experimental results validated the efficacy of the algorithm.

Development of machine schedule at engineering enterprises

The article considers the mathematical formulation of the Resource-Constrained Project Scheduling Problem (RCPSP). The RCPSP structure is represented by a graph. The article regards some special cases of RCPSP for which at present there exist either exact deterministic polynomial algorithms for their solving or approximate heuristic algorithms that find an approximate optimal solution in polynomial time.

Robust resource-constrained project scheduling problem of the project’s subcontractors in a cooperative environment under uncertainty: Social complex construction case study

Improvement of project scheduling is a complicated task due to numerous activities and various resources. Accordingly, the resource-constrained project scheduling problem (RCPSP) is an NP-hard problem that minimizes the time and cost of the project. In this paper, the goal is to model the problem under uncertainty in the availability of the resources and activities duration simultaneously. Subcontractors of the construction projects are motivated to form a coalition to reduce the makespan, increase the availability of the resources and maximize their profits. Initially, the robust optimization (RO) model is developed for the RCPSP based on the multi-objective optimization method in which the uncertainty is modeled in a set of scenarios. The behavior of subcontractors is considered by supper-additivity in cooperation, satisfaction level and stability of coalitions. The results of the proposed model demonstrate that the subcontractors can work together in a coalition and obtain more profit rather than working individually. Then, game theory methods such as Shapley Value, Max-Min core, and Equal Profit Method are applied to fairly allocate excess profit of the coalition.

Survey of quality measures for multi-objective optimization: Construction of complementary set of multi-objective quality measures

Abstract In recent years interest in multiobjective optimization has flourished. Many Quality Measures (QM) have been developed to allow comparison of results gained by many methods. Unfortunately significant amount of various QMs along with the lack of imposed taxonomy have caused vagueness in the naming conventions. Hence a cohesive taxonomy is proposed that allows for classification of both existing and future QMs. This paper additionally provides thorough description of recently used QMs while attempting to unify the nomenclature. Advantages and disadvantages are shown along with the various features of the measures in given problem – as an example Multi–Skill Resource Constrained Project Scheduling Problem is given. Finally, a complementary set of QMs is proposed that can create a meaningful comparison of obtained multiobjective solutions to a multiobjective problem. Supplementary measures are proposed for specialized applications and open issues in the field are identified.

Decomposition based extended project scheduling for make-to-order production

Project scheduling has a critical function for many companies. Although there is a vast literature dedicated to the development of solution methodologies, the real-life applications of those techniques are few and often require over-simplification of the real-life problem. This study deals with the implementation of a project scheduling routine for a “make-to-order” machinery manufacturer. Although the problem is very similar to a resource-constrained project scheduling problem (RCPSP), which is a well-known and well-studied problem in the literature, it has multi-project and multi-mode components which make the project planning more challenging. Because of the multi-dimensional complexity of the problem, it is called a “Rich Project Scheduling Problem”. Our approach employs two techniques to deal with the issue of complexity. The first one is regarding calculation of the latest start time for each activity in the project. The second one is the decomposition method that includes breaking down the big problem into small manageable pieces. The approach was tested on real-life problems of a machine-building company. We also built more complex test cases from the real projects for testing purposes. Our approach produced high-quality solutions to the complex project scheduling problems within reasonable time limits. This work contributes to current research in several ways. An extension to the RCPSP formulation to include multi-project and multi-mode problems is introduced and successfully used for solving real-life problems. Additionally, activities of an RCPSP can be split into multiple sub-activities. Doing so is called preemption. The proposed formulation permits mode-switching during the execution of an activity, and it uses an alternative methodology to calculate latest activity start times.

New Task Domain Propagators with Polynomial Complexity for Resource-Constrained Project Scheduling Problem

We consider a classic Resource-Constrained Project Scheduling Problem (RCPSP) which is known to be NP-hard. For defined project deadline T , each task of the project can be associated with its temporal domain – a time interval in which this task can be processed. In this research, we adopt existing resource-based methods of task domain propagation to generalized statement with time-dependent resource capacity and show how to improve its propagation efficiency. We also present new polynomial-time algorithms (propagators) to tighten such temporal task domains in order to make the optimization problem easier to solve. Moreover, we show how these propagators can be used to calculate lower bound on project makespan.

A project scheduling problem with spatial resource constraints and a corresponding guided local search algorithm

Spatial area is a nonlinear resource encountered in many industries. Using the block assembly process in a shipbuilding company as a case study, we propose a project scheduling problem with spatial resource constraints (2D-RCPSP). Due to the two-dimensional properties of spatial resources, the 2D-RCPSP is more difficult to solve than the well-known NP-hard resource constrained project scheduling problem (RCPSP). For the 2D-RCPSP, we develop a sophisticated guided local search algorithm (GLS). The GLS incorporates penalty terms into the cost function and uses it, instead of the original objective function, to guide the search to the promising regions in search space. Furthermore, rapid improvement strategies are investigated in order to increase the efficiency of the local search. To test our GLS for the 2D-RCPSP, we have designed three classes of problem instances, two of which are adapted from the commonly referenced benchmark instance library PSPLIB for RCPSP, whereas the other is derived from real shipyard production data. Three types of tests, each for one class of instances, are implemented. The computational results on these instances as well as the tuning for key parameter in the GLS are presented.

Fuzzy resource-constrained project scheduling with multiple routes: A heuristic solution

Abstract The resource-constrained project scheduling problem (RCPSP) with multiple routes by considering flexible activities is one of important subjects in project scheduling problems. The ability to select an appropriate route for implementing the flexible activities is a rational reason for indicating more complexity of the problem relative to common RCPSP that attracted the attention of the researchers in the recent decade. On the other hand, due to lack of access to project crisp information, the needs to consider uncertainty concepts in the RCPSP will be significant. Hence, in this paper, a new fuzzy mixed integer nonlinear programming (MINLP) model is presented under uncertain conditions. A hybrid meta-heuristic approach is also proposed to minimize costs of project completion. In this approach, to generate high quality initial solutions, a heuristic algorithm is designed based on distribution rules. Then, to change and assign an appropriate route from available routes for flexible activities, a meta-heuristic algorithm is presented based on binary particle swarm optimization (PSO). Finally, to generate best solution from routes assigned by the binary PSO, a meta-heuristic based on genetic algorithm (GA) is proposed. To appraise the effectiveness of presented model, different test problems are solved by the proposed approach, and comparisons are provided with results obtained by the GA and PSO.

Improved selection in evolutionary multi–objective optimization of multi–skill resource–constrained project scheduling problem

In this paper a modified selection operator is presented in combination with classical Non-dominated Sorting Genetic Algorithm II (NSGA-II). It is shown that various modifications can lead to increased convergence, spread or uniformity of achieved Pareto fronts. A clone prevention method is used to increase the spread of resulting sets. Furthermore a crowding operator is removed from the NSGA-II as it serves a similar purpose as the clone prevention, even though it achieves it in a different manner. The former enforces diversity in a phenotype, while the latter enforces diversity in a genotype. Combinations of multiple selection modifiers are researched and the best configurations are identified. Multiple absolute measures are selected and applied to verify quality of the results. Additionally a relative measure is used to compare the fronts. They indicate that used selection improves convergence and spread of the front at the cost of its uniformity, while at the same time increasing the efficiency of search. Results are compared to the fronts obtained by multiple runs of a single–objective hybrid Differential Evolution with Greedy Algorithm. All experiments are performed on Multi–Skill Resource–Constrained Project Scheduling Problem.