A Differential Evolution Algorithm for Solving Resource Constrained Project Scheduling Problems

In this paper, a renowned metaheuristic algorithm named chemical reaction optimization (CRO) is applied to solve the resource constrained project scheduling problem (RCPSP). This work employed chemical reaction optimization to schedule project tasks to minimize makespan concerning resource and precedence constraints. Chemical reaction optimization is a population-based metaheuristic algorithm. CRO is applied to RCPSP by redesigning its basic operators and taking solutions from the search space using priority-based selection to achieve a better result. The proposed algorithm based on CRO is then tested on large benchmark instances and compared with other metaheuristic algorithms. The experimental results have shown that our proposed method provides better results than other states of art algorithms in terms of both the qualities of result and execution time.

The Resource Constrained Project Scheduling Problem (RCPSP) is been studied under different kinds of constraints and limitations. In this paper, we are going to consider the discounted cash flows for project activities, and delay penalties which occur when the project make span exceeds its deadline as the objective function of the RCPSP. To solve the model, we will take advantage of three different meta-heuristic algorithms - Genetic Algorithm (GA), Imperialist Competitive Algorithm (ICA), and Shuffled Frog Leaping Algorithm (SFLA) - to achieve the optimal solution of the problem. The evaluation of the algorithms performance reveals that, in comparison with ICA and SFLA, GA performs better, especially in large-scale problems.

The Resource-Constrained Project Scheduling Problem (RCPSP) is a general problem class of scheduling problems. It even contains the well-known job shop scheduling problem as a special case. In these problems, jobs demand different amounts from multiple resources at once. The goal is to minimize completion time while satisfying resource capacity constraints throughout the schedule. The RCPSP has several variations and generalizations, one of which is the multi-mode problem. Multiple operation modes are given for jobs, differing in resource usages and execution times. Another generalization is where resources have time-varying capacities instead of a constant limit. The S-graph framework was developed for batch process scheduling and used successfully in various applications. The advantages of this approach motivate research to extend its capabilities to more general problem classes and apply it in various specialized case studies. The authors have previously presented an extension of the S-graph framework for RCPSP and its multi-mode generalization. In this work, a further extension is proposed for handling time-varying capacities. The method relies on a model transformation technique and recent algorithmic developments of the framework.

Solving the Resource Constrained Project Scheduling Problem using the parallel Tabu Search designed for the CUDA platform

The project scheduling and resource allocation problems have been studied using different optimization methods. The resource leveling problem was proposed to reduce the resource fluctuation and was always studied independently resource constraint problem. For example, resource-constrained project scheduling problem (RCPSP) was proposed to optimize scheduling under resource constraints. This research proposed a new model which integrates the resource leveling problem and resource-constrained time-cost tradeoff problem. The evolutionary multi-objective optimization technique, strength Pareto evolutionary approach II (SPEA II) was applied to calculate the Pareto front of time and cost. The resource leveling measured by the metric, resource release/re-hiring, was converted to resource cost. The analysis of the time complexity of the model showed that the runtime of the algorithm was polynomial times of the number of activities. The results of case testing showed that the model was reasonably accurate in comparison with a proposed baseline model.

This paper is concerned with an overview of the Resource-Constrained Project Scheduling Problem (RCPSP) and the conventional meta-heuristic solution techniques that have attracted the attention of many researchers in the field. Therefore, researchers have developed algorithms and methods to solve the problem. This paper addresses the single-mode RCPSP where the objective is to optimize and minimize the project duration while the quantities of resources are constrained during the project execution. In this problem, resource constraints and precedence relationships between activities are known to be the most important constraints for project scheduling. In this context, the standard RCPSP is presented. Then, the classifications of the collected papers according to the year of publication and the different meta-heuristic approaches applied are presented. Five weighted articles and their meta-heuristic techniques developed for RCPSP are described in detail and their results are summarized in the corresponding tables. In addition, researchers have developed various conventional meta-heuristic algorithms such as genetic algorithms, particle swarm optimization, ant colony optimization, bee colony optimization, simulated annealing, evolutionary algorithms, and so on. It is stated that genetic algorithms are more popular among researchers than other meta-heuristics. For this reason, the various conventional meta-heuristics and their corresponding articles are also presented to give an overview of the conventional meta-heuristic optimizing techniques. Finally, the challenges of the conventional meta-heuristics are explored, which may be helpful for future studies to apply new suitable techniques to solve the Resource-Constrained Project Scheduling Problem (RCPSP).

This paper introduces a new practical scheduling problem called the resource-constrained project scheduling problem under multiple time constraints, which involves a duration constraint of activity, temporal constraint, and resource calendar constraint. The duration constraint of the activity exists widely in real-life projects, and it is first proposed as a resource-constrained project scheduling problem in this paper. We prove the defects of the traditional temporal constraint and improve it. The new problem combines three types of time constraints for the first time, which makes it closer to the actual scheduling problem. We developed a constraint programming optimization model for the new problem and used the IBM ILOG CPLEX-CP version 12.9.0 optimizer to solve it. Computational experiments are carried out to show that the CP optimizer is fast and provides a near-optimum solution to the new problem for projects with hundreds of activities within minutes compared to other metaheuristic methods. The results reported in this paper can be used as a benchmark for other researchers to compare and improve. The new problem contributes to developing a practical decision support system for resolving real-life constraints in projects.

Genetic algorithms (GAs) have been widely applied in the civil and construction engineering management research domain to solve difficult and complex problems such as resource-constrained project scheduling problems (RCPSPs). Generally, a trial-and-error calibration approach is used to identify values for the GA parameters. Unlike with other parameters, few studies have been done, theoretically or experimentally, for determining when to terminate GA for optimization of the RCPSP. Two genetic algorithm stopping conditions are compared to demonstrate their suitability for application in the RCPSP and to assess their ability in searching optimal solutions efficiently. The extensive computational results show that the Elitist GA, when using the unique schedule method, provides 10% more optimum values than those obtained from the Elitist GA when using the iteration method with 24% less computational time. The unique schedule stopping approach can be valuable for GA users to design their purpose driven GA for optimization of the RCPSP as it provides a better near-optimal solution with reduced computational time.

Resource constrained project scheduling problems (RCPSPs) are complex optimization problems that aim to minimize project completion time after considering limited resources and precedence-related activities with known durations. However, due to the dynamic nature of real-world applications, activity durations are vulnerable to change. In addition, resource demands along with resource availability at any stage of a project can also vary due to disruptions, which compel practitioners to re-think existing scheduling methodologies. Consequently, to mitigate the conjoint effect of those uncertainties and/or disruptions, this paper proposes a real-time reactive scheduling approach. To deal with uncertain activity durations, a chance constrained based approach is followed, which is later solved by an advanced meta-heuristic based approaches called IGFBIS and IGFBID. After solving an exhaustive list of stochastic RCPSP instances, this paper proves the efficacy of the proposed approaches, which is proven to be more useful to mitigate uncertainty or disruption while executing real-life projects.

We consider an extension of the Resource-Constrained Project Scheduling Problem (RCPSP) to multi-level (or multi-mode) activities. Each activity must be allocated exactly one unit of each required resource and the resource unit may be used at any of its specified levels. The processing time of an activity is given by the maximum of the durations that would result from a specific allocation of resources. The objective is to find the optimal solution that minimizes the overall project cost which includes a penalty for tardiness beyond the specified delivery date as well as a bonus for early delivery. We give some of the most important solution details and we report on the preliminary results obtained. The implementation was designed using the C# language.

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget; and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

In this paper, time crashing is implemented to solve the limitation of buffer insertion when consider the high variability of activities and resources in resource constrained project scheduling problem (RCPSP). The activity duration and resource are considered to be beta and exponential distributed, respectively. To settle the discrete time-cost trade off problem, a nonlinear combinatorial optimisation model is developed to pursuing the time, cost and robustness of the project. Six improvement principles are proposed and three balance points are discovered according to the different situations in the time-cost trade-off process, in which the earliness bonus, tardiness penalty, instability cost and time crashing cost are involved. To minimise total budget of the project, tabu search and starting time criticality heuristic is designed as the solution method. Finally, a numerical example is presented to highlight the efficiency of proposed model and solution method.

Project based planning and execution is used in various phases of a product lifecycle, starting from the conceptual idea and design through to the manufacturing and maintenance. It is common, that an enterprise or an organization executes more than one project in parallel. These projects may share the same resources and may have differing goals. Based on experience the order of task execution is a key factor, having a major impact on the key performance indicators. Our paper presents an extended model and a scheduling method for resource constrained project scheduling problems.

We consider a resource-constrained project scheduling problem with respect to the makespan minimization criterion. The problem accounts for technological constraints of activities precedence together with resource constraints. Activities pre- emptions are not allowed. The problem with renewable resources is NP-hard in the strong sense. We propose an exact branch and bound algorithm for solving the problem with renewable resources. It uses our new branching scheme based on the representation of a schedule in form of the activity list. We use two approaches of constructing the lower bound. We present results of numerical experiments, illustrating the quality of the proposed lower bounds. The test instances are taken from the library of test instances PSPLIB.

Resource-Constrained Project Scheduling Problem (RCPSP) is a well-known NP hard problem and more intelligent optimization algorithms are developed to solve it. In this paper, genetic algorithm(GA) is employed to deal with RCPSP. A priority value encoding scheme is designed to in the algorithm. The numerical results indicate that our methods is slightly better as far as solution quality is concerned and requires smaller solution time than the GA where an activity list encoding with schedule mode is used.