Resource-constrained Multi-project Scheduling Problem Research Articles

Multi Project Scheduling and Material Planning Using Lagrangian Relaxation Algorithm

Resource-constrained project scheduling is one of the well-known problems in project management. There are many cases where the appropriate schedule was determined first and material ordering plan was decided considering the given schedule. This approach ignores the interactions between these decisions. The integration of project scheduling, material procurement, and production planning of non-renewable resources leads to the coordination of project implementation and supplying resources. This coordination reduces total costs, including operating activities, production, ordering, holding, and penalty costs for late project completion. In addition to, there are many organizations that implement the multi project at the same time and decisions are made in a multi project environment. In this paper, a mixed integer programming model is presented for the resource-constrained multi-project scheduling problem and material ordering and production planning. Due to the application of Lagrangian relaxation algorithm in solving complex problems, this algorithm has been used to solve the proposed mathematical model. To evaluate the performance of the proposed model and solution method, a set of sample examples is solved and the numerical results are given. The findings of this paper show the good performance of the model and the solution method and can provide managerial insights for project managers and resource suppliers.

Applying hybrid genetic algorithm to multi-mode resource constrained multi-project scheduling problems

ABSTRACT Multi-mode resource-constrained multi-project scheduling problems (MMRCMPSP) are cases with a precedence relationship among activities, capacity constraints of different execution modes for activities, and multiple resources for multiple projects. In this study, hybrid genetic algorithm (HGA) and heuristic approach are developed to solve MMRCMPSP problems with the aim of minimizing makespan. The proposed HGA contains eight combinations of four typical priority rules (earliest due date, shortest process time, minimum slack, and maximum total work content) and two heuristic methods (serial and parallel) for MMRCMPSP. A total of 48 instances of related MMRCMPSP are considered from available resources and used as test beds for performance evaluation. Results demonstrate that the proposed HGA with parallel method and minimum slack priority rule outperforms a simple genetic algorithm and three activity-mode priority rule combinations from the recent literature. In addition, the superiority of HGA becomes increasingly significant when problem complexity increases.

New summary measures and datasets for the multi-project scheduling problem

In recent years, more researchers have devoted their attention to the resource-constrained multi-project scheduling problem, resulting in a growing body of knowledge on solution procedures. A key factor in the comparison of these procedures is the availability of benchmark datasets that cover a large part of the feature space. Otherwise, one risks that the conclusions from experiments on these sets do not hold when they are repeated on a different set. In this paper we propose new multi-project datasets that contain instances with a wide variety of characteristics. We first develop several new summary measures that describe three types of portfolio characteristics, two of the three types are not present in any of the existing datasets. Second, an algorithm is developed that can generate instances with the desired parameter values in a controlled manner. With this procedure, we create three datasets that each focus on one of the characteristics and a fourth dataset that contains all combinations. The computational results show (a) that these sets cover a significantly larger part of the feature space than existing benchmark libraries and (b) that they are more challenging for advanced algorithms.

A two-phase approach for solving the multi-skill resource-constrained multi-project scheduling problem: a case study in construction industry

PurposeThe purpose of this research is to study the Multi-Skill Resource-Constrained Multi-Project Scheduling Problem (MSRCMPSP), where (1) durations of activities depend on the familiarity levels of assigned workers, (2) more efficient workers demand higher per-day salaries, (3) projects have different due dates and (4) the budget of each period varies over time. The proposed model is bi-objective, and its objectives are minimization of completion times and costs of all projects, simultaneously.Design/methodology/approachThis paper proposes a two-phase approach based on the Statistical Process Control (SPC) to solve this problem. This approach aims to develop a control chart so as to monitor the performance of an optimizer during the optimization process. In the first phase, a multi-objective statistical model has been used to obtain control limits of this chart. To solve this model, a Multi-Objective Greedy Randomized Adaptive Search Procedure (MOGRASP) has been hired. In the second phase, the MSRCMPSP is solved via a New Version of the Multi-Objective Variable Neighborhood Search Algorithm (NV-MOVNS). In each iteration, the developed control chart monitors the performance of the NV-MOVNS to obtain proper solutions. When the control chart warns about an out-of control state, a new procedure based on the Conway’s Game of Life, which is a cellular automaton, is used to bring the algorithm back to the in-control state.FindingsThe proposed two-phase approach has been used in solving several standard test problems available in the literature. The results are compared with the outputs of some other methods to assess the efficiency of this approach. Comparisons imply the high efficiency of the proposed approach in solving test problems with different sizes.Practical implicationsThe proposed model and approach have been used to schedule multiple projects of a construction company in Iran. The outputs show that both the model and the NV-MOVNS can be used in real-world multi-project scheduling problems.Originality/valueDue to the numerous numbers of studies reviewed in this research, the authors discovered that there are few researches on the multi-skill resource-constrained multi-project scheduling problem (MSRCMPSP) with the aforementioned characteristics. Moreover, none of the previous researches proposed an SPC-based solution approach for meta-heuristics in order to solve the MSRCMPSP.

A variable neighborhood search approach for the resource-constrained multi-project collaborative scheduling problem

Multi-mode and multi-skill project scheduling problems widely exist in the real-world industry. Many efforts have been devoted to the multi-mode project scheduling problem and the multi-skill project scheduling problem. However, the integrated multi-mode and multi-skill project scheduling problem was seldom considered. This paper studies the resource-constrained multi-project scheduling problem in the development of high-end equipment and develops an integrated multi-mode and multi-skill scheduling model with different employee abilities. Based on the characteristics of high-end equipment development, we propose several optimal properties and design an effective heuristic algorithm. Since the resource-constrained project scheduling problem is NP-hard, three neighborhoods for the problem are constructed and a Variable Neighborhood Search Algorithm (VNS) is developed to solve the problem in a reasonable time. Finally, computational experiments are carried out to validate the performance of the proposed algorithm.

A graphical processing unit‐based parallel hybrid genetic algorithm for resource‐constrained multi‐project scheduling problem

SummaryIn this article, we present a parallel graphical processing unit (GPU)‐based genetic algorithm (GA) for solving the resource‐constrained multi‐project scheduling problem (RCMPSP). We assumed that activity pre‐emption is not allowed. Problem is modeled in a portfolio of projects where precedence and resource constraints affect the portfolio duration. We also assume that the durations, availability of resources are deterministic and portfolio has a static nature. The objective in this article is to find a start time for each activity of the project so that the portfolio duration is minimized, while satisfying precedence relations and resource availabilities within a reasonable amount of time for small and large problem instances. In order to compare the efficiency of the proposed parallel GPU‐based GA, problem is solved together with a CPU and a GPU. The results showed that GPU‐based parallel GA has high potential for improving the performance of GAs for the RCMPSP particularly, for large‐scale problems.

Modeling and algorithm for resource-constrained multi-project scheduling problem based on detection and rework

PurposeTo meet the requirement of establishing an effective schedule for the assembly process with overall detection and rework, this paper aims to address a new problem named resource-constrained multi-project scheduling problem based on detection and rework (RCMPSP-DR).Design/methodology/approachFirst, to satisfy both online and offline scheduling, a mixed integer programming model is established with a weighted bi-objective minimizing the expected makespan and the solution robustness. Second, an algorithm that combines a tabu search framework with a critical chain-based baseline generation scheme is designed. The tabu search framework focuses on searching for a reasonable resource flow representing the execution sequence of activities, while the critical chain-based baseline generation scheme establishes a buffered baseline schedule by estimating the tradeoff between two aspects of bi-objective.FindingsThe proposed algorithm can get solutions with gaps from −4.45% to 2.33% when compared with those obtained by the commercial MIP solver CPLEX. Moreover, the algorithm outperforms four other algorithms in terms of both objective performance and stability over instances with different weighting parameters, which reveals its effectiveness.Originality/valueThe represented RCMPSP-DR considering the overall detection and rework is an extension of the scheduling problem for large-scale equipment. An effective algorithm is proposed to establish the baseline schedule and determine the execution sequence of activities for the assembly process, which is significant for practical engineering applications.

Performance evaluation of scheduling policies for the dynamic and stochastic resource-constrained multi-project scheduling problem

In this study, we consider the dynamic and stochastic resource-constrained multi-project scheduling problem where projects generate rewards at their completion, completions later than a due date cause tardiness costs, task duration is uncertain, and new projects arrive randomly during the ongoing project execution both of which disturb the existing project scheduling plan. We model this problem as a discrete-time Markov decision process and explore the performance and computational limitations of solving the problem by dynamic programming. We run and compare five different solution approaches, which are: a dynamic programming algorithm to determine a policy that maximises the time-average profit, a genetic algorithm and an optimal reactive baseline algorithm, both generate a schedule to maximise the total profit of ongoing projects, a rule-based algorithm which prioritises processing of tasks with the highest processing durations, and a worst decision algorithm to seek a non-idling policy that minimises the time-average profit. The performance of the optimal reactive baseline algorithm is the closest to the optimal policies of the dynamic programming algorithm, but its results are suboptimal, up to 37.6%. Alternative scheduling algorithms are close to optimal with low project arrival probability but quickly deteriorate their performance as the probability increases.

An Algorithm for Efficient Generation of Customized Priority Rules for Production Control in Project Manufacturing with Stochastic Job Processing Times

Project Planning and Control (PPC) problems with stochastic job processing times belong to the problem class of Stochastic Resource-Constrained Multi-Project Scheduling Problems (SRCMPSP). A practical example of this problem class is the industrial domain of customer-specific assembly of complex products. PPC approaches have to compensate stochastic influences and achieve high objective fulfillment. This paper presents an efficient simulation-based optimization approach to generate Combined Priority Rules (CPRs) for determining the next job in short-term production control. The objective is to minimize project-specific objectives such as average and standard deviation of project delay or makespan. For this, we generate project-specific CPRs and evaluate the results with the Pareto dominance concept. However, generating CPRs considering stochastic influences is computationally intensive. To tackle this problem, we developed a 2-phase algorithm by first learning the algorithm with deterministic data and by generating promising starting solutions for the more computationally intensive stochastic phase. Since a good deterministic solution does not always lead to a good stochastic solution, we introduced the parameter Initial Copy Rate (ICR) to generate an initial population of copied and randomized individuals. Evaluating this approach, we conducted various computer-based experiments. Compared to Standard Priority Rules (SPRs) used in practice, the approach shows a higher objective fulfilment. The 2-phase algorithm can reduce the computation effort and increases the efficiency of generating CPRs.

An efficient genetic algorithm for decentralized multi-project scheduling with resource transfers

<p style='text-indent:20px;'>This paper investigates the decentralized resource-constrained multi-project scheduling problem with transfer times (DRCMPSPTT) in which the transfer times of the global resources among different projects are assumed to be sequence-independent, while transfers of local resources take no time within a project. First, two decision variables (<inline-formula><tex-math id="M1">\begin{document}$ {y_{ijg}} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ {w_{ijg}} $\end{document}</tex-math></inline-formula>) are adopted to express the transition state of global resources between projects. <inline-formula><tex-math id="M3">\begin{document}$ {y_{ijg}} $\end{document}</tex-math></inline-formula> (takes a value of 0 or 1) represents whether activity <i>i</i> transfers global resource <i>g</i> to activity <i>j</i>; accordingly, the transferred quantity is denoted as <inline-formula><tex-math id="M4">\begin{document}$ {w_{ijg}} $\end{document}</tex-math></inline-formula>. Then, we construct an integer linear model with the goal of minimizing the average project delay for the DRCMPSPTT. Second, an adaptive genetic algorithm (GA) is developed to solve the DRCMPSPTT. To gain the schedules for the DRCMPSPTT, the traditional serial and parallel scheduling generation schemes (SGSs) are modified to combine with different resource transfer rules and to design multiple decoding schemes. Third, the numerical experiments are implemented to analyse the effects of eight decoding schemes, and we found that the scheme comprising the parallel SGS and maxRS rule can make the GA work the best; furthermore, the effectiveness of the GA_maxRS (GA embedded with the best scheme) is demonstrated by solving some instances with different sizes.</p>

Fuzzy Mathematical Models for Maximizing Contractors’ and Clients’ Satisfaction by Considering Flexible Start Date of the Project

Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) is considered a significant topic in project management studies and many kinds of research have been carried out in this field which have been proposed numerous approaches. However, in most of them, the viewpoints of clients and contractors, two important stakeholders of the project are not directly considered. The current research tries to introduce a new approach of RCMPSP in order to schedule the project portfolio and allocate the budget as a limited resource simultaneously. In this way, first, the client's and contractors' budget satisfaction is defined. Then some budget allocation models have been proposed to maximize the clients' and the contractors’ satisfaction. These models consider constraints such as the minimum cost required for each project, the maximum budget for each period, and the flexibility for the start date of each project. To illustrate the proposed models, a real case of the project portfolio is considered.

Tabu search and simulated annealing for resource-constrained multi-project scheduling to minimize maximal cash flow gap

In reality, a contractor may implement multiple projects simultaneously and in such an environment, how to achieve a positive balance between cash outflow and inflow by scheduling is an important problem for the contractor has to tackle. For this fact, this paper investigates a resource-constrained multi-project scheduling problem with the objective of minimizing the contractor's maximal cash flow gap under the constraint of a project deadline and renewable resource. In the paper, we construct a non-linear integer programming optimization model for the studied problem at first. Then, for the NP-hardness of the problem, we design three metaheuristic algorithms to solve the model: tabu search (TS), simulated annealing (SA), and an algorithm comprising both TS and SA (SA-TS). Finally, we conduct a computational experiment on a data set coming from existing literature to evaluate the performance of the developed algorithms and analyze the effects of key parameters on the objective function. Based on the computational results, the following conclusions are drawn: Among the designed algorithms, the SA-TS with an improvement measure is the most promising for solving the problem under study. Some parameters may exert an important effect on the contractor's maximal cash flow gap.

Resource-constrained multi-project scheduling: benchmark datasets and decoupled scheduling

In this paper, we propose a new dataset for the resource-constrained multi-project scheduling problem and evaluate the performance of multi-project extensions of the single-project schedule generation schemes. This manuscript contributes to the existing research in three ways. First, we provide an overview of existing benchmark datasets and classify the multi-project literature based on the type of datasets that are used in these studies. Furthermore, we evaluate the existing summary measures that are used to classify instances and provide adaptations to the data generation procedure of Browning and Yassine (J Scheduling 13(2):143-161, 2010a). With this adapted generator we propose a new dataset that is complimentary to the existing ones. Second, we propose decoupled versions of the single-project scheduling schemes, building on insights from the existing literature. A computational experiment shows that the decoupled variants outperform the existing priority rule heuristics and that the best priority rules differ for the two objective functions under study. Furthermore, we analyse the effect of the different parameters on the performance of the heuristics. Third, we implement a genetic algorithm that incorporates specific multi-project operators and test it on all datasets. The experiment shows that the new datasets are challenging and provide opportunities for future research.

Comparing optimization modeling approaches for the multi-mode resource-constrained multi-project scheduling problem

PurposeConstruction firms keep minimal resources to maintain productive working capital. Hence, resources are constrained and have to be shared among multiple projects in an organization. Optimal allocation of resources is a key challenge in such situations. Several approaches and heuristics have been proposed for this task. The purpose of this paper is to compare two approaches for multi-mode resource-constrained project scheduling in a multi-project environment. These are the single-project approach (portfolio optimization) and the multi-project approach (each project is optimized individually, and then heuristic rules are used to satisfy the portfolio constraint).Design/methodology/approachA direct search algorithm called Probabilistic Global Search Lausanne is used for schedule optimization. Multiple solutions are generated that achieve different trade-offs among the three criteria, namely, time, cost and quality. Good compromise solutions among these are identified using a multi-criteria decision making method, Relaxed Restricted Pareto Version 4. The solutions obtained using the single-project and multi-project approaches are compared in order to evaluate their advantages and disadvantages. Data from two sources are used for the evaluation: modified multi-mode resource-constrained project scheduling problem data sets from the project scheduling problem library (PSPLIB) and three real case study projects in India.FindingsComputational results prove the superiority of the single-project approach over heuristic priority rules (multi-project approach). The single-project approach identifies better solutions compared to the multi-project approach. However, the multi-project approach involves fewer optimization variables and is faster in execution.Research limitations/implicationsIt is feasible to adopt the single-project approach in practice; realistic resource constraints can be incorporated in a multi-objective optimization formulation; and good compromise solutions that achieve acceptable trade-offs among the conflicting objectives can be identified.Originality/valueAn integer programming model was developed in this research to optimize the multiple objectives in a multi-project environment considering explicit resource constraints and maximum daily costs constraints. This model was used to compare the performance of the two multi-project environment approaches. Unlike existing work in this area, the model used to predict the quality of activity execution modes is based on data collected from real construction projects.

Research on priority rules for the stochastic resource constrained multi-project scheduling problem with new project arrival

The resource constrained multi-project scheduling problem (RCMPSP) is a general and classic problem, which is usually considered and solved in a deterministic environment. However, in real project management, there are always some unforeseen factors such as one or more new project arrivals that give rise to intermittent changes in the activity duration (or stochastic duration) of the current project in execution by inserting the new project. This study takes two practical factors in terms of stochastic duration of project activities and new project arrivals waiting for insertion into account of the problem space to form a stochastic resource constrained multi-project scheduling problem with new project arrivals (SRCMPSP-NPA). Based on the benchmark of the PSPLIB (Project Scheduling Problem Library), a new data set is built and 20 priority rules (PRs) are applied to solve the problem and their performances are analyzed. In addition, a heuristic hybrid method is designed for solving the problem timely by dividing the entire scheduling process into multi-state scheduling problems solved by the corresponding rules separately. This approach has been verified by experiments and its performance is better than that of a single rule in most situations.

Solving the resource-constrained multi-project scheduling problem with an improved critical chain method

In view of the fact that the critical chain method (CCM) is mainly used in single project scheduling, this article improves the method and applies it to multi-project scheduling. Taking into consideration the flow of the drum resource within and among sub-projects, this study proposes methods that can be used to identify the critical chain and buffer settings, based on the concepts of the task chain, sub-project drum resource flow, and multi-project drum resource flow. The improvement of the CCM includes two aspects. First, by analysing the impact of the drum buffer and capacity constrained buffer on the project buffer and feeding buffer, the calculation methods of these buffers are optimised. Second, a risk contribution index is designed for the modification of these buffers, in order to further improve their anti-interference ability. Then, combined with the improved CCM and the different hierarchical scheduling objectives, a critical chain resource-constrained multi-project scheduling model with a hierarchical strategy is proposed as a way of solving multi-project scheduling plans. Eight theoretical test cases with different scales, and a practical example under different risk levels of uncertainty are used to test this model. The results show that the stability of the scheduling plans clearly improved, and the project duration and tardiness costs were significantly reduced, thus proving the effectiveness of the model.

Multi-agent Learning by Trial and Error for Resource Leveling during Multi-Project (Re)scheduling

In a multi-project context within enterprise networks, reaching feasible solutions to the (re)scheduling problem represents a major challenge, mainly when scarce resources are shared among projects. The multi-project (re)scheduling must achieve the most efficient possible resource usage without increasing the prescribed project constraints, considering the Resource Leveling Problem (RLP), whose objective is to level the consumption of resources shared in order to minimize their idle times and to avoid overallocation conflicts. In this work, a multi-agent solution that allows solving the Resource Constrained Multi-project Scheduling Problem (RCMPSP) and the Resource Investment Problem is extended to incorporate indicators on agents’ payoff functions to address the Resource Leveling Problem in a decentralized and autonomous way, through decoupled rules based on Trial-and-Error approach. The proposed agent-based simulation model is tested through a set of project instances that vary in their structure, parameters, number of resources shared, etc. Results obtained are assessed through different scheduling goals, such as project total duration, project total cost and leveling resource usage. Our results are far better compared to the ones obtained with alternative approaches. This proposal shows that the interacting agents that implement decoupled learning rules find a solution which can be understood as a Nash equilibrium.

Research on a Multi-project Scheduling Optimization Algorithm with Resource Time-Windows

A resource-constrained multi-project scheduling problem with resource time-windows model is established aimed at minimizing the makespan of multi-project. In terms of solution method, a heuristic algorithm based on Serial Scheduling Generated Scheme is designed to generate an initial solution and a tabu search algorithm is proposed to optimize the solution. Experimental results show that the proposed model is feasible and the proposed method is effective.

A lagrangian relaxation algorithm for facility location of resource-constrained decentralized multi-project scheduling problems

Recent literature on multi-project scheduling problems has been focused on the transfer of available resources between project activities, especially in decentralized projects. Determining the right location for storage facilities where resources are moved between activities is major topics in decentralized multi-projects scheduling problems. This paper introduces a new decentralized resource-constrained multi-project scheduling problem. Its purpose is to simultaneously minimize the cost of the project completion time and the cost of facilities location. A mixed integer linear programming model is first presented to solve small-size problems by using conventional solvers. Then, three heuristic/meta-heuristic methods are proposed to solve larger-size problems. To this end, a fast constructive heuristic algorithm based on priority rules is introduced. Then, using the heuristic method structure, a combinatorial genetic algorithm is developed to solve large-size problems in reasonable CPU running time. Finally, the lagrangian relaxation technique and branch-and-bound algorithm are applied to generate an effective lower bound. According to the computational results obtained and managerial insights, total costs can be significantly reduced by selecting an optimal location of resources. By the use of a scenario-based TOPSIS approach, the heuristic methods are ranked based on changes in the importance of metrics. Friedman’s test result of TOPSIS shows that there is no significant difference among the heuristic methods.

A multi-unit combinatorial auction based approach for decentralized multi-project scheduling

In industry, many problems are considered as the decentralized resource-constrained multi-project scheduling problem (DRCMPSP). Existing approaches encounter difficulties in dealing with large DRCMPSP cases while respecting the information privacy requirements of the project agents. In this paper, we tackle DRCMPSP by formulating it as a multi-unit combinatorial auction (Wellman et al. in Games Econ Behav 35(1):271–303, 2001), which does not require sensitive private project information. To handle the hardness of bidder valuation, we introduce the capacity query which uses different item capacity profiles to efficiently elicit valuation information from bidders. Based on the capacity query, we adopt two existing strategies (Gonen and Lehmann in Proceedings of the 2nd ACM conference on electronic commerce, pp 13–20, 2000) for solving multi-unit winner determination problems to find good allocations of the DRCMPSP auctions. The first strategy employs a greedy allocation process, which can rapidly find good allocations by allocating the bidder with the best answer after each query. The second strategy is based on a branch-and-bound process to improve the results of the first strategy, by searching for a better sequence of granting the bids from the bidders. Empirical results indicate that the two strategies can find good solutions with higher quality than state-of-the-art decentralized approaches, and scale well to large-scale problems with thousands of activities from tens of projects.