Resource Leveling Problem Research Articles

Metric estimation approach for managing uncertainty in resource leveling problem

Metric estimation approach for managing uncertainty in resource leveling problem

An Empirical Analysis of a Set of Hybrid Heuristics for the Solution of the Resource Leveling Problem

Consideration is given to the heuristic solution of the resource leveling problem (RLP) in project scheduling with limited resources. The objective is to minimize the changes in the level of resource usage from period to period over the planning horizon of the project while keeping the project duration fixed. First, we present two novel greedy schedule algorithms for the RLP solution. The performance of the proposed algorithms is investigated as low-level hybrids in the context of three famous population-based heuristics, namely differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO). Then, we additionally present two new high-level hybridization schemes (HS), referred to herein as parallel and serial HS, respectively, which combine DE, GA, and PSO in a single hybrid solution algorithm. Detailed experimentation over known complex datasets measures the efficiency of the new hybrids. Statistical analysis employed rank the hybrids according to their solution efficiency. Moreover, comparisons between the developed best hybrid and commercial project management software show a substantial higher performance for the former over real-world construction projects.

A Memetic Algorithm for the Solution of the Resource Leveling Problem

In this paper, we present a novel memetic algorithm (MA) for the solution of the resource leveling problem (RLP). The evolutionary framework of the MA is based on integration of a genetic algorithm and simulated annealing methods along with a resource leveling heuristic. The main objective of the proposed algorithm is to integrate complementary strengths of different optimization methods and incorporate the individual learning as a separate process for achieving a successful optimization method for the RLP. The performance of the MA is compared with the state-of-the-art leveling methods. For small instances up to 30 activities, mixed-integer linear models are presented for two leveling metrics to provide a basis for performance evaluation. The computational results indicate that the new integrated framework of the MA outperforms the state-of-the-art leveling heuristics and meta-heuristics and provides a successful method for the RLP. The limitations of popular commercial project management software are also illustrated along with the improvements achieved by the MA to reveal potential contributions of the proposed integrated framework in practice.

Tüm Arama Uzayı Taranarak Kaynak Dengeleme Probleminin Optimum Çözülmesi

İnşaat süresi boyunca kaynak kullanımında gözlemlenen dalgalanmaların proje süresinde gecikme olmadan asgari düzeye indirilmesi kaynak dengeleme problemi olarak tanımlanır. Bu problem basit kurallar içeren sezgisel, sistematik fakat rassal biçimde arama uzayını tarayan üst-sezgisel ve analitik yöntemlerle çözülmektedir. Ancak aktivite sayısının artması ile arama uzayı çok büyüyen kaynak dengeleme probleminin çözümünde oluşan sorunlara karşı belirtilen yöntemler yetersiz kalmaktadır. Bu çalışmada, aktiviteler arasındaki kısıtlar ihlal edilmeden kritik olmayan aktivitelerin ertelenmesi ile kaç farklı şekilde uygulanabilir çözüm elde edilebileceği hesaplanarak kaynak dengeleme probleminin arama uzayının büyüklüğü belirlenmiştir. Belirlenen arama uzayının tamamı taranarak uygulanabilir en iyi çözüm garantili biçimde elde edilmiştir. Kaynak dağılımının uygunluğu minimum moment ölçeği ile incelenmiştir. Yöntemin uygulanabilmesi için bir hesap tablosu uygulaması oluşturularak Visual Basic programlama dilinde makro yazılmıştır. Literatürden derlenen 27 kaynak dengeleme probleminin geliştirilen yöntemle optimum çözümü elde edilmiştir. Hesap cetveline kaynak dengeleme probleminin nasıl tanıtılacağı çözülen problemler arasından seçilen 2 örnek problem üzerinde detaylı biçimde anlatılarak yöntemin tüm araştırmacılar tarafından uygulanabilmesi sağlanmıştır. Ayrıca geliştirilen yöntem çözüm süresini kısaltmak için C++ dilinde de kodlanmıştır. Test problemleri genetik algoritmayla çözülmüş, hesaplama süreleri ve sunduğu sonuçlar önerilen yöntemin çıktıları ile karşılaştırılmıştır. Çözüm süresi ve çözüm iyiliğinin karşılaştırılması sonucunda geliştirilen yöntemin kaynak dengeleme probleminin kesin çözümünde uygulanabilir olduğu belirlenmiştir. Ayrıca çalışma kaynak dengeleme probleminin arama uzayını belirleyen bir yöntem geliştirerek literatüre katkı sağlamaktadır.

A community detection approach for the resource leveling problem in a multi-project scheduling environment

This paper develops an integrated mathematical formulation that embraces the Resource Leveling Problem (RLP) and the Multi-Project Scheduling Problem (MPSP). To incorporate both aspects into one formulation, the proposed model is bi-objective that seeks to minimize projects’ durations and resource usage, simultaneously. Resources are not available in all time periods because of sickness, failure, maintenance, holidays, training, laying off, etc. This assumption complicates the scheduling process for multiple concurrent projects that share a limited number of resources with finite capacities. To tackle this intricacy, a coherent approach is required that not only schedules activities of multiple projects, but also levels resource consumptions as efficient as possible. Therefore, this study offers an approach based on the Community Detection problem to identify homogeneous communities of activities that have common resource requirements. These communities are obtained by the Vibration Damping Optimization (VDO) method through modularity maximization. The identified communities help the projects’ planner to avoid simultaneous scheduling of the activities within a community; hence, resource consumptions are minimized. A Multi-Objective Gravitational Search Algorithm (MOGSA) is developed to solve the proposed bi-objective problem. The MOGSA uses the communities detected by the VDO and schedules the projects. The MOGSA has been invigorated by using two Cellular Automata (CA), namely “Seeds” and “Wolfram’s elementary cellular automaton” in its procedures. A set of test problems have been examined to compare the efficacy of the MOGSA with some of the best existing algorithms. The results demonstrate that the MOGSA is highly competitive and yields proper solutions comparing to the outputs of well-known optimizers. Besides, a real construction case study has been presented to demonstrate that the proposed model and algorithm can deliver practical solutions.

Hybrid Differential Evolution Particle Swarm Optimization Algorithm for Solving Resource Leveling Problem of Multi-project with Fixed Duration

This paper attempts to substitute Resource Leveling Problem (RLP) into multi-project environment and construct Resource Leveling Problem of Multi-project (RLPMP) model with the goal of minimizing the sum of weighted mean square deviations of multi-resource requirements. A two-stage hybrid differential evolution particle swarm optimization algorithm is used to solve the model. In the first stage, differential evolution algorithm is used to produce new individuals, and in the second stage, particle swarm optimization algorithm uses a new speed update formula. In the first stage, in order to ensure that the optimal individual will not be destroyed by crossover and mutation, and to maintain the convergence of differential evolution algorithm, we try to introduce Elitist reservation (ER) strategy into differential evolution algorithm. In the second stage, we use a kind of Particle Swarm Optimization (PSO) algorithm with dynamic inertia weight. Through the dynamic change of inertia weight, the global search and local search ability of the algorithm can be adjusted flexibly. The case verification shows that the hybrid differential evolution particle swarm optimization algorithm can effectively solve the RLPMP model, and then effectively improve the balance of multi-project resources.

Exact Solution of Resource Leveling Problem by Exhaustive Enumeration with Parallel Programming

Kaynak dengeleme problemi (KDP) sezgisel, modern sezgisel ve matematiksel yöntemlerle çözülmektedir. Fakat belirtilen yöntemler özellikle büyük boyutlu problemler için kesin çözümü garanti edememektedir. Bu çalışmada KDP'nin aktiviteler arasındaki bağımlılık ilişkilerini ihlal etmeden ve proje süresinde uzamaya neden olmayacak şekilde bolluğu olan aktivitelerin ertelenmesi ile elde edilebilecek birbirinden farklı kaç iş programı oluşturulabileceği hesaplanmıştır. Arama uzayı olarak tanımlanan tüm uygulanabilir iş programlarının tamamının denenmesi ile garantili biçimde KDP'nin en iyi çözümü elde edilerek mevcut yöntemlerden farklı biçimde KDP'nin çözülmesi sağlanmıştır. Aktivite sayısı ile arama uzayı arasında seri bağlı aktiviteler için üstel bağıntı formülü türetilerek büyük projelerin tek işlemci ile çözümünün makul sürede gerçekleşemeyeceği belirlenmiştir. Problemin paralel programlama ile tüm işlemcilere eşit sayıda şebeke çözümü düşecek şekilde paylaştırılması sağlanmıştır. Bu çalışmada en büyüğü 36 aktiviteli olan 4 KDP arama uzayının tamamı taranıp makul sürede çözülerek geliştirilen yöntemin uygulanabilir olduğu kanıtlanmıştır. Bu yöntem ile daha küçük parçalara ayırmak sureti ile daha büyük kaynak dengeleme problemlerinin kesin çözümü elde edilebilecektir.

Stochastic resource leveling optimization method for trading off float consumption and project completion probability

AbstractExisting resource leveling (RL) approaches fall short of analyzing the trade‐off relation between the total float consumption and project completion probability in a real‐life project RL problem. This article presents a stochastic resource leveling optimization (SOLO) method that minimizes the total float consumption along with maximizing the project completion probability. It initializes the earliest start times of noncritical activities, measures the level of resource fluctuations of each candidate solution, computes the probability of completing a project in a target deadline by executing simulation‐based scheduling, and identifies optimal solution(s) (i.e., optimal start times of noncritical activities) by implementing genetic algorithm, thereby identifying an optimal resource‐leveled baseline. The study is of value to practitioners because SOLO considers both the amount of total float consumption and project completion probability. This study facilitates experimentation with different computation time‐saving options given various constraints (i.e., the residual of project completion probabilities, threshold of release and rehire, ratio of criticality index, and number of critical activities). Test cases verify the validity of the computational method.

Benders decomposition for a period-aggregated resource leveling problem with variable job duration

We consider a special case of resource leveling problem with variable job duration and period-aggregated resource consumption. The objective function is to minimize the total extra resource cost required to complete all jobs before the hard project deadline. All jobs must be implemented without any preemption. The planning horizon is divided into periods, each period is characterized by an available level of resources of each type. For each job, resource consumption varies from one period to another. It is possible to control the speed of the job execution: if more resources are allocated to a job, then the job is executed faster if fewer resources are used, the job takes more time. A problem solution defines the start and end times for each job, but also its resource usage per period. On contrary to former models of this problem, our formulation allows an independent resource usage for each resource type. This approach can reach more flexible solutions with lower cost objective function value. We develop a Benders decomposition algorithm to solve this new formulation. Several enhancements are also implemented, such as the construction of effective bounds and multi-cut generation with the single search tree (Branch&Benders cuts). Numerical experiments on several sets of instances demonstrate the advantage of the algorithm in comparison with the basic model and a CPLEX built-in Benders decomposition.

Dynamic resource levelling in projects under uncertainty

In the resource levelling problem (RLP) under uncertainty, existing studies focus on obtaining an open-loop activity list that is not updated during project execution. In project management practice, it is also necessary to address more situations, such as activity overlaps and resource breakdowns. In this paper, we extend the uncertain RLP by proposing a resource levelling problem with multiple uncertainties (RLP-MU) that simultaneously considers uncertainties in activity durations, activity overlaps and resource availabilities. We formulate the RLP-MU as a Markov decision process model. Aimed at levelling resource usage by dynamically scheduling activities at each decision point based on the observed information, we develop a hybrid open–closed-loop approximate dynamic programming algorithm (HOC-ADP). In the HOC-ADP, we devise a closed-loop rollout policy to approximate the cost-to-go function and use the concept of the average project to avoid time-consuming simulation. A greedy-decoding-based estimation of distributed algorithm is also devised to construct an open-loop policy that is embedded in the HOC-ADP to further improve it. We additionally develop a simulation algorithm to evaluate the resource levelling performance of the HOC-ADP. Computational experiments on a benchmark dataset consisting of 540 problem instances are conducted to analyze the performance of the HOC-ADP, and the impact of various factors on resource levelling are investigated. The comparison experimental results indicate that our HOC-ADP outperforms the state-of-the-art meta-heuristics.

The multi resource leveling and materials procurement problem: an integrated approach

PurposeThis paper proposes an integrated approach that seeks to jointly optimize project scheduling and material lot sizing decisions for time-constrained project scheduling problems.Design/methodology/approachA mixed integer linear programming model is devised, which utilizes the splitting of noncritical activities as a mean toward leveling the renewable resources. The developed model minimizes renewable resources leveling costs along with consumable resources related costs, and it is solved using IBM ILOG CPLEX optimization package. A hybrid metaheuristic procedure is also proposed to efficiently solve the model for larger projects with complex networks structure.FindingsThe results confirmed the significance of the integrated approach as both the project schedule and the material ordering policy turned out to be different once compared to the sequential approach under same parameter settings. Furthermore, the integrated approach resulted in substantial total costs reduction for low values of the acquiring and releasing costs of the renewable resources. Computational experiments conducted over 240 test instances of various sizes, and complexities illustrate the efficiency of the proposed metaheuristic approach as it yields solutions that are on average 1.14% away from the optimal ones.Practical implicationsThis work highlights the necessity of having project managers address project scheduling and materials lot sizing decisions concurrently, rather than sequentially, to better level resources and minimize materials related costs. Significant cost savings were generated through the developed model despite the use of a small-scale example which illustrates the great potential that the integrated approach has in real life projects. For real life projects with complex network topology, practitioners are advised to make use of the developed metaheuristic procedure due to its superior time efficiency as compared to exact solution methods.Originality/valueThe sequential approach, wherein a project schedule is established first followed by allocating the needed resources, is proven to yield a nonoptimized project schedule and materials ordering policy, leading to an increase in the project's total cost. The integrated approach proposed hereafter optimizes both decisions at once ensuring the timely completion of the project at the least possible cost. The proposed metaheuristic approach provides a viable alternative to exact solution methods especially for larger projects.

A common approximation framework for early work, late work, and resource leveling problems

We study the approximability of four scheduling problems on identical parallel machines. In the late work minimization problem, the jobs have arbitrary processing times and a common due date, and the objective is to minimize the late work, defined as the sum of the portion of the jobs done after the due date. A related problem is the maximization of the early work, defined as the sum of the portion of the jobs done before the due date. We describe a polynomial time approximation scheme for the early work maximization problem, and we extended it to the late work minimization problem after shifting the objective function by a positive value that depends on the problem data. We also prove an inapproximability result for the latter problem if the objective function is shifted by a constant which does not depend on the input. These results remain valid even if the number of the jobs assigned to the same machine is bounded. This leads to an extension of our approximation scheme to two variants of the resource leveling problem with unit time jobs, for which no approximation algorithm is known.

Resource Allocation and Leveling in Construction Management Projects with Resource Histogram

Resource allocation and leveling in construction management projects have been an enthusiastic subject to plenty of researchers since the advancement of the scheduling techniques. Many researchers have studied various versions of the benchmark resource leveling and allocation optimization problems using various scheduling techniques. However, in this study, a straightforward scheduling technique called resource histogram is utilized to allocate and level the available resources. Moreover, the maximum number of resources at peak time is considered as a significant aspect of the case study. Since peak demand isn’t a preferred by the contractor. The effects of resources are also examined in order to demonstrate the variation of the total duration of the project which provides flexibility to decision-makers in making intelligent decisions regarding the use of the resources. Thereby, a construction project with seven activities taken from the technical literature is examined with constrained as well as unconstrained conditions using Microsoft Excel. However, task scheduling is performed using critical path method (CPM). The results indicate that limitation on resources significantly affect the performance and cause the project to be extended beyond the scheduled duration. Moreover, besides renewable, non-renewable resources (e.g., cost demand) may also be significant parameters and this extension can be considered in future research.

Float-Based Resource Leveling Optimization of Linear Projects

In recent years, the linear scheduling method (LSM) approach to the linear project scheduling optimization problem has been widely studied by researchers. In this paper, the problem of resource leveling of linear projects under the framework of LSM is studied. Firstly, the concept of a third type of float is proposed, and the advantages of this third type of float to the optimization of linear project resource leveling are analyzed. On this basis, a two-stage optimization process of the linear project resource leveling problem based on the third type of float is proposed. The process takes into account new constraints such as total resource constraint, resource utilization constraint, and construction mileage constraint, and it aims to maximize the space-time flexibility of construction activities and realize the depth optimization of linear project resource leveling. According to the integer nonlinear characteristic of the model, a quantum particle swarm optimization algorithm with a constraint processing mechanism and particle search range restriction is designed. Finally, the effectiveness of the proposed model is verified by case analysis and comparison of the results in previous studies.

A Generalized MILP Formulation for the Period-Aggregated Resource Leveling Problem with Variable Job Duration

We study a resource leveling problem with variable job duration. The considered problem includes both scheduling and resource management decisions. The planning horizon is fixed and separated into a set of time periods of equal length. There are several types of resources and their amount varies from one period to another. There is a set of jobs. For each job, a fixed volume of work has to be completed without any preemption while using different resources. If necessary, extra resources can be used at additional costs during each time period. The optimization goal is to minimize the total overload costs required for the execution of all jobs by the given deadline. The decision variables specify the starting time of each job, the duration of the job and the resource amount assigned to the job during each period (it may vary over periods). We propose a new generalized mathematical formulation for this optimization problem. The formulation is compared with existing approaches from the literature. Theoretical study and computational experiments show that our approach provides more flexible resource allocation resulting in better final solutions.

Genetic algorithm based optimization for resource leveling problem with precedence constrained scheduling

Resource Leveling Problem (RLP) in construction projects mainly deals with reducing the peaks and valleys of daily resource requirements. RLP is an interesting field of research and several researchers have tried to solve it over the past few decades. Numerical methods and heuristics do not provide good results for solving Non-deterministic polynomial-hard (NP-hard) problems. So that, a metaheuristic approach is highly required to predict the solution with greater efficiency. This research work aims to solve RLP using Genetic Algorithm as the meta-heuristic approach, developed in a programming platform. Modified critical path scheduling method, was adopted to develop a schedule that determines the partial critical nature of activity with a start to start precedence relationship. Activities from a real-time construction project were considered to evaluate the proposed idea. The result obtained was significantly better than the results provided by existing commercial project management software and helps to solve RLP with the advantage of considering real-time floats.

Optimization of resource leveling problem under multiple objective criteria using a symbiotic organisms search

Bad scheduling and resource management can cause delays or cost overruns. Optimization in solving resource leveling is necessary to avoid those problems. Several objective criteria are used to solve resource leveling. Each of them has the same objective, which is to reduce the fluctuation of resource demand of the project. This study compares the performance of particle swarm optimization (PSO) and symbiotic organisms search (SOS) in solving resource leveling problems using separate objective functions in order to find which one produces a better solution. The results show that SOS produced a better solution than PSO, and one objective function is better in solving resource leveling than the others.

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.

Resource Leveling Based on Line of Balance and Constraint Programming

AbstractThis study investigated resource leveling problems concerning linear construction projects based on the line of balance (LOB) technique and constraint programming. In addition, an LOB‐based scheduling optimization model for resource leveling is proposed. This model retains the advantages of the conventional models, including multiple‐resource management and natural rhythm concept, and showcases new abilities: scheduling optimization without specifying a fixed schedule; scheduling optimization on more comprehensive optimization objects and variable values; maintaining continuity of resource while completely eliminating the occurrence of idle time; handling more comprehensive constraints after the addition of logical constraints and explicit expression of certain new constraints. The flexibility, practicality, and solution quality of the proposed model were enhanced accordingly. Further, a scheduling system was developed to assist in schedule optimization and visualization. Lastly, effectiveness of the proposed model was verified based on four case studies involving three case projects investigated in extant LOB‐based studies.

Resource levelling optimization model considering float loss impact

Purpose The purpose of this paper is to propose a Non-Linear Integer Programming (NLIP) model that solves the resource leveling problem while reducing the negative effect of the total float loss on risk. Design/methodology/approach An NLIP model is formulated to solve the resource leveling optimization problem incorporating float loss cost (FLC). The proposed model is implemented using “What’s Best solver” for Excel. The FLC is calculated using the float commodity approach. An example is solved using the proposed model in order to illustrate its applicability. Sensitivity analysis is also performed. Findings The results confirmed that resource leveling reduces the available float of non-critical activities; decreases schedule flexibility and reduces the probability of project completion. The probability of timely completion dropped from 50 percent (for the normal schedule with 32 resource fluctuations) to 13.5 percent for leveled resources with zero fluctuations. Using the proposed method, the number of resource fluctuations is 8 but the probability of completing the project on time improved to 20 percent. Practical implications The proposed model allows project managers to exercise new trade-offs between resource leveling and schedule flexibility which will ultimately improve the chances of successful project delivery. Originality/value Resource leveling techniques result in reducing the available total float for the non-critical activities. Existing methods focus on moving noncritical activities within their available float and ignore the impact of the resulting float loss. This reduces the schedule flexibility and increase the risk of project delays. The proposed model incorporates the FLC into the resource leveling optimization problem resulting in more efficient schedules with improved resource utilization while keeping some schedule flexibility.