A Parallel Branch and Bound Algorithm for the Resource Leveling Problem with Minimal Lags

[EN] The efficient use of resources is a key factor to minimize the cost while meeting time deadlines and quality requirements; this is especially important in construction projects where field operations take fluctuations of resources unproductive and costly. Resource Leveling Problems (RLP) aim to sequence the construction activities that maximize the resource consumption efficiency over time, minimizing the variability. Exact algorithms for the RLP have been proposed throughout the years to offer optimal solutions; however, these problems require a vast computational capability ( combinatorial explosion ) that makes them unpractical. Therefore, alternative heuristic and metaheuristic algorithms have been suggested in the literature to find local optimal solutions, using different libraries to benchmark optimal values; for example, the Project Scheduling Problem LIBrary for minimal lags is still open to be solved to optimality for RLP. To partially fill this gap, the authors propose a Parallel Branch and Bound algorithm for the RLP with minimal lags to solve the RLP with an acceptable computational effort. This way, this research contributes to the body of knowledge of construction project scheduling providing the optimums of 50 problems for the RLP with minimal lags for the first time, allowing future contributors to benchmark their heuristics meth-ods against exact results by obtaining the distance of their solution to the optimal values. Furthermore, for practitioners,the time required to solve this kind of problem is reasonable and practical, considering that unbalanced resources can risk the goals of the construction project.This research was supported by the FAPA program of the Universidad de Los Andes (Colombia). The authors would like to thank the research group of Construction Engineering and Management (INgeco), especially J. S. Rojas-Quintero, and the Department of Systems Engineering at the Universidad de Los Andes. The authors are also grateful to the anonymous reviewers for their valuable and constructive suggestions.Ponz Tienda, JL.; Salcedo-Bernal, A.; Pellicer Armiñana, E. (2017). A Parallel Branch and Bound Algorithm for the Resource Leveling Problem with Minimal Lags. COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING. 32:474-498. doi:10.1111/mice.12233S47449832Adeli, H. (2000). High-Performance Computing for Large-Scale Analysis, Optimization, and Control. Journal of Aerospace Engineering, 13(1), 1-10. doi:10.1061/(asce)0893-1321(2000)13:1(1)ADELI, H., & KAMAL, O. (2008). Parallel Structural Analysis Using Threads. Computer-Aided Civil and Infrastructure Engineering, 4(2), 133-147. doi:10.1111/j.1467-8667.1989.tb00015.xAdeli, H., & Kamal, O. (1992). Concurrent analysis of large structures—II. applications. Computers & Structures, 42(3), 425-432. doi:10.1016/0045-7949(92)90038-2Adeli, H., Kamat, M. 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Balancing labor requirements in a manufacturing environment

“This research examines construction environments within manufacturing facilities, specifically semiconductor manufacturing facilities, and develops a new optimization method that is scalable for large construction projects with multiple execution modes and resource constraints. The model is developed to represent real-world conditions in which project activities do not have a fixed, prespecified duration but rather a total amount of work that is directly impacted by the level of resources assigned. To expand on the concept of resource driven project durations, this research aims to mimic manufacturing construction environments by allowing a non-continuous resource allocation to project tasks. This concept allows for resources to shift between projects in order to achieve the optimal result for the project manager. Our model generates a novel multi-objective resource constrained project scheduling problem. Specifically, two objectives are studied; the minimization of the total direct labor cost and the minimization of the resource leveling. This research will utilize multiple techniques to achieve resource leveling and discuss the advantage each one provides to the project team, as well as a comparison of the Pareto Fronts between the given resource leveling and cost minimization objective functions. Finally, a heuristic is developed utilizing partial linear relaxation to scale the optimization model for large scale projects. The computation results from multiple randomly generated case studies show that the new heuristic method is capable of generating high quality solutions at significantly less computational time”--Abstract, page iv

Optimized Resource-Constrained Method for Project Schedule Compression

Construction projects are unique and can be executed in an accelerated manner to meet market conditions. Accordingly, contractors need to compress project durations to meet client changing needs and related contractual obligations and recover from delays experienced during project execution. This acceleration requires resource planning techniques such as resource leveling and allocation. Various optimization methods have been proposed for the resource-constrained schedule compression and resource allocation and leveling individually. However, in real-world construction projects, contractors need to consider these aspects concurrently. For this purpose, this study proposes an integrated method that allows for joint consideration of the above two aspects. The method aims to optimize project duration and costs through the resources and cost of the execution modes assigned to project activities. It accounts for project cost and resource-leveling based on costs and resources imbedded in these modes of execution. The method's objective is to minimize the project duration and cost, including direct cost, indirect cost, and delay penalty, and strike a balance between the cost of acquiring and releasing resources on the one hand and the cost of activity splitting on the other hand. The novelty of the proposed method lies in its capacity to consider resource planning and project scheduling under uncertainty simultaneously while accounting for activity splitting. The proposed method utilizes the fuzzy set theory (FSs) for modeling uncertainty associated with the duration and cost of project activities and genetic algorithm (GA) for scheduling optimization. The method has five main modules that support two different optimization methods: modeling uncertainty and defuzzification module; scheduling module; cost calculations module; sensitivity IV analysis module; and decision-support module. The two optimization methods use the genetic algorithm as an optimization engine to find a set of non-dominated solutions. One optimization method uses the elitist non-dominated sorting genetic algorithm (NSGA-II), while the other uses a dynamic weighted optimization genetic algorithm. The developed scheduling and optimization method is coded in python as a stand-alone automated computerized tool to facilitate the needed iterative rescheduling of project activities and project schedule optimization. The developed method is applied to a numerical example to demonstrate its use and to illustrate its capabilities. Since the adopted numerical example is not a resource-constrained optimization example, the proposed optimization methods are validated through a multi-layered comparative analysis that involves performance evaluation, statistical comparisons, and performance stability evaluation. The performance evaluation results demonstrated the superiority of the NSGA-II against the dynamic weighted optimization genetic algorithm in finding better solutions. Moreover, statistical comparisons, which considered solutions’ mean, and best values, revealed that both optimization methods could solve the multi-objective time-cost optimization problem. However, the solutions’ range values indicated that the NSGA-II was better in exploring the search space before converging to a global optimum; NSGA-II had a trade-off between exploration (exploring the new search space) and exploitation (using already detected points to search the optimum). Finally, the coefficient of variation test revealed that the NSGA-II performance was more stable than that of the dynamic weighted optimization genetic algorithm. It is expected that the developed method can assist contractors in preparation for efficient schedule compression, which optimizes schedule and ensures efficient utilization of their resources

Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

A heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

Highlights • Project staffing with discrete time/resource trade-offs and calendar constraints. • An iterated local search procedure is proposed. • Different problem decomposition techniques are applied. Abstract When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability and activities are planned each with its own duration and resource requirements. In resource scheduling, important assumptions are made with respect to the staffing requirements. Both problems are typically solved in a sequential manner leading to a suboptimal outcome. We integrate these two interrelated scheduling problems to determine the optimal personnel budget that minimises the overall cost. Integrating these problems increases the scheduling flexibility, which improves the overall performance. In addition, we consider some resource demand flexibility in this research as an activity can be performed in multiple modes. In this paper, we present an iterated local search procedure for the integrated multi-mode project scheduling and personnel staffing problem. Detailed computational experiments are presented to evaluate different decomposition heuristics and comparison is made with alternative optimisation techniques

Research on Cloud Enterprise Resource Integration and Scheduling Technology Based on Mixed Set Programming

With the development of Industry 4.0 and intelligent manufacturing, aiming at the incompatibility of heterogeneous manufacturing resource interfaces and the low efficiency of collaborative scheduling of manufacturing resources among enterprises，we proposed the resource integration and scheduling strategy among enterprises based on Mixed Set Programming [1]. By using the metadata and ontology modeling methods, we were able to realize a standardized model description of manufacturing resources. At last, an enterprise application case was discussed to verify the resources integration and scheduling strategy based on Mixed Set Programming is effective to optimize and improve the efficiency of the collaborative scheduling of resources among enterprises. The resources integration and scheduling strategy based on Mixed Set Programming could be applied to promote the optimal allocation of manufacturing resources

A Decision Support System for Dynamic Integrated Project Scheduling and Equipment Operation Planning

Common practice in scheduling under limited resource availability is to first schedule activities with the assumption of unlimited resources, and then assign required resources to activities until available resources are exhausted. The process of matching a feasible resource plan with a feasible schedule is called resource allocation. Then, to avoid sharp fluctuations in the resource profile, further adjustments are applied to both schedule and resource allocation plan within the limits of feasibility constraints. This process is referred to as resource leveling in the literature. Combination of these three stages constitutes the standard approach of top-down scheduling. In contrast, when scarce and/or expensive resource is to be scheduled, first a feasible and economical resource usage plan is established and then activities are scheduled accordingly. This practice is referred to as bottom-up scheduling in the literature. Several algorithms are developed and implemented in various commercial scheduling software packages to schedule based on either of these approaches. However, in reality resource loaded scheduling problems are somewhere in between these two ends of the spectrum. Additionally, application of either of these conventional approaches results in just a feasible resource loaded schedule which is not necessarily the cost optimal solution. In order to find the cost optimal solution, activity scheduling and resource allocation problems should be considered jointly. In other words, these two individual problems should be formulated and solved as an integrated optimization problem. In this research, a novel integrated optimization model is proposed for solving the resource loaded scheduling problems with concentration on construction heavy equipment being the targeted resource type. Assumptions regarding this particular type of resource along with other practical assumptions are provided for the model through inputs and constraints. The objective function is to minimize the fraction of the execution cost of resource loaded schedule which varies based on the selected solution and thus, considered to be the model's decision making criterion. This fraction of cost which hereafter is referred to as operation cost, encompasses four components namely schedule delay cost, shipping, rental and ownership costs for equipment

Multi-Mode Resource Constrained Project Scheduling Using Differential Evolution Algorithm

Project scheduling is a tool that manages the work and resources associated with delivering a project on time. Project scheduling is important to organize, keep track of the finished and in-progress tasks and manage the quality of work delivered. However, many problems arise during project scheduling. Minimizing project duration is the primary objective. Project cost is also a critical matter, but there will always be a trade off between project time and cost (Ghoddousiet et al., 2013), so scheduling activities can be challenging due to precedence activities, resources, and execution modes. Schedule reduction is heavily dependent on the availability of resources (Zhuo et al., 2013). There have been several methods used to solve the project scheduling problem. This dissertation will focus on finding the optimal solution with minimum makespan at lowest possible cost. Schedules should help manage the project and not give a general estimate of the project duration. It is important to have realistic time estimates and resources to give accurate schedules. Generally, project scheduling problems are challenging from a computational point of view (Brucker et al., 1999). This dissertation applies the differential evolution algorithm (DEA) to multi mode, multi resource constrained project scheduling problems. DEA was applied to a common 14- task network through different scenarios, which includes Multi Mode Single Non Renewable Resource Constrained Project Scheduling Problem (MMSNR) and Multi Mode Multiple Non Renewable Resource Constrained Project Scheduling Problem (MMMNR). DEA was also applied when each scenario was faced with a weekly constraint and when cost and time contingencies such as budget drops or change in expected project completion times interfere with the initial project scheduling plan. A benchmark problem was also presented to compare the DEA results with other optimization techniques such as a genetic algorithm (GA), a particle swarm optimization (PSO) and ant colony optimization (ACO). The results indicated that our DEA performs at least as good as these techniques as far as the project time is concerned and outperforms them in computational times and success rates. Finally, a pareto frontier was investigated, resulting in optimal solutions for a multi objective problem focusing on the tradeoff of the constrained set of parameters

Multi-Objective Multi-Project Construction Scheduling Optimization

In construction industry, contractors usually manage and execute multiple projects simultaneously within their portfolio. This involves sharing of limited resources such as funds, equipment, manpower, and others among different projects, which increases the complexity of the scheduling process. The allocation of scarce resources then becomes a major objective of the problem and several compromises should be made to solve the problem to the desired level of optimality. In such cases, contractors are generally concerned with optimizing a number of different objectives, often conflicting among each other. Thus, the main objective of this research is to develop a multi-objective scheduling optimization model for multiple construction projects considering both financial and resource aspects under a single platform. The model aims to help contractors in devising schedules that obtain optimal/near optimal tradeoffs between different projects’ objectives, namely: duration of multiple projects, total cost, financing cost, maximum required credit, profit, and resource fluctuations. Moreover, the model offers the flexibility in selecting the desired set of objectives to be optimized together. Three management models are built in order to achieve the main objective which involves the development of: (1) a scheduling model that establishes optimal/near optimal schedules for construction projects; (2) a resource model to calculate the resource fluctuations and maximum daily resource demand; and (3) a cash flow model to calculate projects’ financial parameters. The three management models are linked with the designed optimization model, which consequently performs operations of the elitist non-dominated sorting genetic algorithm (NSGA-II) technique, in three main phases: (1) population initialization; (2) fitness evaluation; and (3) generation evolution. The optimization model is implemented and tested using different case studies of different project sizes obtained from literature. Finally, an automated tool using C# language is built with a friendly graphical user interface to facilitate solving multi-objective scheduling optimization problems for contractors and practitioners