resource-constrained project scheduling
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Nowadays, the project scheduling problem with limited resources has become one of the most important optimization issues. Given the enormous costs spent on projects as well as materials, resources, and forces, projects are expected to be successful and finish at the planned time. This schedule in functional mode will have many uncertainties due to the needs of the moment. Such a goal requires careful planning and advanced algorithms to solve these complex issues in a short and reasonable time. In this research, a new method is presented using the Intelligent Water Drops (IWD) algorithm for the resource-constrained project scheduling problem. For this reason and because of the importance of these projects, in this research, an optimization model has been developed for project scheduling in the state of uncertainty, which can solve many implementation obstacles. For this purpose, first, the problem is formulated as a mixed-inter linear programming (MILP) model. Next, the model is optimized using the IDW algorithm. To evaluate the performance of the proposed method, the standard data set was used in previous research and articles, and four datasets with different scales were selected from the PSLIB library. The results show that the proposed method is capable of obtaining the best precision in terms of the least critical deviation from the optimal solution. Moreover, the results of the proposed method were compared with metaheuristic algorithms, such as the particle congestion algorithm (PSO) , which was able to get the best solution among these algorithms.Keywords: Resource-Constrained Project Scheduling, Intelligent Water Drop Algorithm, Particle Swarm Optimization, Metaheuristic Algorithms, Optimization
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به طور سنتی مسیله ی زمان بندی پروژه مستقل از مسیله ی سفارش دهی مواد برنامه ریزی می شود. این در حالی است که با برنامه ریزی هم زمان این دو می توان هزینه های کلی پروژه را کاهش داد. در این پژوهش، مسیله ی تسطیح منابع به عنوان نوعی زمان بندی پروژه که هدفش کنترل نوسانات استفاده از منابع در طول اجرای پروژه است، با مسیله ی سفارش دهی مواد به طور همزمان برنامه ریزی می شود، همچنین فعالیت ها با شدت اجرای متغیر تکمیل می شود. بدین منظور، یک مدل برنامه ریزی ریاضی عدد صحیح مختلط ارایه می شود که در آن متغیرها به نحوی تعیین می شود که علاوه بر کمینه سازی هزینه ی نوسانات استفاده از منابع، مجموع هزینه های سفارش دهی مواد کمینه شود. نتایج محاسباتی نشان گر وجود موازنه یی بین این دو هزینه است. در نهایت، مدل ارایه شده توسط نرم افزار گمز و الگوریتم ژنتیک برای مسایل با اندازه های مختلف حل می شود، و نتایج آن مورد بحث قرار می گیرد.
کلید واژگان: زمان بندی پروژه با منابع محدود، تسطیح منابع، سفارش دهی مواد، شدت اجرای متغیر، تخفیف کلیThe Project Scheduling Problem (PSP) is to determine the sequence and schedule of activities of a project in a way that decision-makers' objectives are optimized without violating precedence constraints. Due to the scarcity of resources, in recent decades, the Resource-Constrained Project Scheduling Problem (RCPSP) has attracted the attention of researchers and practitioners. The main feature of the resource-constrained project scheduling problem is that it takes into account resource constraints, which significantly affect the solutions obtained for project scheduling problems, in addition to other usual constraints, e.g. precedence constraints. The Resource Leveling Problem (RLP) is a special case of the resource-constrained project scheduling problem in which the resource usage variation between consecutive time periods is minimized. Traditionally, the project scheduling problem and the material ordering problem are separately investigated. However, simultaneous planning of both these problems, i.e., resource constrained project scheduling and material procurement, which can reduce total project costs, has been rarely addressed. In this study, the resource leveling problem which aims at controlling the variations of using the resources during the project execution and the material ordering problem are simultaneously addressed. The material ordering is considered to be subject to all-unit discount. In this regard, a mixed-integer linear programing model is proposed in which the starting and ending times of activities are determined so that in addition to minimizing the variations of resource utilization, total costs related to the material ordering problem (sum of ordering costs as well as holding and purchase costs) are minimized. It is assumed that the intensity of the variable execution directly affects the progress of activities. Also, the duration of activities is considered flexible. Numerical results confirm a tradeoff between material ordering and resource leveling costs. Finally, GAMS software as well as genetic algorithm are used to solve different-sized test problems, and results are discussed.
Keywords: Resource constrained project scheduling, resource levelling, material ordering, variable execution intensities, all-unit discount -
A multi-objective resource-constrained project scheduling problem with time lags and fuzzy activity durationsThe resource-constrained project scheduling problem is to find a schedule that minimizes the project duration subject to precedence relations and resource constraints. To further account for economic aspects of the project, one may add an objective of cash nature to the problem. In addition, dynamic nature and variations in real world are known to introduce uncertainties into data. Therefore, this study is aimed at proposing a multi-objective model for resource-constrained project scheduling problem, with the model objectives being to minimize makespan, and maximize net present value of the project cash flows; the proposed model has activity times expressed in fuzzy numbers where the corresponding uncertainties are taken into account. The project environment is considered to be a multi-resource environment where more than one resource is needed for the execution of any activity. Also, the proposed model comes with time lags in precedence relations between activities. The proposed model is validated by using epsilon-constraint method. The α-cut approach as well as the expression of acceptable risk level by the project manager is used to defuzzificate fuzzy activity durations. Since the problem is NP-hard, a NSGA-II meta-heuristic algorithm is proposed to solve the problem. The algorithm performance has been evaluated in terms of different criteria.Keywords: Resource-constrained project scheduling, fuzzy activity times, time lags, Cash Flows, α-cut, NSGA-II evolutionary algorithm
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Proper and realistic scheduling is an important factor of success for every project. In reality, project scheduling often involves several objectives that must be realized simultaneously, and faces numerous uncertainties that may undermine the integrity of the devised schedule. Thus, the manner of dealing with such uncertainties is of particular importance for effective planning. A realistic schedule must also take account of the time-based variations in the capacity of renewable resources and the amount of resources needed to undertake the activities and the overall effect of such variations on the schedule. In this study, we propose a multi-objective project scheduling optimization model with time-varying resource requirements and capacities.This model, with the objectives of minimizing the project makespan, maximizing the schedule robustness, and maximizing the net present value, considers the interests of both project owner and contractor simultaneously. Two multi-objective solution algorithms, NSGA-II and MOPSO, are modified and adjusted with Taguchi method to be used for determination of the set of Pareto optimal solutions for the proposed problem. The proposed solution methods are evaluated by the use of fifteen problems of different sizes derived from Project Scheduling Problem Library (PSPLIB). Finally, solutions of the algorithms are evaluated in terms of five evaluation criteria. The comparisons show that NSGA-II yields better results than MOPSO algorithm. Also, we show that ignoring the time-based variations in consumption and availability of resources may lead to underestimation of project makespan and significant deviation from the optimal activity sequence.Keywords: Resource-constrained project scheduling, Net Present Value (NPV), Robusts cheduling, Resource variation, Multi-objective optimization
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International Journal of Supply and Operations Management, Volume:3 Issue: 3, Autumn 2016, PP 1391 -1412This paper presents the formulation and solution of the Combinatorial Multi-Mode Resource Constrained Multi-Project Scheduling Problem. The focus of the proposed method is not on finding a single optimal solution, instead on presenting multiple feasible solutions, with cost and duration information to the project manager. The motivation for developing such an approach is due in part to practical situations where the definition of optimal changes on a regular basis. The proposed approach empowers the project manager to determine what is optimal, on a given day, under the current constraints, such as, change of priorities, lack of skilled worker. The proposed method utilizes a simulation approach to determine feasible solutions, under the current constraints. Resources can be non-consumable, consumable, or doubly constrained. The paper also presents a real-life case study dealing with scheduling of ship repair activities.Keywords: Resource Constrained Project Scheduling, Mathematical Formulation, Discrete Event Simulation, Decision Support System
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International Journal of Research in Industrial Engineering, Volume:2 Issue: 3, Summer 2013, PP 47 -57In this paper, we study a resource-constrained project-scheduling problem in which the objective is minimizing total Resource Tardiness Penalty Costs. We assume renewable resources that are limited in number, are restricted to very expensive equipment and machines, therefore they are rented and used in other projects, and are not available in all project periods. In other words, there exists a predefined ready-date as well as a due date for each renewable resource type. In this way, no resource is utilized before its ready date. Nevertheless, resources are allowed to be used after their due date by paying penalty costs depending on the resource type. The objective is to minimize the costs of renewable resource usages. We formulated and mathematically modeled this problem as an integer-Linear programming model. Since our problem is NP-hard and also exact methods are only applicable in small scale, therefore metaheuristic methods are practical approaches for this problem; this means that metaheuristics are better for this problem. In order to authenticate the model and solution algorithm in small scale, we consider a network with low activity, and then solve the model of this network with both exact algorithms and SA-GA-TS metaheuristic algorithms. For more activities, as well as getting closer to the real world, we present a Simulated Annealing Algorithm to solve this problem. In order to examine the performance of this algorithm, data that had been derived from studied literature were used, and their answers were compared with Genetic Algorithm (GA) and Tabu Search Algorithm (TS). Results show that in average, quality of SA answers was better than those of the GA and TS algorithms. In addition, we use relaxation method to achieve an even higher validation for the SA algorithm. Finally all results in this paper indicate that both model and solution algorithm have high validity.Keywords: Resource constrained project scheduling, Resource tardiness penalty costs, Metaheuristic Algorithms
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