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作者： Jordan M. Ticktin California Polytechnic State University San Luis Obispo

学位级别：硕士

It's commonly assumed that experience leads to efficiency, yet this is largely unaccounted for in resource-constrained project scheduling. This thesis considers the idea that learning effects could allow selected activities to be completed within reduced time, if they're scheduled after activities where workers learn relevant skills. This paper computationally explores the effect of this autonomous, intra-project learning on optimal makespan and problem difficulty. A learning extension is proposed to the standard RCPSP scheduling problem. Multiple parameters are considered, including project size, learning frequency, and learning intensity. A test instance generator is developed to adapt the popular PSPLIB library of scheduling problems to this model. Four different Constraint Programming model formulations are developed to efficiently solve the model. Bounding techniques are proposed for tightening optimality gaps, including four lower bounding model relaxations, an upper bounding model relaxation, and a Destructive Lower Bounding method. Hundreds of thousands of scenarios are tested to empirically determine the most efficient solution approaches and the impact of learning on project schedules. Potential makespan reduction as high as 50% is discovered, with the learning effects resembling a learning curve with a point of diminishing returns. A combination of bounding techniques is proven to produce significantly tighter optimality gaps.

关键词： Operations research Constraint programming IBM ILOG CP Optimizer resource-constrained project scheduling problem RCPSP Lower and upper bounding

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scheduling non-professional table-tennis leagues

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期200卷 358-367页

作者： Knust, Sigrid Univ Osnabruck Inst Comp Sci D-49069 Osnabruck Germany

In this paper we consider a sports league scheduling problem which occurs in planning non-professional table-tennis leagues. The problem consists in finding a schedule for a time-relaxed double round robin tournament where different hard and soft constraints have to be taken into account. We model the problem as an integer linear program and a multi-mode resource-constrained project scheduling problem, respectively. Based on the second model a heuristic solution algorithm is proposed, which proceeds in two stages using local search and genetic algorithms. Computational results show the efficiency of the approaches. (C) 2009 Elsevier B.V. All rights reserved.

关键词： scheduling Sports league resource-constrained project scheduling problem Partially renewable resources Genetic algorithm

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A bi-objective robust resource allocation model for the RCPSP considering resource transfer costs

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2021年第2期59卷 367-387页

作者： Wang, Jianjiang Hu, Xuejun Demeulemeester, Erik Zhao, Yan Natl Univ Def Technol Sch Syst Engn Changsha Hunan Peoples R China Hunan Univ Business Sch Changsha Hunan Peoples R China Katholieke Univ Leuven Res Ctr Operat Management Fac Econ & Business Leuven Belgium Zhongnan Univ Econ & Law Sch Business Adm Wuhan Hubei Peoples R China

resource allocation is one of the core issues in project scheduling to ensure the effective use of scare renewable resources, and has been regularly encountered in production systems in the manufacturing and service industries. The transfers of renewable resources between activities generally incur certain scheduling costs and affect the robustness of a certain schedule in an uncertain environment. To address this issue, a bi-objective optimisation model is proposed to make the resource transfer decisions, which aims to minimise the transfer cost and maximise solution robustness in the presence of activity duration variability. The proposed model employs a novel resource-oriented flow formulation that is different from those of the previous literature. A NSGA-II and a Pareto simulated annealing (PSA) algorithm have been applied as the solution methodologies. Besides, the effectiveness of the metaheuristics are evaluated in comparison with a -constraint method. In detail, the algorithms are carried out on a set of benchmarks and are compared to test their efficiencies based on four performance metrics: number of non-dominated solutions, general distance, hypervolume and spacing. Finally, a case study of a real project further indicates that the suggested model and algorithms are applicable and beneficial to the problem in practice.

关键词： resource-constrained project scheduling problem robust resource allocation resource transfer cost multi-objective optimisation duration uncertainty

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Hybridization of ABC and PSO algorithms for improved solutions of RCPSP

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2016年第6期39卷 727-734页

作者： Jia, Qiong Guo, Yue Hohai Univ Hohai Business Sch Dept Management Nanjing Jiangsu Peoples R China Hohai Univ Dept Mkt Nanjing Jiangsu Peoples R China

A resource-constrained project scheduling problem (RCPSP) is one of the most famous intractable NP-hard problems in the operational research area in terms of its practical value and research significance. To effectively solve the RCPSP, we propose a hybrid approach by integrating artificial bee colony (ABC) and particle swarm optimization (PSO) algorithms. Moreover, a novel structure of ABC-PSO is devised based on embedded ABC-PSO (EABC-PSO) and sequential ABC-PSO (SABC-PSO) strategies. The EABC-PSO strategy mainly applies the PSO algorithm to update the process of the ABC algorithm while the SABC-PSO strategy demonstrates an approach in which computational results obtained from the ABC algorithm are further improved based on the PSO algorithm. In both strategies, bees in the ABC process are entitled to learning capacity from the best local and global solutions in terms of the PSO concept. Subsequently, the updates of solutions are premeditated with crossover and insert operators together with double justification methods. Computational results obtained from the tests on benchmark sets show that the proposed ABC-PSO algorithm is efficient in solving RCPSP problems, demonstrating clear advantages over the pure ABC algorithm, the PSO algorithm, and a number of listed heuristics.

关键词： resource-constrained project scheduling problem activity-list representation artificial bee colony optimization particle swarm optimization

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Bi-objective Optimization of RCPSP under Time-of-use Electricity Tariffs

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KSCE JOURNAL OF CIVIL ENGINEERING 2022年第12期26卷 4971-4983页

作者： He, Lihua Zhang, Yajun China Univ Petr East China Sch Econ & Management Qingdao 266580 Shandong Peoples R China

In recent years, to alleviate the peak load of the power grid, many countries have implemented time-of-use (TOU) electricity tariffs. When both manpower and equipment are needed to perform project activities, wage and electricity costs become the main components of the total project cost. High-power activities can be implemented during off-peak periods to reduce energy costs and peak demand for electricity. Labor shift differential payments will increase wage costs for off-peak labor overtime. This paper proposes a bi-objective mixed-integer nonlinear programming model for resource-constrained project scheduling problems under TOU. Machine-level decisions are made to minimize total project cost and completion time. This model has an enormous solution space when there are many tasks and long durations, especially when the time granularity is small, which is not conducive to an accurate solution. Therefore, an improved NSGA-II algorithm is presented to effectively solve the model. The results show that the proposed model and algorithm can effectively reduce the total project cost and construction period while reducing peak power demand.

关键词： resource-constrained project scheduling problem Time-of-use electricity tariffs Bi-objective optimization NSGA-II algorithm Labor shift differential payments

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A linear programming and constraint propagation-based lower bound for the RCPSP

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2000年第2期127卷 355-362页

作者： Brucker, P Knust, S Univ Osnabruck Fachbereich Math Informat D-49069 Osnabruck Germany

A new destructive lower bound for the resource-constrained project scheduling problem (RCPSP) is presented. Given are n activities which have to be processed without preemptions. During the processing period of an activity constant amounts of renewable resources are needed where the available capacity of each resource type is limited. Furthermore, finish-start precedence relations between the activities are given. The objective is to determine a schedule with minimal makespan. The lower bound calculations are based on two methods for proving infeasibility of a given threshold value T for the makespan. The first uses constraint propagation techniques, while the second is based on a linear programming formulation. A column generation procedure is presented for the linear programming formulation and computational results are reported for an algorithm combining both concepts. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： scheduling resource-constrained project scheduling problem lower bounds column generation constraint propagation

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Best-order crossover for permutation-based evolutionary algorithms

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APPLIED INTELLIGENCE 2015年第4期42卷 751-776页

作者： Andreica, Anca Chira, Camelia Univ Babes Bolyai Dept Comp Sci R-3400 Cluj Napoca Romania Tech Univ Cluj Napoca Dept Comp Sci Cluj Napoca Romania

Permutation-based encoding is used by many evolutionary algorithms dealing with combinatorial optimization problems. An important aspect of the evolutionary search process refers to the recombination process of existing individuals in order to generate new potentially better fit offspring leading to more promising areas of the search space. In this paper, we describe and analyze the best-order recombination operator for permutation-based encoding. The proposed operator uses genetic information from the two parents and from the best individual obtained up to the current generation. These sources of information are integrated to determine the best order of values in the new permutation. In order to evaluate the performance of best-order crossover, we address three well-known -hard optimization problems i.e. Travelling Salesman problem, Vehicle Routing problem and resource-constrained project scheduling problem. For each of these problems, a set of benchmark instances is considered in a comparative analysis of the proposed operator with eight other crossover schemes designed for permutation representation. All crossover operators are integrated in the same standard evolutionary framework and using the same parameter setting to allow a comparison focused on the recombination process. Numerical results emphasize a good performance of the proposed crossover scheme which is able to lead to overall better quality solutions.

关键词： Evolutionary algorithms Crossover Travelling salesman problem Vehicle routing problem resource-constrained project scheduling problem

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Modelling and solving a multimode and multisite industrial problem: Lagrangean relaxation and heuristic approaches

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EUROPEAN JOURNAL OF INDUSTRIAL ENGINEERING 2008年第2期2卷 190-206页

作者： Gourgand, Michel Tchomte, Sylverin Kemmoe Quilliot, Alain Univ Clermont Ferrand LIMOS F-63177 Aubiere France

In this paper, we tackle the problem of scheduling multisite and multimode activities in order to minimise the project duration that meets the constraints imposed by limited resources. The industrial system is composed of many production sites, and each site has its own resources called local resources, and every site can receive resources called global resources. The objective is to support the repartition of all the lots of pieces on different sites in a cooperative way, and to assign resources. The system reduced to only one site highlights the well-known problem of the Multimode resource-constrained project scheduling problem (MRCPSP). We propose a mathematical programming approach based on competitive feasible solutions and strong lower bounds, within quite reasonable computation times. The basic ingredients of this approach are the Lagrangean relaxation. We also propose a method based on stochastic descent with restart to compute large-sized industrial instances. The experiments show that this technique gives solutions close to the optimum. This seems to indicate that these resolution methods are good candidates for real industrial problems. [Received: 1 February 2007;Revised: 31 July 2007;Accepted: 31 October 2007]

关键词： resource-constrained project scheduling problem RCPSP multisite multimode scheduling Lagrangean relaxation stochastic descent

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Heuristic algorithm for RCPSP with the objective of minimizing activities' cost

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Journal of Systems Engineering and Electronics 2006年第1期17卷 96-102页

作者： Liu Zhenyuan Wang Hongwei Inst. of Systems Engineering Huazhong Univ. of Science and Technology Wuhan 430074 P. R. China

resource-constrained project scheduling problem（RCPSP） is an important problem in research on project management. But there has been little attention paid to the objective of minimizing activities＇ cost with the resource constraints that is a critical sub-problem in partner selection of construction supply chain management because the capacities of the renewable resources supplied by the partners will effect on the project scheduling. Its mathematic model is presented firstly, and analysis on the characteristic of the problem shows that the objective function is non-regular and the problem is NP-complete following which the basic idea for solution is clarified. Based on a definition of preposing activity cost matrix, a heuristic algorithm is brought forward. Analyses on the complexity of the heuristics and the result of numerical studies show that the heuristic algorithm is feasible and relatively effective.

关键词： systems engineering resource-constrained project scheduling problem activities' cost preposing activity cost matrix heuristic algorithm.

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Explaining the cumulative propagator

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CONSTRAINTS 2011年第3期16卷 250-282页

作者： Schutt, Andreas Feydy, Thibaut Stuckey, Peter J. Wallace, Mark G. Univ Melbourne Natl ICT Australia Dept Comp Sci & Software Engn Melbourne Vic 3010 Australia Monash Univ Sch Comp Sci & Software Engn Clayton Vic 3800 Australia

The global cumulative constraint was proposed for modelling cumulative resources in scheduling problems for finite domain (FD) propagation. Since that time a great deal of research has investigated new stronger and faster filtering techniques for cumulative, but still most of these techniques only pay off in limited cases or are not scalable. Recently, the "lazy clause generation" hybrid solving approach has been devised which allows a finite domain propagation engine possible to take advantage of advanced SAT technology, by "lazily" creating a SAT model of an FD problem as computation progresses. This allows the solver to make use of SAT explanation and autonomous search capabilities. In this article we show how, once we use lazy clause generation, modelling the cumulative constraint by decomposition creates a highly competitive version of cumulative. Using decomposition into component parts automatically makes the propagator incremental and able to explain itself. We then show how, using the insights from the behaviour of the decomposition, we can create global cumulative constraints that explain their propagation. We compare these approaches to explaining the cumulative constraint on resource constrained project scheduling problems. All our methods are able to close a substantial number of open problems from the well-established PSPlib benchmark library of resource-constrained project scheduling problems.

关键词： Cumulative constraint Explanations Nogood learning Lazy clause generation resource-constrained project scheduling problem

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