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Integer programming for multi-mode resource-constrained project scheduling

ANNALS OF OPERATIONS RESEARCH 2025年 1-28页

作者： Klein, Nicklas Univ Bern Dept Business Adm Engehaldenstr 4 CH-3012 Bern Switzerland

project scheduling is a vital management task in many organizations across various industries. A project typically consists of activities that require time and scarce resources for execution. In many projects, there are trade-offs between the resource requirements and the duration of activities. These trade-offs can be represented via multiple execution modes of activities, which are considered in the multi-mode resource-constrained project scheduling problem (MRCPSP). The MRCPSP comprises determining the activities' start times and execution modes to minimize the project completion time while respecting precedence relations and availabilities of renewable and nonrenewable resources. In this paper, we propose several discrete-time (DT) and one continuous-time (CT) mixed-integer linear programming (MILP) model for the MRCPSP based on models for the single-mode resource-constrained project scheduling problem (RCPSP). We first analyze the models' LP relaxations and show an equivalence between DT models. Then, we compare the computational performance of the models on benchmark instances. Our results indicate that the proposed CT model outperforms the state-of-the-art models on large problem instances and problem instances with relatively long activity durations, while it is competitive on smaller problem instances. A possible explanation for this outperformance is that the LP relaxations of the proposed CT model can be solved considerably faster than the LP relaxations of the state-of-the-art models.

关键词： project scheduling Mixed-integer linear programming multi-mode resource-constrained project scheduling Experimental comparison

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multi-mode resource-constrained project scheduling problem with alternative project structures

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 125卷 333-347页

作者： Tao, Sha Dong, Zhijie Sasha Nanjing Univ Sch Management & Engn Nanjing 210093 Jiangsu Peoples R China Texas State Univ Ingram Sch Engn Ind Engn Program San Marcos TX 78666 USA

This paper proposes to consider alternative project structures when dealing with the multi-mode resource constrained project scheduling problem. An AND-OR network is used to present this alternative project structures innovatively. The problem is formulated as a bi-objective linear integer program, which minimizes the makespan and total cost. A hybrid metaheuristic is developed based on AND-OR network to solve this NP-hard problem efficiently, which nests adapted Tabu Search (outer layer) and NSGA-II algorithm (inner layer). A large amount of computational experiments of different sizes are conducted, and compared with solutions generated by CPLEX, traditional Tabu Search, enumeration-based method and single-layer NSGA-II. The experimental results show the advantages of the proposed model and method, especially with large-size problems.

关键词： multi-mode resource-constrained project scheduling Time-cost trade-off Alternative project structures AND-OR network Hybrid metaheuristic

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multi-mode resource-constrained project scheduling problem with multiple shifts and dynamic energy prices

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2024年第7期63卷 2483-2506页

作者： Peng, Wuliang Yu, Dongmin Xie, Fang Yantai Univ Sch Econ & Management Yantai 264005 Peoples R China

Considering the characteristics of time-of-use tariffs and multi-shifts in real-life project execution scenarios, we present a multi-mode resource-constrained project scheduling problem with multi-shift and time-of-use tariffs (MRCPSP-MS-TOU). The MRCPSP-MS-TOU is a bi-objective scheduling problem that aims to simultaneously minimise both project duration and energy costs. In this problem, renewable resources are the critical equipment that consumes the most energy and can work continuously for multiple shifts. Activities that require critical equipment with high energy consumption are given priority for shifts with lower electricity prices under time-of-use tariffs. We construct a mixed integer linear programming model for the MRCPSP-MS-TOU. For small-scale projects, the epsilon-constraint method is implemented to solve the MRCPSP-MS-TOU using the Gurobi optimiser. For large-scale projects, this paper develops meta-heuristic algorithms in the framework of the two non-dominated sorting genetic algorithm versions. The MRCPSP-MS-TOU enables manufacturers and the construction industry to schedule projects using time-of-use tariffs and multi-shifts in a more efficient manner since it can control the intensity of energy consumption, reduce project costs, make full use of energy-intensive equipment, and effectively reduce order delivery time.

关键词： multi-mode resource-constrained project scheduling time-of-use tariffs multiple shifts fast non-dominant genetic algorithm energy-aware scheduling

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An effective shuffled frog-leaping algorithm for multi-mode resource-constrained project scheduling problem

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INFORMATION SCIENCES 2011年第20期181卷 4804-4822页

作者： Wang, Ling Fang, Chen Tsinghua Univ TNList Dept Automat Beijing 100084 Peoples R China

In this paper, an effective shuffled frog-leaping algorithm (SFLA) is proposed for solving the multi-mode resource-constrained project scheduling problem (MRCPSP). In the SFLA, the virtual frogs are encoded as the extended multi-mode activity list (EMAL) and decoded by the multi-mode serial schedule generation scheme (MSSGS). Initially, the mode assignment lists of the population are generated randomly, and the activity lists of the population are generated by the regret-based sampling method and the latest finish time (LFT) priority rule. Then, virtual frogs are partitioned into several memeplexes that evolve simultaneously by performing the simplified two-point crossover (STPC). To enhance the exploitation ability, the combined local search including the multi-mode permutation based local search (MPBLS) and the multi-mode forward-backward improvement (MFBI) is further performed in each memeplex. To maintain the diversity of each memeplex, virtual frogs are periodically shuffled and reorganized into new memeplexes. Computational results based on the well-known benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed SFLA. (C) 2011 Elsevier Inc. All rights reserved.

关键词： multi-mode resource-constrained project scheduling Shuffled frog-leaping algorithm multi-mode serial schedule generation scheme multi-mode permutation based local search multi-mode forward-backward improvement Combined local search

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Two continuous-time assignment-based models for the multi-mode resource-constrained project scheduling problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 129卷 346-353页

作者： Gnaegi, Mario Rihm, Tom Zimmermann, Adrian Trautmann, Norbert Univ Bern Dept Business Adm Schuetzenmattstr 14 CH-3012 Bern Switzerland

In the multi-mode resource-constrained project scheduling problem, a set of precedence-related project activities and, for each activity, a set of alternative execution modes are given. Each activity requires some time and some scarce resources during execution;these requirements depend on the selected execution mode. Sought is a project schedule, i.e, a start time and an execution mode for each activity, such that the project makespan is minimized. In the literature, besides a large variety of specific solution approaches, several Mixed-Integer Linear Programming (MILP) models have been proposed for this problem. We present two novel MILP models that are based on mode-selection, resource-assignment and sequencing variables;we enhance the performance of the models by eliminating some symmetric solutions from the search space and by adding some redundant sequencing constraints for pairs and for triples of activities that cannot be processed in parallel. In a comparison with reference models from the literature, it turned out that the advantages of the novel models are a simple structure, an enhanced flexibility, and a superior performance when the range of the activities' durations is relatively large.

关键词： Operations research Mixed-integer linear programming multi-mode resource-constrained project scheduling

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A multi-mode resource-constrained project scheduling reformulation for the waterway ship scheduling problem

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JOURNAL OF scheduling 2019年第2期22卷 173-182页

作者： Hill, Alessandro Lalla-Ruiz, Eduardo Voss, Stefan Goycoolea, Marcos Univ Adolfo Ibanez Sch Business Santiago Chile Univ Hamburg Inst Informat Syst IWI Hamburg Germany Calif Polytech State Univ San Luis Obispo Dept Ind & Mfg Engn San Luis Obispo CA 93407 USA Univ Twente Dept Ind Engn & Business Informat Syst Enschede Netherlands Pontificia Univ Catolica Valparaiso Escuela Ingn Ind Valparaiso Chile

In this paper, we address the waterway ship scheduling problem (WSSP), which finds applications in the management of ship arrivals and departures at maritime ports near channels and waterways. It incorporates practically relevant conflicts which stem from tidal changes, curfews, ship properties or traffic. We propose a reformulation of the WSSP as a variant of the multi-mode resource-constrained project scheduling problem, which incorporates time-dependent resource capacities besides earliest and latest start times for the tasks. This problem is solved through integer programming, using a compact mathematical formulation. Our approach outperforms previous methods by solving all the existing literature instances to optimality. Most of them are solved at the root node within less than 2s.

关键词： Waterway ship scheduling problem multi-mode resource-constrained project scheduling Time-dependent resource availability Maritime logistics Mathematical programming

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An effective estimation of distribution algorithm for the multi-mode resource-constrained project scheduling problem

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COMPUTERS & OPERATIONS RESEARCH 2012年第2期39卷 449-460页

作者： Wang, Ling Fang, Chen Tsinghua Univ Tsinghua Natl Lab Informat Sci & Technol TNList Dept Automat Beijing 100084 Peoples R China

In this paper, an estimation of distribution algorithm (EDA) is proposed to solve the multi-mode resource-constrained project scheduling problem (MRCPSP). In the EDA, the individuals are encoded based on the activity-mode list (AML) and decoded by the multi-mode serial schedule generation scheme (MSSGS), and a novel probability model and an updating mechanism are proposed for well sampling the promising searching region. To further improve the searching quality, a multi-mode forward backward iteration (MFBI) and a multi-mode permutation based local search method (MPBLS) are proposed and incorporated into the EDA based search framework to enhance the exploitation ability. Based on the design-of-experiment (DOE) test, suitable parameter combinations are determined and some guidelines are provided to set the parameters. Simulation results based on a set of benchmarks and comparisons with some existing algorithms demonstrate the effectiveness of the proposed EDA. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： multi-mode resource-constrained project scheduling Estimation of distribution algorithm Probability model Permutation based local search

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Properties of multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第1期175卷 279-295页

作者： Buddhakulsomsiri, Jirachai Kim, David S. Thammasat Univ Sch Mfg Syst & Mech Engn Sirindhorn Int Inst Technol Pathum Thani 12121 Thailand Oregon State Univ Dept Ind & Mfg Engn Corvallis OR 97331 USA

This paper presents results from an extensive computational study of the multi-mode resource-con strained project scheduling problem when activities can be split during scheduling under situations where resources may be temporarily not available. All resources considered are renewable and each resource unit may not be available at all times due to resource vacations, which are known in advance, and assignment to other finite duration activities. A designed experiment is conducted that investigates project makespan improvement when activity splitting is permitted in various project scenarios, where different project scenarios are defined by parameters that have been used in the research literature. A branch-and-bound procedure is applied to solve a number of small project scheduling problems with and without activity splitting. The results show that, in the presence of resource vacations and temporary resource unavailability, activity splitting can significantly improve the optimal project makespan in many scenarios, and that the makespan improvement is primarily dependent on those parameters that impact resource utilization. (c) 2005 Elsevier B.V. All rights reserved.

关键词： multi-mode resource-constrained project scheduling activity splitting time-varying resource capacities branch-and-bound

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A Cross-Entropy Based Population Learning Algorithm for multi-mode resource-constrained project scheduling Problem with Minimum and Maximum Time Lags

A Cross-Entropy Based Population Learning Algorithm for Mult...

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2nd International Conference on Computational Collective Intelligence: Technologies and Applications

作者： Jedrzejowicz, Piotr Skakovski, Aleksander Gdynia Maritime Univ Chair Informat Syst Ul Morska 83F PL-81225 Gdynia Poland Gdynia Maritime Univ Dept Navigat PL-81225 Gdynia Poland

ISBN: (纸本)9783642166921

The multi-mode resource-constrained project scheduling problem with minimum and maximum time lags is considered in the paper. An activity is performed in a mode, which determines the demand of renewable and nonrenewable resources required for its processing and minimum and maximum time lags between adjacent activities. The goal is to find a mode assignment to the activities and their start times such that all constraints are satisfied and the project duration is minimized. Because the problem is NP-hard a population-learning algorithm (PLA2) is proposed to tackle the problem. PLA2 is a population-based approach which takes advantage of the features common to the social education system rather than to the evolutionary processes. The proposed approach perfectly suits for multi-agent systems because it is based on the idea of constructing a hybrid algorithm integrating different optimization techniques complementing each other and producing a synergetic effect. Results of the experiment were compared to the results published in project scheduling Problem Library.

关键词： multi-mode resource-constrained project scheduling minimum and maximum time lags evolutionary computation population learning algorithm

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Optimizing time, cost and quality in multi-mode resource-constrained project scheduling

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BUILT ENVIRONMENT project AND ASSET MANAGEMENT 2019年第1期9卷 44-63页

作者： Kannimuthu, Marimuthu Raphael, Benny Palaneeswaran, Ekambaram Kuppuswamy, Ananthanarayanan Indian Inst Technol Madras Dept Civil Engn Chennai Tamil Nadu India Swinburne Univ Technol Dept Civil & Construct Engn Hawthorn Vic Australia Swinburne Univ Technol Dept Civil & Construct Engn Fac Sci Engn & Technol Hawthorn Vic Australia

Purpose - The purpose of this paper is to develop a framework to optimize time, cost and quality in a multi-mode resource-constrained project scheduling environment. Design/methodology/approach - A case study approach identified the activity execution modes in building construction projects in India to support multi-mode resource-constrained project scheduling. The data required to compute time, cost and quality of each activity are compiled from real construction projects. A binary integer-programming model has been developed to perform multi-objective optimization and identify Pareto optimal solutions. The RR-PARETO3 algorithm was used to identify the best compromise trade-off solutions. The effectiveness of the proposed framework is demonstrated through sample case study projects. Findings - Results show that good compromise solutions are obtained through multi-objective optimization of time, cost and quality. Research limitations/implications - Case study data sets were collected only from eight building construction projects in India. Practical implications - It is feasible to adopt multi-objective optimization in practical construction projects using time, cost and quality as the objectives;Pareto surfaces help to quantify relationships among time, cost and quality. It is shown that cost can be reduced by increasing the duration, and quality can be improved only by increasing the cost. Originality/value - The use of different activity execution modes compiled from multiple projects in optimization is illustrated, and good compromise solutions for the multi-mode resource-constrained project scheduling problems using multi-objective optimization are identified.

关键词： multi-objective optimization Global optimization Construction quality assessment system (CONQUAS) multi-criterion decision-making multi-mode resource-constrained project scheduling Time-cost-quality

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