多模式资源受限项目调度问题（MRCPSP）是建设项目进度优化问题的重要数学模型。但传统的MRCPSP模型难以同时表征工序时长、成本与资源需求之间的多种关系。为了解决这一问题，该文提出了一种MRCPSP模型，并利用约束规划（CP）对算例进行了求解。该问题模型通过定义生产力函数以及各工序对各类资源总需求的组合表征工序时长、成本以及资源需求之间的关系。经验证，该模型可以模拟施工过程中生产力变化的情况，并允许在优化求解时考虑工艺选择对结果的影响，相比传统的MRCPSP模型，求解结果有更明确的工程含义，具有实际应用价值。
The multimode resource-constrained project scheduling problem (MRCPSP) is an essential mathematical model for construction schedule optimization. However, such models cannot easily simultaneously represent multiple relationships between activity duration, cost, and resource requirements. This paper presents an MRCPSP model that includes multiple relationships that is solved using constraint programming (CP). The model represents the relationships between activity duration, cost, and resource requirements by introducing a productivity function and the total resource requirements for combinations of activities. The model can simulate the construction productivity changes and the influence of construction methods on the results. The results then have a more explicit engineering meaning to improve actual projects than the traditional MRCPSP.
[1] GIRAN O, TEMUR R, BEKDAŞ G. Resource constrained project scheduling by harmony search algorithm[J]. KSCE Journal of Civil Engineering, 2017, 21(2):479-487. DOI:10.1007/s12205-017-1363-6.
[2] KASRAVI M, MAHMOUDI A, FEYLIZADEH M R. A novel algorithm for solving resource-constrained project scheduling problems:A case study[J]. Journal of Advances in Management Research, 2019, 16(2):194-215.
[3] BRUCKER P, DREXL A, MÖHRING R, et al. Resource-constrained project scheduling:Notation, classification, models, and methods[J]. European Journal of Operational Research, 1999, 112(1):3-41. DOI:10.1016/s0377-2217(98)00204-5.
[4] BLAZEWICZ J, LENSTRA J K, KAN A H G R. Scheduling subject to resource constraints:Classification and complexity[J]. Discrete Applied Mathematics, 1983, 5(1):11-24. DOI:10.1016/0166-218x(83)90012-4.
[5] MENESI W, HEGAZY T. Multimode resource-constrained scheduling and leveling for practical-size projects[J]. Journal of Management in Engineering, 2015, 31(6):04014092. DOI:10.1061/(ASCE)ME.1943-5479.0000338.
[6] LIU S S, WANG C J. Resource-constrained construction project scheduling model for profit maximization considering cash flow[J]. Automation in Construction, 2008, 17(8):966-974. DOI:10.1016/j.autcon.2008.04.006.
[7] LIU J, LU M. Constraint programming approach to optimizing project schedules under material logistics and crew availability constraints[J]. Journal of Construction Engineering and Management, 2018, 144(7):0401804. DOI:10.1061/(ASCE)CO.1943-7862.0001507.
[8] MENESI W, GOLZARPOOR B, HEGAZY T. Fast and near-optimum schedule optimization for large-scale projects[J]. Journal of Construction Engineering and Management, 2013, 139(9):1117-1124. DOI:10.1061/(ASCE)CO.1943-7862.0000722.
[9] ABUWARDA Z, HEGAZY T. Flexible activity relations to support optimum schedule acceleration[J]. Journal of Construction Engineering and Management, 2016, 142(11):06016004. DOI:10.1061/(ASCE)CO.1943-7862.0001193.
[10] GOLNARAGHI S, ZANGENEHMADAR Z, MOSELHI O, et al. Application of artificial neural network(s) in predicting formwork labour productivity[J]. Advances in Civil Engineering, 2019, 2019:5972620. DOI:10.1155/2019/5972620.
[11] GARCÍA-NIEVES J D, PONZ-TIENDA J L, SALCEDO-BERNAL A, et al. The multimode resource-constrained project scheduling problem for repetitive activities in construction projects[J]. Computer-aided Civil and Infrastructure Engineering, 2018, 33(8):655-671. DOI:10.1111/mice.12356.
[12] ABUWARDA Z, HEGAZY T. Work-package planning and schedule optimization for projects with evolving constraints[J]. Journal of Computing in Civil Engineering, 2016, 30(6):04016022. DOI:10.1061/(ASCE)CP.1943-5487.0000587.
[13] 刘雪红, 程海寅, 陆建飞, 等. 铝合金模板体系施工技术及其效益分析[J]. 施工技术, 2012, 41(23):79-82, 104. LIU X H, CHENG H Y, LU J F, et al. Construction technology of aluminum alloy formwork system and its benefit analysis[J]. Construction Technology, 2012, 41(23):79-82, 104. (in Chinese)
