基于机器学习的场地受限型项目调度与物料订购集成优化

doi:10.16381/j.cnki.issn1003-207x.2024.2109

摘要/Abstract

摘要：

施工场地受限下，活动进度与物料供应之间的精准协同是建筑工程项目顺畅执行的关键。本文从协同优化角度探究场地空间受限下的项目调度与物料订购集成优化问题，旨在通过集成决策活动进度安排和物料订购方案最小化项目总成本。首先，抽象并表达活动进度与物料订购之间的动态依赖关系，构建包含库存平衡式的集成优化模型；其次，结合模型特征设计改进的串行调度方案生成机制，进而开发并测试四种元启发式求解算法；再次，基于大规模算例上各算法的性能测试数据，采用6种机器学习技术训练算例特征与最佳算法之间的映射关系，从而构建了可为每个算例针对性地选择最佳求解算法的自动推荐方法。最后，通过大规模数值实验验证集成优化模型和算法的有效性。实验结果表明：基于随机森林的算法自动推荐方法在准确率和求解质量上优于其他单一算法和其他算法推荐方法。研究发现，在场地空间制约下，单位物料存储成本的增加对项目总成本的恶化效应更显著。

关键词: 项目调度, 物料订购, 集成优化模型, 机器学习, 算法推荐

Abstract:

The implementation of construction projects involves multiple spaces such as construction sites and prefabricated component manufacturers. How to realize the coordination between on-site activity scheduling and off-site material supply is critical to ensure the smooth execution of these projects. Meanwhile， the cramped site space furtherly renders the parallel execution of activities and limits the materials ordering plan through warehouse capacity. In order to solve the above practical dilemmas， the integrated optimization problem of project scheduling and material procurement under the limited space is explored is investigated in this paper.According to practical scenarios of construction projects with limited site space， the considered project scheduling and material ordering problem is defined. On this basis， considering the precedence relationships between activities， resource availability， inventory dynamic balance equations and site space constraints， the project scheduling and material ordering model with site space constraints is formulated. Through concurrently optimizing activity timetables and material ordering plan， the integrated model aims to minimize the total project cost.In order to solve the proposed problem， the complexity of the problem is analyzed. Based on the NP-hard characteristics of the problem， an algorithm automatic recommendation approach embedded with four meta-heuristics is developed using machine learning. Firstly， an improved serial scheduling generation scheme is proposed based on the problem structure， and four meta-heuristic algorithms are accordingly designed. Secondly， based on the extracted 91 instance features， the performance of five machine learning algorithms is tested， and the decision tree algorithms is selected to build the algorithm recommendation model due to its highest accuracy. Finally， the model parameters that make the approach perform best are determined by grid search method.To verify the effectiveness of the proposed method， large-scale numerical experiments are carried out based on the instances generated by ProGen and PSPLIB. The effectiveness of the proposed integrated model is verified by comparing with the independent model. The superiority the of developed automatic algorithm recommendation approach is also proved. Besides， comparative experiments among CPLEX， the proposed recommendation approach and other algorithms are set up， and experimental results demonstrate that the algorithm recommendation method based on random forest behaves best on accuracy and solution quality.The solution framework of the PSMOP is constructed by constructing an automatic algorithm recommendation approach embedded with multiple meta-heuristics. Meanwhile， the integrated decision making on both project scheduling and material ordering can provide more comprehensive decision supports for project managers. Moreover， reference values for the research on construction project management is provided.

Key words: project scheduling, material ordering, integrated optimization model, machine learning, algorithm recommendation

中图分类号:

C935

田宝峰,张静文,陈志. 基于机器学习的场地受限型项目调度与物料订购集成优化[J]. 中国管理科学, 2026, 34(10): 175-185.

Baofeng Tian,Jingwen Zhang,Zhi Chen. An Automatic Algorithm Recommendation Approach for the Project Scheduling and Material Ordering Problem with Site Space Constraints Through Machine Learning[J]. Chinese Journal of Management Science, 2026, 34(10): 175-185.

图/表 15

表1

参数符号"

集合	描述
$V$	活动集合， $V = 1, 2, ⋯, J$
$E$	优先关系集合， $E ⊂ V × V$
$R$	可更新资源集合， $R = 1, ⋯, k, ⋯, K$
$N R$	物料（不可更新资源）集合， $N R = 1, ⋯, m, ⋯, M$
$P r e j$	活动 $j$ 的紧前活动集合
$S u c j$	活动 $j$ 的紧后活动集合
参数
$d j$	活动j的工期
$R k$	可更新资源k的供应限量
$r j k$	活动j在每个阶段对资源k的需求量
$u j m$	活动j在每个阶段对物料m的消耗量
$U j m$	活动j对物料m的总消耗量， $U j m = d j ∙ u j m$
$W m$	物料m的仓库容量
$L m$	物料m的订购提前期
$O m$	物料m的单次订购成本
$H m$	物料m的单位存储成本
$D$	项目合同工期
$R e$	项目提前完工的单位工期奖励
$e f j / l f j$	活动j的最早结束时间/最晚结束时间
中间变量
$I m t$	第t阶段末期物料m的库存量
$y m t$	0-1辅助变量，若第t阶段发布物料m的订购订单， $y m t = 1$ ，否则 $y m t = 0$
决策变量
$x j t$	若活动j在第t阶段执行结束，则 $x j t = 1,$ 否则 $x j t = 0$
$P j m t$	若活动j所需物料m在第t阶段订购，则 $P j m t = 1$ ，否则 $P j m t = 0$

表1

图1

表2

算例参数设置"

O_m

H_m

m=1

J10、J20： $D = 0.7 × ∑ j ∈ V d j$

J30、J60、J90： $D = 0.4 × ∑ j ∈ V d j$

m=2

m=3

表2

表3

图2

图3

图4

表4

表5

集成决策与分散决策模型对比表"

M	分散决策	集成决策	$I r a t e$ (%)	$I c o s t$
M=1	3589.75	3328.04	7.86	261.71
M=2	5599.42	5299.18	5.67	300.23
M=3	8487.19	8116.68	4.56	370.52
平均	5892.12	5581.30	6.03	310.82

表5

图5

表6

表7

表8

图6

图7

参考文献 33

[1]	Zhang J， Li L， Demeulemeester E， et al. A three-dimensional spatial resource-constrained project scheduling problem： Model and heuristic［J］. European Journal of Operational Research， 2024， 319（3）： 943-966.
[2]	Yin J， Huang R， Sun H， et al. Multi-objective optimization for coordinated production and transportation in prefabricated construction with on-site lifting requirements［J］. Computers & Industrial Engineering， 2024， 189： 110017.
[3]	Tian B， Zhang J， Demeulemeester E， et al. A chance-constrained optimization approach integrating project scheduling and material ordering to manage the uncertain material supply［J］. Computers & Operations Research， 2024， 166： 106624.
[4]	Zhang Y， Cui N. Project scheduling and material ordering problem with storage space constraints［J］. Automation in Construction， 2021， 129： 103796.
[5]	胡雪君，王建江，崔南方，等. 项目调度与物料订购集成优化研究综述［J］. 控制与决策， 2022， 37（9）： 2189-2200.
	Hu X J， Wang J J， Cui N F， et al. Integrated project scheduling and material ordering： A literature review［J］. Control and Decision， 2022， 37（9）： 2189-2200.
[6]	Hartmann S， Briskorn D. An updated survey of variants and extensions of the resource-constrained project scheduling problem［J］. European Journal of Operational Research， 2022， 297（1）： 1-14.
[7]	Aquilano N J， Smith D E. A formal set of algorithms for project scheduling with critical path scheduling/material requirements planning［J］. Journal of Operations Management， 1980， 1（2）： 57-67.
[8]	Sha Y， Zhang J， Cao H. Multistage stochastic programming approach for joint optimization of job scheduling and material ordering under endogenous uncertainties［J］. European Journal of Operational Research， 2021， 290（3）： 886-900.
[9]	Parchami Afra A， Kheirkhah A， Ahadi H. Systematic literature review of integrated project scheduling and material ordering problem： Formulations and solution methods［J］. Computers & Industrial Engineering， 2022， 173： 108711.
[10]	Fu F. Integrated scheduling and batch ordering for construction project［J］. Applied Mathematical Modelling， 2014， 38（2）： 784-797.
[11]	Asadujjaman M， Rahman H F， Chakrabortty R K， et al. Supply chain integrated resource-constrained multi-project scheduling problem［J］. Computers & Industrial Engineering， 2024， 194： 110380.
[12]	Zhang Y， Cui N， Hu X， et al. Robust project scheduling integrated with materials ordering under activity duration uncertainty［J］. Journal of the Operational Research Society， 2020， 71（10）： 1581-1592.
[13]	Afra A P， Kheirkhah A. A Lagrangian heuristic for integrated production planning， material ordering and investment multi-project scheduling in a project-driven supply chain［J］. Engineering Optimization， 2024， 56（10）： 1639-1659.
[14]	雷晓琪，崔南方，杨丁凤，等. 装配式建筑环境下集成物料订货重复性项目调度优化［J］. 系统工程学报， 2024， 39（5）： 676-690.
	Lei X Q， Cui N F， Yang D F， et al. Integrating material ordering with repetitive project scheduling in prefabricated buildings［J］. Journal of Systems Engineering， 2024， 39（5）： 676-690.
[15]	Wolpert D H， Macready W G. No free lunch theorems for optimization［J］. IEEE Transactions on Evolutionary Computation， 1997， 1（1）： 67-82.
[16]	Messelis T， De Causmaecker P. An automatic algorithm selection approach for the multi-mode resource-constrained project scheduling problem［J］. European Journal of Operational Research， 2014， 233（3）： 511-528.
[17]	Müller D， Müller M G， Kress D， et al. An algorithm selection approach for the flexible job shop scheduling problem： Choosing constraint programming solvers through machine learning［J］. European Journal of Operational Research， 2022， 302（3）： 874-891.
[18]	张亚宁，白思俊，陈志，等. 基于深度学习的RCPSP调度优先规则实时动态选择算法［J］. 系统工程理论与实践， 2023， 43（7）： 2142-2153.
	Zhang Y N， Bai S J， Chen Z， et al. Real-time dynamic selection algorithm of RCPSP scheduling priority rules based on deep learning［J］. Systems Engineering —Theory & Practice， 2023， 43（7）： 2142-2153.
[19]	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.
[20]	Kerschke P， Hoos H H， Neumann F， et al. Automated algorithm selection： Survey and perspectives［J］. Evolutionary Computation， 2019， 27（1）： 3-45.
[21]	Rice J R. The algorithm selection problem［J］Advances in Computers， 1976， 15： 65-118.
[22]	Bredael D， Vanhoucke M. A genetic algorithm with resource buffers for the resource-constrained multi-project scheduling problem［J］. European Journal of Operational Research， 2024， 315（1）： 19-34.
[23]	del Valle Y， Venayagamoorthy G K， Mohagheghi S， et al. Particle swarm optimization： Basic concepts， variants and applications in power systems［J］. IEEE Transactions on Evolutionary Computation， 2008， 12（2）： 171-195.
[24]	He Y， Jia T， Zheng W. Simulated annealing for centralised resource-constrained multiproject scheduling to minimise the maximal cash flow gap under different payment patterns［J］. Annals of Operations Research， 2024， 338（1）： 115-149.
[25]	Alcaraz J， Maroto C， Ruiz R. Solving the multi-mode resource-constrained project scheduling problem with genetic algorithms［J］. Journal of the Operational Research Society， 2003， 54（6）： 614-626.
[26]	Kolisch R. Serial and parallel resource-constrained project scheduling methods revisited： Theory and computation［J］European Journal of Operational Research， 1996， 90（2）： 320-333.
[27]	Hartmann S. A competitive genetic algorithm for resource-constrained project scheduling［J］. Naval Research Logistics， 1998， 45（7）： 733-750.
[28]	Kolisch R， Sprecher A， Drexl A. Characterization and generation of a general class of resource-constrained project scheduling problems［J］. Management Science， 1995， 41（10）： 1693-1703.
[29]	Kolisch R， Sprecher A. PSPLIB - A project scheduling problem library［J］. European Journal of Operational Research， 1997， 96（1）： 205-216.
[30]	Chu X， Li S， Gao F， et al. A data-driven meta-learning recommendation model for multi-mode resource constrained project scheduling problem［J］. Computers & Operations Research，2023，157： 106290.
[31]	Pascoe T L. Allocation of resources CPM［J］. Revue Francaise De Recherche Operationnelle， 1966， 10（38）： 31-38.
[32]	Demeulemeester E， Vanhoucke M， Herroelen W. RanGen： A random network generator for activity-on-the-node networks［J］. Journal of Scheduling， 2003， 6（1）： 17-38.
[33]	Patterson J H. Project scheduling： The effects of problem structure on heuristic performance［J］. Naval Research Logistics Quarterly， 1976， 23（1）： 95-123.

算法	预测值
算法	GA	SA	PSO	DE
GA	267	1	1	36
SA	32	3	0	0
PSO	20	0	361	40
DE	31	0	33	255

备选算法	TP Rate	FR Rate	Precision
GA	0.875	0.107	0.763
SA	0.086	0.001	0.750
PSO	0.857	0.052	0.914
DE	0.799	0.100	0.770
平均	0.820	0.080	0.824

算法	比例(%)
GA	27.43
SA	3.30
PSO	41.17
DE	28.11

算法	Accuracy（%）	Cost	Gap（%）	AvgTime
BA	100	23930.41	0	20.529
AARA（本文）	82.04	24179.29	1.04	19.592
AARA-LMT	79.44	24734.47	3.36	17.607
AARA-RT	78.15	24796.21	3.62	18.615
GA	27.43	26849.44	12.20	17.218
SA	3.30	28678.68	19.84	19.782
PSO	41.17	26188.47	9.44	22.232
DE	28.11	26695.63	11.56	16.885
Rand	24.17	27139.48	13.41	19.565

算例	BA	CPLEX		AACA（本文）		Rand
算例	Cost	Cost	Gap（%）	Cost	Gap（%）	Cost	Gap（%）
J10	5586.51	5581.30	-0.09	5645.22	1.05	6292.94	12.65
J20	11518.42	-	-	11734.97	1.88	13029.24	13.12
J30	17180.33	-	-	17374.53	1.13	19532.44	13.69
J60	35097.07	-	-	35443.78	0.99	39937.45	13.79
J90	50269.73	-	-	50356.16	0.17	57198.17	13.78