考虑信息处理投入的随机资源需求反应性项目调度优化

doi:10.16381/j.cnki.issn1003-207x.2022.1629

Abstract

Abstract:

As one of the important uncertainty factors of the project， stochastic resource requirements are usually highly variable. And resource conflict caused by highly variable stochastic resource requirements often leads to disruptions in project implementation. Therefore， it is crucial to take measures to reduce the variability of stochastic resource requirements. Besides， information handling input is an effective measure， which can be used to accurately estimate the resource requirements of project activities， thereby ultimately reducing the variability of the resource requirements of project activities.Based on the above facts， the reactive project scheduling optimization problem with stochastic resource requirements is investigated considering information handling input. In this study， the quantitative relationship between the information handling input and the reduced variability of activity resource requirements is established first. After defining the problem， the optimization model is constructed to minimize the total implementation cost of the project， where， the decision variable of the model is the information handling input scheme， and the total implementation cost of the project is defined as the sum of the cost incurred by the information handling input scheme and the reactive adjustment cost caused by the execution of baseline schedule under the scheme. Especially， the reactive adjustment cost caused by the execution of baseline schedule under the scheme can only be obtained by calculating the weighted sum of the deviations between the activity start time in the realized reactive schedule and those in the baseline schedule， whereas the corresponding reactive schedule when the baseline schedule is interrupted needs to be determined by the reactive project scheduling model. Furthermore， according to the NP-hard property of the studied problem， a variable neighborhood search algorithm is developed to solve the models.At last， a typical practical case is utilized to illustrate the research problem， demonstrating the effectiveness of reasonable investment in information handling to control the total implementation cost of the project. And then， by analyzing the sensitivity of several key parameters， it is concluded that the total implementation cost of the project rises with increase in the per unit cost of information handling input and the activity weight， and drops with the increase in the renewable resource availability.A new idea is provided for project managers to manage and control the project cost， and quantitative decision support is also provided for reactive project scheduling with stochastic resource requirements considering information processing input. Besides， it also supplies some references for further research.

Key words: reactive project scheduling, optimization model, variable neighborhood search algorithm, stochastic resource requirements, information handling input

CLC Number:

C935

Xiao Cui, Zhengwen He, Nengmin Wang. Optimization of Reactive Project Scheduling with Stochastic Resource Requirements Considering Information Handling Input[J]. Chinese Journal of Management Science, 2025, 33(8): 218-229.

Figures/Tables 9

方案	相关成本及相应反应性计划
Y^*	TC(Y^*)	303.4
	EC(Y^*)	96
	AC(Y^*)	$S 1'$ ={0,0,6,9,18,22,24,24,0,36,42,43,43,3,71,86,89,89,6,95,102,104,104,14,116,123,125,89,19,102,110,112,129,144}	120	207.4
		$S 2'$ ={0,0,6,0,18,22,24,24,5,36,42,71,43,14,71,86,89,89,6,97,104,106,106,9,118,125,127,89,20,104,112,114,131,146}	401
		$S 3'$ ={0,0,6,0,18,22,24,24,5,36,42,43,43,14,71,86,89,89,6, 97,104,106,106,9,118,125,127,89,20,102,112,114,131,146}	283
		$S 4'$ ={0,0,6,0,18,22,26,24,0,36,42,43,43,14,71,86,89,89,6,95,102,104,104,9,116,123,125,89,20,102,110,112,129,144}	94
		$S 5'$ ={0,0,6,6,18,22,24,24,11,36,42,43,43,20,71,86,89,89,6,95,102,104,104,9,116,123,125,89,14,102,110,112,129,144}	139
Y	TC(Y)	447.6
	EC(Y)	248
	AC(Y)	$S 1 ″$ ={0,0,6,9,18,22,24,24,0,36,42,43,43,3,71,86,89,89,6,95,102,104,104,20,116,123,125,89,14,102,110,112,129,144}	125	199.6
		$S 2 ″$ ={0,0,6,3,18,22,24,24,0,36,42,71,43,8,71,86,89,89,6,97,104,106,106,9,118,125,127,89,14,102,112,114,131,146}	347
		$S 3 ″$ ={0,0,6,0,18,22,24,24,5,36,42,71,43,15,71,86,89,89,6,95,102,104,104,9,116,123,125,97,9,110,118,120,129,144}	299
		$S 4 ″$ ={0,0,6,0,18,22,24,24,0,36,42,43,43,14,71,86,89,89,6,95,102,104,104,9,116,123,125,89,20,102,110,112,129,144}	88
		$S 5 ″$ ={0,0,6,6,18,22,24,24,6,36,42,43,43,14,71,86,89,89,6,95,102,108,104,9,116,123,125,95,11,102,110,112,129,144}	139

References 24

[1]	Lamas P， Demeulemeester E. A purely proactive scheduling procedure for the resource-constrained project scheduling problem with stochastic activity durations［J］. Journal of Scheduling， 2016， 19（4）： 409-428.
[2]	马志强，徐小峰，何正文，等. 复杂不确定环境下活动可拆分的项目资源鲁棒性调度优化［J］. 中国管理科学， 2022， 30（3）： 117-130.
	Ma Z Q， Xu X F， He Z W， et al. Robust scheduling optimization of project resources with activity splitting under complex and uncertain environments［J］. Chinese Journal of Management Science，2022，30（3）： 117-130.
[3]	Van de Vonder S， Ballestín F， Demeulemeester E， et al. Heuristic procedures for reactive project scheduling［J］. Computers & Industrial Engineering， 2007， 52（1）： 11-28.
[4]	Davari M， Demeulemeester E. The proactive and reactive resource-constrained project scheduling problem［J］. Journal of Scheduling， 2019， 22（2）： 211-237.
[5]	丰景春，董灵莉.多资源约束下基于关键链的项目群工期-费用优化［J］.中国管理科学，2022，30（4）： 132-143.
	Feng J C， Dong L L. Construction period-cost optimization of program based on critical chain method under multi-resource constraints［J］. Chinese Journal of Management Science， 2022， 30（4）： 132-143.
[6]	Lambrechts O， Demeulemeester E， Herroelen W. Time slack-based techniques for robust project scheduling subject to resource uncertainty［J］. Annals of Operations Research， 2011， 186（1）： 443-464.
[7]	Chakrabortty R K， Rahman H F， Haque K M A， et al. An event-based reactive scheduling approach for the Resource Constrained Project Scheduling Problem with unreliable resources［J］. Computers & Industrial Engineering， 2021， 151： 106981.
[8]	李佳媛，何正文. 基于资源随机中断的反应性多模式项目调度优化［J］. 运筹与管理， 2015， 24（6）： 44-50.
	Li J Y， He Z W. Optimization of reactive multi-mode project scheduling based on stochastic breakdown of resources［J］. Operations Research and Management Science， 2015， 24（6）： 44-50.
[9]	谢芳，徐哲，于静. 资源可用量不确定和活动多模式情形下的随机项目调度问题［J］. 管理工程学报， 2022， 36（3）： 170-178.
	Xie F， Xu Z， Yu J. Stochastic scheduling of projects with uncertain resource availabilities and multiple modes［J］. Journal of Industrial Engineering and Engineering Management， 2022， 36（3）： 170-178.
[10]	彭武良，林家利. 一种改进的多模式项目反应性调度问题［J］. 运筹与管理， 2022， 31（7）： 28-34.
	Peng W L， Lin J L. An improved reactive scheduling problem of multi-mode RCPSP［J］.Operations Research and Management Science， 2022， 31（7）： 28-34.
[11]	Bartusch M， Möhring R H， Radermacher F J. Scheduling project networks with resource constraints and time windows［J］. Annals of Operations Research， 1988， 16（1）： 199-240.
[12]	Cavalcante C C B， Carvalho de Souza C， Savelsbergh M W P， et al. Scheduling projects with labor constraints［J］. Discrete Applied Mathematics， 2001， 112（1-3）： 27-52.
[13]	Wan Z， He J， Tang G. Construction project scheduling problem with uncertain resource constraints［J］. Chinese Journal of Engineering Mathematics， 2005， 22（3）： 399-406.
[14]	Drezet L E， Billaut J C. A project scheduling problem with labour constraints and time-dependent activities requirements［J］. International Journal of Production Economics， 2008， 112（1）： 217-225.
[15]	Fündeling C U， Trautmann N. A priority-rule method for project scheduling with work-content constraints［J］. European Journal of Operational Research， 2010， 203（3）： 568-574.
[16]	Zhang H， Tam C M， Shi J J. Application of fuzzy logic to simulation for construction operations［J］. Journal of Computing in Civil Engineering， 2003， 17（1）： 38-45.
[17]	何立华. 资源不确定条件下项目调度多目标优化研究［D］. 天津：天津大学博士学位论文， 2013.
	He L H. Research on the multiple objective optimization of project scheduling under uncertain resource conditions［D］. Tianjin： Doctoral Dissertation of Tianjin University， 2013.
[18]	卢辉，王红卫，李锋，等. 考虑供应不确定性与需求非平稳性的项目调度与材料供应集成优化［J］. 系统工程理论与实践， 2019， 39（3）： 647-658.
	Lu H， Wang H W， Li F， et al. Integrated scheduling and material supply planning under nonstationary stochastic demand and random supply yield［J］. Systems Engineering-Theory & Practice， 2019， 39（3）： 647-658.
[19]	Shariatmadari M， Nahavandi N. A new resource buffer insertion approach for proactive resource investment problem［J］.Computers & Industrial Engineering， 2020， 146： 106582.
[20]	Madadi M， Iranmanesh H. A management oriented approach to reduce a project duration and its risk （variability）［J］. European Journal of Operational Research， 2012， 219（3）： 751-761.
[21]	Martens A， Vanhoucke M. The impact of applying effort to reduce activity variability on the project time and cost performance［J］. European Journal of Operational Research， 2019， 277（2）： 442-453.
[22]	崔晓，何正文，王能民. 考虑信息处理成本的反应性项目调度优化［J］. 系统工程理论与实践， 2021， 41（10）： 2581-2594.
	Cui X， He Z W， Wang N M. Reactive project scheduling with information handling cost［J］. Systems Engineering-Theory & Practice， 2021， 41（10）： 2581-2594.
[23]	Fleszar K， Hindi K S. Solving the resource-constrained project scheduling problem by a variable neighbourhood search［J］. European Journal of Operational Research， 2004， 155（2）： 402-413.
[24]	He Z， He H， Liu R， et al. Variable neighbourhood search and tabu search for a discrete time/cost trade-off problem to minimize the maximal cash flow gap［J］. Computers & Operations Research，2017，78： 564-577.

强相关文献	不确定性因素			不确定性因素处理方式		降低不确定性因素的变化性	分析目标			解决方法
强相关文献	工期	资源需求	资源可用量	随机变量	模糊数	降低不确定性因素的变化性	时间	成本	其他	解决方法
Van de Vonder等^[3]	√	-	-	√	-	-	-	√	-	优先列表/抽样/加权提前-延迟法等
Davari和Demeulemesster^[4]	√	-	-	√	-	-	-	√	-	动态规划
Chakrabortty等^[7]	-	-	√	√	-	-	√	-	-	基于事件反应法
彭武良和林家利^[10]	-	-	√	√	-	-	-	-	√	两阶段法
Zhang等^[16]	-	√	-	-	√	-	-	-	√	仿真分析
何立华^[17]	-	√	-		√	-	√	√	-	遗传算法
卢辉等^[18]	-	√	-	√	-	-	-	√	-	代理模型优化法
Shariatmadari和Nahavandi^[19]	-	√	-	√	-	-	-	-	√	鲁棒性提升算法
Madadi和Iranmanesh^[20]	√	-	-	√	-	√	√		-	仿真分析
Martens和Vanhoucke^[21]	√	-	-	√	-	√	√	√	-	仿真分析
本文	-	√	-	√	-	√	-	√	-	变邻域算法

编号	类别	项目活动名称	*d_i*	*w_i*	μ_i₁	σ _i₁	*μ_i2*	σ _i₁
0	开始	虚开始活动	0	0	0	0	0	0
1	控制功能	数据库设计及评审	6	6	8	2.9	5	4.7
2		控制页面UI和回执文件控制逻辑编码	12	4	5	4.1	2	1.5
3		创建及评审控制功能用例	5	5	2	1.9	3	2.8
4		实施及创建控制功能自测和单元测试	4	2	6	2.7	4	1.5
5		评审控制功能代码	2	5	4	1.7	2	1.4
6		控制功能测试	5	3	2	1.5	2	1.2
7	生成文件功能	生成文件功能编码	12	8	3	4.2	2	1.8
8		创建及评审生成文件功能用例	3	3	2	3.1	3	2.5
9		实施及创建生成文件功能自测和单元测试	6	2	7	1.6	3	2.9
10		评审生成文件功能代码	1	5	4	2.4	2	1.9
11		生成文件功能测试	4	4	3	2.8	5	3.2
12	投递选择功能	投递选择功能编码	28	9	8	4.7	4	3.2
13		创建及评审投递选择功能用例	6	3	3	1.4	5	3.7
14		实施及创建投递选择功能自测和单元测试	15	4	6	3.2	3	1.9
15		评审投递选择功能代码	3	2	4	2.4	2	1.4
16		投递选择功能测试	8	5	2	1.5	4	2.7
17	邮递显示功能	邮递显示功能编码	6	9	4	2.4	3	2.5
18		创建及评审邮递显示功能测试用例	3	6	2	1.8	5	3.8
19		实施及创建邮递显示功能自测和单元测试	7	2	6	2.9	2	1.6
20		评审邮递显示功能代码	2	2	3	2.7	3	2.6
21		邮递显示功能测试	6	3	2	2.1	4	2.7
22	收据及查询功能	收据及查询功能编码	12	9	3	3.4	2	1.5
23		创建及评审收据及查询功能测试用例	5	5	2	1.5	5	2.2
24		实施及创建收据及查询功能自测和单元测试	7	3	7	3.7	3	2.6
25		评审收据及查询功能代码	2	2	4	2.9	2	1.1
26		收据及查询功能测试	4	7	2	1.4	4	3.3
27	分发管理功能	分发管理功能编码	13	6	3	3.5	2	1.7
28		创建及评审分发管理功能测试用例	6	5	2	2.7	6	2.3
29		实施及创建分发管理功能自测和单元测试	8	3	4	3.4	3	2.9
30		评审分发管理功能代码	2	4	6	2.7	4	2.9
31		分发管理功能测试	7	4	2	1.8	4	1.9
32	集成测试	软件集成测试、检测及修复缺陷任务	15	8	4	3.6	6	4.8
33	结束	虚结束活动	0	46	0	0	0	0

方案及降后标准差		元素值
Y^* 及其降后标准差	y_i1	{0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}
	y_i2	{0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0}
	σ'_i1 (Y^* )	{0, 2.9, 3.8, 1.9, 2.7, 1.7, 1.5, 4.2, 2.9, 1.6, 2.4, 2.8, 4.7, 1.4, 3.2, 2.4, 1.3, 2.0, 1.5, 2.5, 2.7, 2.1, 3.4, 1.5, 3.7, 2.9, 1.4, 2.8, 2.7, 3.4, 2.7, 1.8, 3.6, 0}
	σ'_i2 (Y^* )	{0, 4.2, 1.3, 2.8, 1.2, 1.4, 1.2, 1.8, 2.5, 2.9, 1.9, 2.1, 2.6, 2.9, 1.9, 1.4, 2.5, 2.3, 3.3, 1.3, 2.6, 2.3, 1.2, 2.2, 2.2, 1.1, 3.3, 1.7, 2.0, 2.9, 2.9, 1.9, 4.8, 0}
Y 及其降后标准差	y_i1	{0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 1, 0, 2, 2, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 2, 1, 1, 0}
	y_i2	{0, 2, 1, 2, 2, 2, 2, 1, 2, 2, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 1, 0, 2, 1, 0}
	σ'_i1 (Y)	{0, 2.9, 3.6, 1.9, 2.7, 1.7, 1.5, 4.2, 2.9, 1.6, 2.4, 2.8, 3.8, 1.2, 2.7, 2.0, 1.3, 2.4, 1.3, 2.1, 2.7, 2.1, 2.7, 1.4, 3.7, 2.9, 1.4, 2.8, 2.2, 2.7, 2.1, 1.4, 2.9, 0}
	σ'_i2 (Y)	{0, 4.2, 1.3, 2.2, 0.9, 0.9, 0.8, 1.5, 1.6, 2.5, 1.9, 3.2, 2.9, 2.4, 1.6, 1.4, 2.7, 2.5, 3.3, 1.3, 2.6, 2.0, 1.2, 1.9, 2.2, 0.9, 2.2, 1.6, 2.0, 2.7, 2.9, 1.2, 4.1, 0}

*e_ik*	TC	EC	AC	*w_i*	TC	EC	AC	*R_k*	TC	EC	AC
0.8	170.63	52.27	118.36	0.8	156.04	54.04	102.00	1.0	323.26	89.33	232.93
1.0	181.05	58.22	122.83	1.0	196.80	58.04	138.76	1.1	150.47	47.47	103.00
1.2	208.72	68.80	139.92	1.2	207.56	67.20	140.36	1.2	87.68	42.49	45.19

Optimization of Reactive Project Scheduling with Stochastic Resource Requirements Considering Information Handling Input

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 9

References 24

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Baofeng Tian, Jingwen Zhang, Lubo Li, Junjie Chen. Integrated Resource-constrained Project Scheduling and Material Ordering Problem with Limited Storage Space [J]. Chinese Journal of Management Science, 2025, 33(8): 144-155.
[2]	Wuliang Peng, Xuejun Lin. A Dynamic Reactive Scheduling Method for the Resource Constrained Project Scheduling Problem [J]. Chinese Journal of Management Science, 2025, 33(7): 200-209.
[3]	Yanting Wang, Weibo Zheng, Zhiqiang Ma, Zhengwen He. Robustness Threshold-based Max-NPV Project Scheduling Optimization on Different Clients’ Payment Modes [J]. Chinese Journal of Management Science, 2025, 33(4): 185-196.
[4]	Yidan He,Zhengwen He,Nengmin Wang,Zhiqiang Ma. Resource-constrained Max-NPV Multi-project Scheduling Optimization under Sharing Economy Environment [J]. Chinese Journal of Management Science, 2024, 32(9): 260-270.
[5]	Jingchun Feng,Yaqi Yan,Ke Zhang,Daisong Hu. Robust Optimization Model of Water Environment Treatment Portfolio of Big Rivers for Maximizing Enterprise Income——Taking Yangtze River Protection as an Example [J]. Chinese Journal of Management Science, 2024, 32(6): 323-334.
[6]	GAO Jia-jing, ZHEN Lu. Research on Routing Problem for Joint Delivery System Based on Multiple Trucks and Robots [J]. Chinese Journal of Management Science, 2023, 31(3): 48-57.
[7]	LI Yang, FAN Hou-ming, ZHANG Xiao-nan. A Periodic Optimization Model and Solution for Capacitated Vehicle Routing Problem with Dynamic Requests [J]. Chinese Journal of Management Science, 2022, 30(8): 254-266.
[8]	MA Zhi-qiang, XU Xiao-feng, HE Zheng-wen, WANG Neng-min. Robust Scheduling Optimization of Project Resources with Activity Splitting under Complex and Uncertain Environments [J]. Chinese Journal of Management Science, 2022, 30(3): 117-130.
[9]	ZHANG Meng-ling, WANG Jing, HUANG Jun. Research on Robust Optimization of Emergency Resource Allocation Based on Supplier Participation Mechanism under Uncertain Demand [J]. Chinese Journal of Management Science, 2020, 28(7): 102-111.
[10]	MA Yong, HE Zheng-wen, ZHENG Wei-bo. Proactive Project Scheduling Optimization Based on Flexible Resource Constraint [J]. Chinese Journal of Management Science, 2020, 28(7): 220-230.
[11]	CUI Yu-quan, LIU Bing-jie, LIU Cong, QU Jing-jing. Optimization Model Analysis of New Order Agricultural Cooperation Model [J]. Chinese Journal of Management Science, 2020, 28(12): 140-150.
[12]	ZHANG Yao, SUN Meng-yang, GUAN Xin. Method of Selecting Project Risk Response Strategies Considering Total Risk Interdependence [J]. Chinese Journal of Management Science, 2020, 28(1): 32-44.
[13]	WU Zhi-qiao, LU Xiang-yuan, MU Li-feng, TANG Jia-fu. An Optimization Model for System Component Selection to Minimize Cost and Combinational Risk [J]. Chinese Journal of Management Science, 2017, 25(8): 158-165.
[14]	LAN Bo-xiong, WANG Tong-shu. Optimization Model and Algorithms for Large-scale Rail Passenger Transport Network Operation [J]. Chinese Journal of Management Science, 2016, 24(6): 159-170.
[15]	LI Gen, LIU Jia-guo, ZHAO Jin-lou. Scenario Analysis of Complete Energy Intensity of Manufacturing Industry in China Based on Input and Output and Non-linear Optimization [J]. Chinese Journal of Management Science, 2016, 24(3): 31-40.