基于全局空闲资源再分配的多技能项目群调度优化

doi:10.16381/j.cnki.issn1003-207x.2024.1406

Abstract

Abstract:

Large engineering projects are often managed by project groups. There is a logical relationship between subprojects， and the project information is fully shared. At the same time， it is necessary to consider the overall optimization objectives of the project group and the optimization objectives of each subproject. Therefore， the project group scheduling problem is a special multi project scheduling optimization problem with practical application scenarios. When considering multi skilled human resources， the difference in the skill level of global resources and the change in the use of local resources will lead to the change of activity duration. Large projects tend to be completed and put into use as soon as possible， that is， project group managers usually need to consider how to reduce the project group duration； When the sub project is responsible for its own profits and losses within the budget， it often reduces the cost of the sub project as much as possible to protect its own interests， that is， the sub project manager usually needs to consider how to reduce the cost of the sub project. Therefore， the global and local objectives are to minimize the total duration of the project group and the cost of each sub project.To solve this problem， a global and local two-stage hierarchical scheduling optimization model is established. Under the global and local resource constraints， the project group manager establishes a global scheduling optimization model to minimize the total duration of the project group. Under the global resource constraints and sub project duration constraints given by the project group manager， the sub project managers establish a local scheduling optimization model with the goal of minimizing the sub project cost. To solve this problem， a two-stage solution mechanism based on idle global resource reallocation is proposed， and an adaptive improved multi population genetic algorithm is designed to solve the global scheduling problem.The experimental research was carried out based on Ran Gen randomly generated project group example set. According to the problem size， the example is divided into three problem subsets， and each problem subset contains two groups of project group examples generated by 27 different parameter combinations. The experimental results show that under the same problem scale， the stronger the global resource conflict intensity and the greater the network density of the project group， the longer the total duration of the project group， and the greater the local resource demand intensity， the greater the average cost of the sub project. The experiment further proves that the idle global resource reallocation mechanism designed in this paper can reasonably allocate the global multi skilled human resources and effectively reduce the cost of sub projects on the premise of ensuring the total duration of the project group. In addition， the idle resource reallocation strategy can provide a reference for project group managers when allocating project group resources.The research gap of project group scheduling problem is made up for considering multi skilled human resources， and the door for further research on project group scheduling problem considering human resources balance and multi skilled human resources project group scheduling problem under uncertainty is opened. Due to the multi skill heterogeneity of human resources and the different needs of activities， the working hours of employees tend to be unbalanced， which is not conducive to the use and management of human resources. Therefore， in the follow-up study， the work time balance will be considered for further research. At the same time， more efficient meta heuristic algorithm or artificial intelligence algorithm is explored to solve the problem， so as to further improve the optimization effect of project group scheduling problem.

Key words: project group scheduling, multi-skilled human resources, variable duration, multi population genetic algorithm

CLC Number:

N945

Songqing Guo,Zhe Xu,Yixuan Su. Optimization of Multi Skill Project Group Scheduling Based on Global Idle Resource Reallocation[J]. Chinese Journal of Management Science, 2026, 34(6): 187-201.

Figures/Tables 21

对比算法	TSABMPGA			TSABSA			TSABPSO
算例集	项目群总工期			项目群总工期			项目群总工期
算例集	$N B S d$	$A R D d$	$M R D d$	$N B S d$	$A R D d$	$M R D d$	$N B S d$	$A R D d$	$M R D d$
10_4	54	0	0	0	0.352	0.408	0	0.172	0.283
10_6	54	0	0	0	0.295	0.35	0	0.117	0.213
10_12	53	0.009	0.009	0	0.248	0.286	1	0.053	0.107
全部算例	161	0.003	0.009	0	0.299	0.408	1	0.114	0.283
算例集	子项目平均成本			子项目平均成本			子项目平均成本
算例集	$N B S c$	$A R D c$	$M R D c$	$N B S c$	$A R D c$	$M R D c$	$N B S c$	$A R D c$	$M R D c$
10_4	34	0.021	0.059	20	0.146	0.42	0	0.196	0.374
10_6	32	0.037	0.121	22	0.228	0.475	0	0.228	0.366
10_12	54	0	0	0	0.319	0.6	0	0.245	0.472
全部算例	120	0.019	0.059	42	0.246	0.475	0	0.223	0.374

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现有研究及局限性				本文的研究要点
调度问题	问题描述	研究要点	局限性	本文的研究要点
项目群调度问题	问题假设	将子项目视为活动^[3，12]	未考虑内部调度	考虑子项目内部调度及子项目成本目标
	问题假设	仅考虑子项目内部调度^{[1，10，11，13，14]}	未考虑局部利益	考虑子项目内部调度及子项目成本目标
	优化目标	时间类^[1]	仅考虑项目群整体目标，未考虑子项目局部目标	同时考虑项目群整体目标与各子项目局部目标，即以项目群总工期与各子项目成本为优化目标
	优化目标	工期-费用优化^[3，10-14]	仅考虑项目群整体目标，未考虑子项目局部目标	同时考虑项目群整体目标与各子项目局部目标，即以项目群总工期与各子项目成本为优化目标
多技能多项目调度问题	问题假设	无局部资源约束^{[15，19，20]}	未考虑局部资源数量限制	局部资源限制下同时考虑全局资源技能水平与局部资源投入数量对活动工期的影响
多技能多项目调度问题	问题假设	仅考虑多技能资源技能水平对活动工期影响^{[16-18，21-23]}	未考虑局部资源投入对活动工期的影响	局部资源限制下同时考虑全局资源技能水平与局部资源投入数量对活动工期的影响

编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本	编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本
1	1.2	0.6	0.8	3	11	0.8	0	1.4	3
2	0.8	0	1	2	12	0.6	0	1.4	2
3	1.2	1	1.4	4	13	0.8	1.4	0	3
4	1	0.8	0.6	3	14	0.6	1.4	1	3
5	0.8	1.4	0.8	3	15	1.2	0.6	0	2
6	1.4	1.4	0.6	4	16	0.8	0.8	0.6	3
7	0.8	1.2	0.8	3	17	0.6	1.2	1.4	4
8	1.4	0.6	0.8	3	18	1	1	1.2	4
9	1.4	1	1	4	19	1.4	0.8	0.6	3
10	0.6	0.6	1	3	20	1.4	1.2	0	3

再分配策略	工期	局部资源1	局部资源2	全局技能1	全局技能2	全局技能3	全局资源编号
OUFGRRS	2	8	3	0.8	1.2	1.2	11	20	18
UFGRRS	2	8	3	0.8	0.6	1.4	11	15	12

类型	参数	取值
子项目	次序强度 OS-L	0.25、0.5、0.75
	资源系数 RF	0.25、0.5、0.75
	资源强度 RS	0.25、0.5、0.75
	每个活动需要的全局技能	{技能1、技能2、技能3}中随机选取两个
项目群	次序强度OS-G	0.25、0.5、0.75
	全局资源技能水平	0.6、0.8、1.0、1.2、1.4
	全局人力资源可用量	20、10
	人均掌握技能数	{2，3}中随机选取
	全局技能种类	3

算法	算法阶段	参数	参数水平	是否显著	数值
TSABMPGA	全局	子种群数量	2、3、4	是	2
		子种群大小	25、50、75	是	50
		交叉概率	0.5、0.7、0.9	是	0.9
		变异概率	0.5、0.7、0.9	否	0.5
	局部	种群大小	25、50、75	是	50
		交叉概率	0.5、0.7、0.9	是	0.9
		变异概率	0.5、0.7、0.9	否	0.5
TSABSA	全局	初始温度	50、100、200	是	100
		温度衰减系数	0.9、0.925、0.95	否	0.9
		马尔科夫链长度	100、150、200	是	200
		变异概率	0.5、0.7、0.9	是	0.9
	局部	初始温度	5、7.5、10	是	10
		温度衰减系数	0.7、0.75、0.8	是	0.8
		马尔科夫链长度	50、75、100	否	100
		变异概率	0.5、0.7、0.9	是	0.9
TSABPSO	全局	惯性权重	0.2、0.35、0.5	是	0.5
		自我学习因子	0.3、0.5、0.7	是	0.3
		群体学习因子	0.7、0.5、0.3	是	0.7
	局部	惯性权重	0.2、0.35、0.5	是	0.5
		自我学习因子	0.3、0.5、0.7	是	0.3
		群体学习因子	0.7、0.5、0.3	是	0.7

Optimization of Multi Skill Project Group Scheduling Based on Global Idle Resource Reallocation

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编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本	编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本
1	1.2	0.6	0.8	3	11	0.8	0	1.4	3
2	0.8	0	1	2	12	0.6	0	1.4	2
3	1.2	1	1.4	4	13	0.8	1.4	0	3
4	1	0.8	0.6	3	14	0.6	1.4	1	3
5	0.8	1.4	0.8	3	15	1.2	0.6	0	2
6	1.4	1.4	0.6	4	16	0.8	0.8	0.6	3
7	0.8	1.2	0.8	3	17	0.6	1.2	1.4	4
8	1.4	0.6	0.8	3	18	1	1	1.2	4
9	1.4	1	1	4	19	1.4	0.8	0.6	3
10	0.6	0.6	1	3	20	1.4	1.2	0	3

活动编号	活动工期		全局资源成本		局部资源成本		活动总成本
活动编号	OUFGRRS	UFGRRS	OUFGRRS	UFGRRS	OUFGRRS	UFGRRS	OUFGRRS	UFGRRS
合计	-	-	453	376	367	343	820	719
3-0	0	0	0	0	0	0	0	0
3-1	6	6	18	12	0	0	18	12
3-2	1	1	3	4	9	9	12	13
3-3	12	12	132	132	66	60	198	192
3-4	11	8	66	32	72	72	138	104
3-5	2	2	20	14	22	22	42	36
3-6	4	3	24	18	28	24	52	42
3-7	9	9	54	54	132	126	186	180
3-8	10	8	90	72	30	24	120	96
3-9	10	10	30	30	0	0	30	30
3-10	4	2	16	8	8	6	24	14
3-11	0	0	0	0	0	0	0	0

算例集	算例数	全局资源可用量	子项目数	活动数	问题规模	平均技能利用系数（AUF）
10_4	27	20	4	10	40	0.450
10_4	27	10	4	10	40	0.958
10_6	27	20	6	10	60	0.533
10_6	27	10	6	10	60	1.137
10_12	27	20	12	10	120	0.704
10_12	27	10	12	10	120	1.487

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编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本	编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本
1	1.2	0.6	0.8	3	11	0.8	0	1.4	3
2	0.8	0	1	2	12	0.6	0	1.4	2
3	1.2	1	1.4	4	13	0.8	1.4	0	3
4	1	0.8	0.6	3	14	0.6	1.4	1	3
5	0.8	1.4	0.8	3	15	1.2	0.6	0	2
6	1.4	1.4	0.6	4	16	0.8	0.8	0.6	3
7	0.8	1.2	0.8	3	17	0.6	1.2	1.4	4
8	1.4	0.6	0.8	3	18	1	1	1.2	4
9	1.4	1	1	4	19	1.4	0.8	0.6	3
10	0.6	0.6	1	3	20	1.4	1.2	0	3

编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本	编号	全局技能1水平	全局技能2水平	全局技能3水平	全局资源单位成本
1	1.2	0.6	0.8	3	11	0.8	0	1.4	3
2	0.8	0	1	2	12	0.6	0	1.4	2
3	1.2	1	1.4	4	13	0.8	1.4	0	3
4	1	0.8	0.6	3	14	0.6	1.4	1	3
5	0.8	1.4	0.8	3	15	1.2	0.6	0	2
6	1.4	1.4	0.6	4	16	0.8	0.8	0.6	3
7	0.8	1.2	0.8	3	17	0.6	1.2	1.4	4
8	1.4	0.6	0.8	3	18	1	1	1.2	4
9	1.4	1	1	4	19	1.4	0.8	0.6	3
10	0.6	0.6	1	3	20	1.4	1.2	0	3