不同业主支付方式下基于鲁棒性阈值的净现值最大化项目调度优化

doi:10.16381/j.cnki.issn1003-207x.2022.0306

Abstract

Abstract:

In practical project management， there exist many uncertain factors， such as weather changes， shortage of resource supply， untimely capital payment， may influence the activity duration and the contractor’s cash flow arrangement during the whole project implementation process， and finally cause the loss of project profit. At the meanwhile， different clients payment modes determine the time and scales of cash inflow， the project contractor optimizes the arrangement of project activities and cash outflow according to the cash inflow by client， so as to ensure the smooth implementation and completion of the project. Therefore， it has a very important guiding significance for the optimal scheduling and management of cash flow of the actual project， and how to choose a reasonable client payment mode while dealing with the interference of uncertainty factors so that the project can obtain the maximum benefit.Considering the impact of the clients payment modes on project cash flow distribution and profit under uncertain environment， the robust Max-NPV project scheduling optimization problem is studied on different clients payment modes， where time buffer strategy is applied to strengthen the baseline schedule robustness， and at the same time the robustness threshold constraint is formulated. Firstly， the research problem is defined， and on basis of the robustness threshold， a two-stage project payment Max-NPV scheduling optimization model under different payment modes （progress-based， cost-based， time-based， milestone-based） is constructed； The first stage is a robustness maximization scheduling model， to obtain the maximal robustness value and solve the resource constraint based on the resource flow network， and the second stage is to solve the Max-NPV optimization problem under the given robustness threshold constraint. Then， according to the NP-hard property of the problem， a tabu search heuristic algorithm is designed， and considering the algorithms’ neighborhood quantity and search strategy on performance， the variable neighborhood heuristics， multi-start iteration improvement and random generation algorithms are adopted as benchmarks. The four algorithms are tested on a set of randomly generated large scall standard instances， and moreover， the sensitivity of key parameters on project net present value is analyzed.The conclusions of the research are as follows. Firstly， compared with the four algorithms， the designed tabu search algorithm performs better other three algorithms with acceptable time. Then， compared with the four clients payment modes with different algorithms， the results show that different payment modes have an important impact on the contractor’s project net present value， among which， the progress-based payment mode performs the best， and the cost-based and milestone-based rank the second， while the time-based payment mode is the worst. Moreover， the influences of the key parameters including the payment numbers， the project deadline， the payment proportion， the discount rate， the buffer cost per unit time， the robustness threshold coefficient on the project net present value are analyzed， and the following results are drawn： the contractor's net present value increases with the increase of the client payment numbers and the payment proportion， and decreases with the increase of the discount rate， the buffer cost per unit time and the robustness threshold coefficient， and first rises and then decreases with the increase of the project deadline. It is more important to note that， a reasonable robustness threshold can increase the project’s net present value， but too high or too small may induce a decrease conversely.The research in this paper can help project managers to determine the optimal payment strategy and schedule under uncertainty environment， ensuring the smooth implementation and the best benefits of the project. Therefore， it can provide effective decision supports for project scheduling of maximizing the net present value in reality.

Key words: Max-NPV project scheduling, different payment modes, robustness threshold, optimization model, heuristic algorithms

CLC Number:

C935

Yanting Wang,Weibo Zheng,Zhiqiang Ma, et al. Robustness Threshold-based Max-NPV Project Scheduling Optimization on Different Clients’ Payment Modes[J]. Chinese Journal of Management Science, 2025, 33(4): 185-196.

Figures/Tables 5

参数	取值
基本算例参数
非虚活动数n	10，20，40，60
起始和终止活动数	随机地从1，2和3中选取
最大紧前和紧后活动数	3
可更新资源种类K	2
资源需求量r_ik	随机地从均匀分布U[1, 10]中选取
活动工期均值 $μ (d i)$	随机地从均匀分布U[5, 20]中选取
活动工期标准差σ(d_i )	随机地从均匀分布U[1, 5]中选取
活动基本成本c_i	随机地从均匀分布U[10, 30]中选取
活动挣值v_i	ρc_i，ρ随机地从均匀分布U[1, 5]中选取
活动i权重w_i	由三角分布 $P (w i = x) = 0.21 - 0.02 x, x ∈ [1,10]$ 随机生成，且 $w n + 1 = 10 × ∑ i = 1 n w i / n$
关键敏感性参数
支付次数F	3, 5, 7, 9和11
项目截止日期D	$D = n d ∙ C m a x$ , nd取值1.1, 1.2, 1.3, 1.4,1.5, $C m a x$ 为关键路径长度
折现率 $α$	0.0040, 0.0050, 0.0060, 0.0070和0.0080
支付比例 $θ$	0.1, 0.3, 0.5, 0.7和0.9
单位时间缓冲成本 $β i$	$β i = n r ∙ σ (d i),$ nr取值0.1, 0.3, 0.5, 0.7,0.9
鲁棒性阈值系数 $λ$	0.0, 0.2, 0.4, 0.6和0.8

参数	数值	里程碑型支付	时间型支付	进展型支付	费用型支付	参数	数值	里程碑型支付	时间型支付	进展型支付	费用型支付
参数	数值	NPV	NPV	NPV	NPV	参数	数值	NPV	NPV	NPV	NPV
F	3	212.41	234.26	264.95	261.77	$θ$	0.1	112.69	106.25	179.58	167.01
	5	222.19	244.31	293.44	292.54		0.3	143.60	141.56	227.15	213.56
	7	245.04	258.65	329.03	311.61		0.5	181.65	184.64	257.08	242.34
	9	259.04	262.83	347.08	334.83		0.7	202.95	208.45	268.03	252.52
	11	268.86	272.39	359.61	346.74		0.9	225.98	232.53	277.07	260.21
nd	1.1	238.76	246.33	281.38	269.99	$α$	0.004	235.72	232.93	286.63	274.77
	1.2	234.37	248.22	299.01	292.74		0.005	200.47	200.97	259.80	247.22
	1.3	243.19	249.30	303.26	305.76		0.006	171.23	174.32	235.96	224.19
	1.4	226.02	236.35	286.32	277.16		0.007	147.13	152.31	215.57	204.22
	1.5	147.60	146.20	203.43	182.33		0.008	127.77	133.76	197.94	186.52
nr	0.1	286.06	292.88	365.37	364.90	$λ$	0	178.14	180.75	242.52	229.93
	0.3	218.42	224.75	293.10	285.58		0.2	178.31	180.75	242.50	229.90
	0.5	163.22	164.90	229.30	214.76		0.4	178.18	180.76	242.47	229.84
	0.7	122.44	120.82	174.23	155.12		0.6	176.58	179.31	239.07	227.72
	0.9	92.18	90.92	133.88	116.56		0.8	171.10	172.71	229.32	219.52

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支付方式	N	TS					VNS					MSII					RG
支付方式	N	ARD	MRD	CV	ACT	MCT	ARD	MRD	CV	ACT	MCT	ARD	MRD	CV	ACT	MCT	ARD	MRD	CV	ACT	MCT
里程碑型	10	0.03	0.12	0.05	0.08	0.10	0.03	0.08	0.06	0.10	0.11	0.12	0.26	0.03	0.07	0.09	0.10	0.21	0.06	0.09	0.13
	20	0.03	0.12	0.04	0.35	0.45	0.06	0.18	0.04	0.48	0.56	0.16	0.26	0.08	0.34	0.41	0.18	0.34	0.11	0.35	0.51
	40	0.01	0.04	0.02	2.33	2.75	0.15	0.20	0.05	3.34	4.05	0.31	0.94	0.29	2.23	2.61	0.48	1.17	0.38	1.92	2.07
	60	0.01	0.04	0.01	6.13	6.81	0.11	0.20	0.04	9.94	11.3	0.32	0.73	0.28	6.01	6.64	0.58	1.12	0.40	5.32	5.50
	avg.	0.02	0.08	0.03	2.22	2.52	0.09	0.17	0.05	3.47	4.01	0.23	0.54	0.17	2.16	2.44	0.33	0.71	0.24	1.92	2.05
时间型	10	0.07	0.18	0.07	0.08	0.11	0.01	0.09	0.08	0.10	0.12	0.13	0.29	0.03	0.07	0.09	0.05	0.17	0.05	0.08	0.09
	20	0.04	0.11	0.05	0.33	0.40	0.04	0.20	0.05	0.48	0.55	0.16	0.25	0.06	0.31	0.37	0.15	0.30	0.07	0.32	0.40
	40	0.01	0.07	0.02	2.67	3.51	0.15	0.25	0.05	3.30	4.66	0.17	0.58	0.18	2.00	2.16	0.43	1.13	0.31	1.80	1.95
	60	0.00	0.01	0.00	6.16	6.61	0.14	0.22	0.05	9.79	10.98	0.20	0.41	0.16	5.65	5.98	0.50	0.86	0.27	5.01	5.45
	avg.	0.03	0.09	0.04	2.31	2.66	0.09	0.19	0.06	3.42	4.08	0.17	0.38	0.11	2.00	2.15	0.28	0.62	0.17	1.80	1.97
进展型	10	0.05	0.16	0.06	0.08	0.12	0.02	0.09	0.05	0.10	0.11	0.13	0.22	0.03	0.07	0.09	0.06	0.12	0.03	0.07	0.09
	20	0.03	0.11	0.04	0.35	0.41	0.06	0.24	0.04	0.43	0.60	0.14	0.20	0.09	0.33	0.39	0.14	0.30	0.09	0.32	0.38
	40	0.01	0.05	0.02	2.66	3.75	0.14	0.24	0.05	3.17	4.21	0.14	0.38	0.14	2.22	2.37	0.33	0.88	0.25	2.00	2.17
	60	0.00	0.00	0.00	6.87	7.40	0.11	0.17	0.03	9.93	10.62	0.19	0.39	0.15	6.40	6.70	0.38	0.66	0.21	5.72	5.98
	avg.	0.02	0.08	0.03	2.49	2.92	0.08	0.19	0.04	3.41	3.88	0.15	0.30	0.10	2.26	2.39	0.23	0.49	0.15	2.03	2.15
费用型	10	0.05	0.13	0.05	0.08	0.10	0.02	0.14	0.08	0.10	0.13	0.12	0.25	0.04	0.08	0.09	0.06	0.16	0.05	0.08	0.09
	20	0.03	0.08	0.03	0.38	0.45	0.05	0.17	0.05	0.48	0.59	0.12	0.18	0.07	0.36	0.43	0.13	0.24	0.06	0.36	0.43
	40	0.03	0.16	0.06	2.64	2.84	0.13	0.23	0.04	3.18	3.74	0.14	0.33	0.13	2.40	2.60	0.33	0.89	0.25	2.17	2.36
	60	0.01	0.06	0.02	7.45	7.78	0.11	0.14	0.03	10.26	11.87	0.19	0.43	0.15	7.07	7.54	0.38	0.72	0.22	6.33	6.52
	avg.	0.03	0.11	0.04	2.64	2.79	0.08	0.17	0.05	3.50	4.08	0.14	0.30	0.10	2.48	2.67	0.23	0.50	0.15	2.23	2.35

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Robustness Threshold-based Max-NPV Project Scheduling Optimization on Different Clients’ Payment Modes

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