Project portfolio selection based on multi-project synergy

Zonghan Wang; Moses Olabhele Esangbedo; Sijun Bai

doi:10.3934/jimo.2021177

Article Contents

2023, Volume 19, Issue 1: 117-138. Doi: 10.3934/jimo.2021177

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Project portfolio selection based on multi-project synergy

a.
School of Management, Northwestern Polytechnical University, 710072, Xi'an, China
b.
Yangtze River Delta Research Institute of NPU, Northwestern Polytechnical University, Taicang, Jiangsu 215400, China

^* Corresponding author: Moses Olabhele Esangbedo
^* Corresponding author: Moses Olabhele Esangbedo

Received: June 2021

Revised: August 2021

Early access: October 2021

Published: January 2023

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Abstract

To date, the selection of a project portfolio that maximises the decision-making outcome remains essential. However, existing research on project synergy has mainly focused on two projects, while there are multiple projects in some cases. Two kinds of synergies among multiple projects are proposed. First, multiple projects must be selected together, in order to produce synergy. Second, some projects depend on synergy with other projects, leading to a synergetic increase in performance. Furthermore, we present strategic synergy, with benefits, resources, and technology, which is quantified for a procurement project concerning a COVID-19 pandemic recovery plan. A design structure matrix is used to describe the technology diffusion among the projects. Then, strategic alignment is utilised to measure the strategic contribution of projects. Next, a portfolio selection model considering uncertainty is established, based on the strategic utility. Finally, our results indicate that selecting projects considering multi-project synergy is more advantageous.

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Mathematics Subject Classification: Primary: 90b50; Secondary: 90C70.

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Figure 1. Relationships between four synergy types

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Figure 2. Relationships between four synergy types (type II)

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Figure 3. Benefit synergy; lower triangular matrix

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Figure 4. Technology diffusion relationships

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Figure 5. Three strategic contribution solution scenarios

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Figure 6. Technology diffusion relationship

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Table 1. Research Trends on Synergy in Project Portfolio

Related Works	Aspects		Type of Synergy		Strategic Utility Goals	Uncertainty
Related Works	Benefit/ Resource/ Technology	Strategy	Two Projects	Multiple projects	Strategic Utility Goals	Uncertainty
[8,10,14,16,24,25,28]	√	$ \times $	√	$ \times $	$ \times $	$ \times $
[6,32,34,50,53,48,18,11,52,55]	$ \times $	$ \times $	$ \times $	$ \times $	$ \times $	√
[1,39,48]	√	$ \times $	√	$ \times $	$ \times $	√
[8]	√	$ \times $	√	√	$ \times $	√
This paper	√	√	√	√	√	√

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Table 2. Strategic indicators

Overall goal	First-level indicators, $ B_i $ (Local weights)	Second-level indicators, $ i $ (Local weight)
Non- economic indicators	1 Development potential (0.54)	1, Market demand [7] (0.57)
		2, Brand lead [45] (0.29)
		3, Customer satisfaction [7] (0.14)
	2 Technical advantages (0.30)	4, Product technical strength [45] (0.12)
		5, Product innovation and patent [45,51] (0.43)
		6, Product life-cycle [51] (0.29)
		7, Product market orientation [45] (0.16)
	3 Social reputation (0.16)	8, Corporate social image recognition [7] (0.56)
		9, Corporate social responsibility realisation [51] (0.32)
		10, Corporate social appeal [51] (0.12)

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Table 3. Fuzzy data of benefit, resources, and success probability

Project	${{v}_{i}}$	$r_{i}^{1}$	$r_{i}^{2}$	$r_{i}^{3}$	${{p}_{i}}$
1	(40,50,62.5)	(4.6,5.2,7.2)	(5.4,6.2,8.2)	(5,6,8.2)	(0.39,0.45,0.505)
2	(20,22,32)	(2.8,3.1,4,1)	(3.6,4.3,5.07)	(1.6,2,3.1)	(0.64,0.72,0.86)
3	(35,42,52)	(4.4,5,6.1)	(5.2,6.5,8.16)	(4.2,5,7.2)	(0.43,0.51,0.61)
4	(20,26,31)	(1.5,2.1,3.1)	(2.6,3.3,4.07)	(3.2,4.1,5.1)	(0.63,0.7,0.81)
5	(35,40,46.5)	(4.3,5,6.1)	(4.12,5,6.1)	(3.4,4.1,5.1)	(0.65,0.7,0.81)
6	(55,60,66.25)	(6.8,7.5,9.2)	(7,8,10.2)	(6,7.2,8.09)	(0.39,0.45,0.56)
7	(32,36,41)	(2.6,3.8,5.1)	(4,2,5,6.1)	(3.3,3.6.4.04)	(0.43,0.51,0.61)
8	(28,30,36.25)	(2.64,3.1,4.1)	(2.8,3.2,4.09)	(2.78,3.8,5.1)	(0.61,0.69,0.87)
9	(32,36,41)	(2.9.3.5,4.05)	(2.6,3.2,5.2)	(3.1,3.7,4.03)	(0.58,0.64,0.76)
10	(30,37,47)	(2.6,3.8,5.1)	(2.54,3.2,5.2)	(3.2,3.7,5.14)	(0.54,0.62,0.71)

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Table 4. Basic data of projects

Project	1	2	3	4	5	6	7	8	9	10
$ {{v}_{i}} $	60	30	50	30	45	65	40	35	40	45
$ r_{i}^{1} $	7	4	6	3	6	9	5	4	4	5
$ r_{i}^{2} $	8	5	8	4	6	10	6	4	5	4
$ r_{i}^{3} $	8	3	7	5	5	8	4	5	4	5
$ {{p}_{i}} $	0.5	0.85	0.6	0.8	0.8	0.55	0.6	0.85	0.75	0.7
$ {{s}_{i}} $	4.41	3.52	4.31	3.63	4.13	4.56	3.09	3.74	3.97	3.32

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Table 5. Strategic fuzzy data

Project	$ {{B}_{1}} $	$ {{B}_{2}} $	$ {{B}_{3}} $	$ S $
1	(4.3, 4.5, 4.7)	(4.5, 4.7, 4.9)	(4.55, 4.75, 4.95)	(4.4, 4.6, 4.8)
2	(3.4, 3.8, 4.3)	(3.6, 3.9, 4.7)	(3.65, 4.24, 4.8)	(3.5, 3.9, 4.5)
3	(4.1, 4.75, 4.94)	(4.4, 4.85, 4.96)	(4.6625, 4.875, 4.965)	(4.28, 4, 8, 4.95)
4	(3.4, 3.7, 4.3)	(3.7, 4.3, 4.7)	(4.15, 4.45, 4.8)	(3.61, 4, 4, 5)
5	(4.1, 4.45, 4.89)	(4.2, 4.6, 4.92)	(4, 4.5, 4.9)	(4.11, 4.5, 4.9)
6	(4.5, 4.88, 5)	(4, 6, 4.92, 5)	(4.56, 4.93, 5)	(4.54, 4.9, 5)
7	(2.8, 3, 3.4)	(3.2, 3.4, 3.8)	(3.8, 4.125, 4.65)	(3.08, 3.3, 3.72)
8	(3.5, 3.8, 4.4)	(3.7, 4.4, 4.8)	(4.375, 4.55, 4.9)	(3.7, 4.1, 4.6)
9	(4, 4.45, 4.6)	(3.8, 4.55, 4.8)	(4, 4.7, 4.85)	(3.94, 4.52, 4.7)
10	(3.2, 3.4, 3.8)	(3.5, 3.8, 4.4)	(3.325, 3.65, 4.55)	(3.31, 3.56, 4.1)
target	(4, 4.2, 4.5)	(4.2, 4.4, 4.6)	(3.625, 3,825, 4.3125)	(4, 4.2, 4.5)

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Table 6. Strategic contribution distance and its effect

Project	Distance	$ 1+{{d}_{(\widetilde{I}, \widetilde{G})}} $	Effect
1	0.3707	1.3707	lead
2	-0.3083	0.6917	lag
3	0.4765	1.4765	lead
4	-0.2501	0.7499	lag
5	0.3027	1.3027	lead
6	0.587	1.587	lead
7	-0.8672	0.1328	lag
8	-0.1708	0.8292	lag
9	0.1309	1.1309	lead
10	-0.4433	0.5567	lag

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Table 7. Result of benefit synergy

Results	Benefit synergy relationship
Results	1, 2	1, 6	2, 4	3, 9	6, 8	1, 2, 5	1,6, 7	1, 6, 7, 9	1,6, 7, 9, 10	4, 5, 8
	15	10	8	11	12	18	16	4	3	13

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Table 8. Result of resource synergy

Result	Resource synergy relationship
$ r^1 $	1, 4	2,6	4, 8	5, 6	1, 2, 9	4, 6, 7	4, 6, 7, 9	4, 6, 7, 9, 10
$ r^1 $	1	2	1	1	2	2	1	1.5
$ r^2 $	2, 3	3, 5	3, 6	6, 10	1, 2, 5	1, 2, 4, 5	3, 4, 7 ,8
$ r^2 $	2	2	2	3	1	2	2.5
$ r^3 $	3, 5	3, 10	6, 7	3, 7, 8	5, 7, 10
$ r^3 $	1	2	2	2.5	2

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Table 9. Result of strategic synergy

	Strategic synergy relationship
Result	2, 1	6, 1	9, 3	4, 10	5, 6	1, 2, 5
	0.1	0.15	0.2	0.1	0.25	0.05

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Table 10. Result of technology synergy

	Technology synergy relationship
Result	1, 2	2, 8	8, 2	8, 9	6, 8	6, 2	5, 9	1, 2, 8	1, 2, 8, 9
	0.1	0.1	0.05	0.05	0.1	0.2	0.14	0.036	0.0162

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Table 11. Results of selected project portfolio

Selected portfolio	Selected project	Benefit	Resource consumption			Probability of success	Strategic unity
Selected portfolio	Selected project	Benefit	$ r^1 $	$ r^2 $	$ r^3 $	Probability of success	Strategic unity
1100110110	1, 2, 5, 6, 8, 9	232.03	29	32	30	5.09	24.86

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Table 12. Selected project portfolio results

Type of Synergy	Selected portfolio	Selected project	Benefit	Resource consumption			Probability of success	Strategic unity
Type of Synergy	Selected portfolio	Selected project	Benefit	$ r^1 $	$ r^2 $	$ r^3 $	Probability of success	Strategic unity
Non-project synergy [12,5]	0011101011	3, 4, 5, 7, 9, 10	173.25	28	31	31	4.5	17.62
Non-multi-project synergy [10,25]	0110110110	2, 3, 5, 6, 8, 9	217.18	30	32	31	5.04	24.08
Multi-project synergy (this paper)	1100110110	1, 2, 5, 6, 8, 9	232.03	29	32	30	5.09	24.86

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