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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

Received  June 2021 Revised  August 2021 Early access October 2021

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.

Citation: Zonghan Wang, Moses Olabhele Esangbedo, Sijun Bai. Project portfolio selection based on multi-project synergy. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021177
##### References:

show all references

##### References:
Relationships between four synergy types
Relationships between four synergy types (type II)
Benefit synergy; lower triangular matrix
Technology diffusion relationships
Three strategic contribution solution scenarios
Technology diffusion relationship
Research Trends on Synergy in Project Portfolio
 Related Works Aspects Type of Synergy Strategic Utility Goals Uncertainty Benefit/ Resource/ Technology Strategy Two Projects Multiple projects [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 √ √ √ √ √ √
 Related Works Aspects Type of Synergy Strategic Utility Goals Uncertainty Benefit/ Resource/ Technology Strategy Two Projects Multiple projects [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 √ √ √ √ √ √
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)
 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)
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)
 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)
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
 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
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)
 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)
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
 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
Result of benefit synergy
 Results Benefit synergy relationship 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
 Results Benefit synergy relationship 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
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 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 2 2 2 3 1 2 2.5 $r^3$ 3, 5 3, 10 6, 7 3, 7, 8 5, 7, 10 1 2 2 2.5 2
 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 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 2 2 2 3 1 2 2.5 $r^3$ 3, 5 3, 10 6, 7 3, 7, 8 5, 7, 10 1 2 2 2.5 2
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
 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
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
 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
Results of selected project portfolio
 Selected portfolio Selected project Benefit Resource consumption Probability of success Strategic unity $r^1$ $r^2$ $r^3$ 1100110110 1, 2, 5, 6, 8, 9 232.03 29 32 30 5.09 24.86
 Selected portfolio Selected project Benefit Resource consumption Probability of success Strategic unity $r^1$ $r^2$ $r^3$ 1100110110 1, 2, 5, 6, 8, 9 232.03 29 32 30 5.09 24.86
Selected project portfolio results
 Type of Synergy Selected portfolio Selected project Benefit Resource consumption Probability of success Strategic unity $r^1$ $r^2$ $r^3$ 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
 Type of Synergy Selected portfolio Selected project Benefit Resource consumption Probability of success Strategic unity $r^1$ $r^2$ $r^3$ 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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