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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 & Management Optimization, doi: 10.3934/jimo.2021177
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show all references

References:
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B. Alvarez-García and A. Fernández-Castro, A comprehensive approach for the selection of a portfolio of interdependent projects. An application to subsidized projects in Spain, Computers & Industrial Engineering, 118 (2018), 153-159.  doi: 10.1016/j.cie.2018.02.025.  Google Scholar

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M. AnissehF. Hemmati and R. Shahraki, Best selection of project portfolio using Fuzzy AHP and Fuzzy TOPSIS, J. Engineering Management and Competitiveness, 8 (2018), 3-10.   Google Scholar

[3]

C. AnyaecheD. Ighravwe and T. Asokeji, Project portfolio selection of banking services using COPRAS and Fuzzy-TOPSIS, J. Project Management, (2017), 51-65.  doi: 10.5267/j.jpm.2017.6.004.  Google Scholar

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N. P. Archer and F. Ghasemzadeh, An integrated framework for project portfolio selection, International J. Project Management, 17 (1999), 207-216.  doi: 10.1016/S0263-7863(98)00032-5.  Google Scholar

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M. Ashrafi, H. Davoudpour and M. Abbassi, Developing a decision support system for R&D project portfolio selection with interdependencies, In AIP Conference Proceedings, 1499 (2012), 370-378. doi: 10.1063/1.4769016.  Google Scholar

[6]

S. M. Avdoshin and A. A. Lifshits, Project portfolio formation based on fuzzy multi-objective model, Business Informatics, 27 (2014), 14-22.   Google Scholar

[7]

L. BaiH. ChenQ. Gao and W. Luo, Project portfolio selection based on synergy degree of composite system, Soft Computing, 22 (2018), 5535-5545.  doi: 10.1007/s00500-018-3277-8.  Google Scholar

[8]

R. BhattacharyyaP. Kumar and S. Kar, Fuzzy R&D portfolio selection of interdependent projects, Comput. Math. Appl., 62 (2011), 3857-3870.  doi: 10.1016/j.camwa.2011.09.036.  Google Scholar

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[10]

A. F. Carazo, Multi-criteria project portfolio selection, Handbook on Project Management and Scheduling, 2 (2015), 709-728.  doi: 10.1007/978-3-319-05915-0_3.  Google Scholar

[11]

W. ChenD. Li and Y.-J. Liu, a novel hybrid ICA-FA algorithm for multiperiod uncertain portfolio optimization model based on multiple criteria, IEEE Transactions on Fuzzy Systems, 27 (2019), 1023-1036.  doi: 10.1109/TFUZZ.2018.2829463.  Google Scholar

[12]

W. ChenS.-S. LiJ. Zhang and M. K. Mehlawat, A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model, Soft Computing, 24 (2020), 2515-2526.  doi: 10.1007/s00500-018-3595-x.  Google Scholar

[13]

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[14]

C. G. da SilvaJ. MeidanisA. V. MouraM. A. SouzaP. ViadannaM. R. de OliveiraM. R. de OliveiraL. H. JardimG. A. C. Lima and R. S. de Barros, An improved visualization-based approach for project portfolio selection, Computers in Human Behavior, 73 (2017), 685-696.  doi: 10.1016/j.chb.2016.12.083.  Google Scholar

[15]

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[17]

K. F. DoernerW. J. GutjahrR. F. HartlC. Strauss and C. Stummer, Pareto ant colony optimization with ILP preprocessing in multiobjective project portfolio selection, European J. Oper. Res., 171 (2006), 830-841.  doi: 10.1016/j.ejor.2004.09.009.  Google Scholar

[18]

A. M. DaryaniM. M. OmranA. MakuiE. Zavadskas and J. Antucheviciene, A novel heuristic, based on a new robustness concept, for multi-objective project portfolio optimization, Computers & Industrial Engineering, 139 (2020).   Google Scholar

[19]

M. O. EsangbedoS. BaiS. Mirjalili and Z. Wang, Evaluation of human resource information systems using grey ordinal pairwise comparison MCDM methods, Expert Systems with Applications, 182 (2021).  doi: 10.1016/j.eswa.2021.115151.  Google Scholar

[20]

T. Fliedner and J. Liesiö, Adjustable robustness for multi-attribute project portfolio selection, European J. Oper. Res., 252 (2016), 931-946.  doi: 10.1016/j.ejor.2016.01.058.  Google Scholar

[21]

S. F. GhannadpourA. R. HoseiniM. Bagherpour and E. Ahmadi, Appraising the triple bottom line utility of sustainable project portfolio selection using a novel multi-criteria house of portfolio, Environment, Development and Sustainability, 23 (2021), 3396-3437.  doi: 10.1007/s10668-020-00724-y.  Google Scholar

[22]

R. GhasemiyehR. Moghdani and S. S. Sana, A hybrid artificial neural network with metaheuristic algorithms for predicting stock price, Cybernetics and Systems, 48 (2017), 365-392.  doi: 10.1080/01969722.2017.1285162.  Google Scholar

[23]

X.-Y. Gu, R & D project dynamic investment decision-making model based on real option, Chinese Journal of Management Science, 23 (2015), 94-102.  doi: 10.16381/j.cnki.issn1003-207x.2015.07.012.  Google Scholar

[24]

P. GuoJ. J. LiangY. M. Zhu and J. F. Hu, R&D project portfolio selection model analysis within project interdependencies context, 2008 IEEE International Conference on Industrial Engineering and Engineering Management, (2008), 994-998.  doi: 10.1109/IEEM.2008.4738019.  Google Scholar

[25]

Y. GuoL. WangS. LiZ. Chen and Y. Cheng, Balancing strategic contributions and financial returns: A project portfolio selection model under uncertainty, Soft Computing, 22 (2018), 5547-5559.  doi: 10.1007/s00500-018-3294-7.  Google Scholar

[26]

N. G. HallD. Z. LongJ. Qi and M. Sim, Managing underperformance risk in project portfolio selection, Oper. Res., 63 (2015), 660-675.  doi: 10.1287/opre.2015.1382.  Google Scholar

[27]

X. Huang and T. Zhao, Project selection and scheduling with uncertain net income and investment cost, Appl. Math. Compu., 247 (2014), 61-71.  doi: 10.1016/j.amc.2014.08.082.  Google Scholar

[28]

V. KalashnikovF. BenitaF. López-Ramos and A. Hernández-Luna, Bi-objective project portfolio selection in lean six sigma, International J. Production Economics, 186 (2017), 81-88.  doi: 10.1016/j.ijpe.2017.01.015.  Google Scholar

[29]

G. KaraA. Özmen and G.-W. Weber, Stability advances in robust portfolio optimization under parallelepiped uncertainty, Central European J. Oper. Research, 27 (2019), 241-261.  doi: 10.1007/s10100-017-0508-5.  Google Scholar

[30]

E. C. Y. KohN. H. M. Caldwell and P. J. Clarkson, A method to assess the effects of engineering change propagation, Research in Engineering Design, 23 (2012), 329-351.  doi: 10.1007/s00163-012-0131-3.  Google Scholar

[31]

X.-m. LIH.-j. WeiX.-l. Gou and J.-x. Qi, Study of Bi-objective project portfolio selection model based on the divisibility, Chinese J. Management Science, (2014), 154-157.  doi: 10.16381/j.cnki.issn1003-207x.2014.s1.047.  Google Scholar

[32]

X. LiY. WangQ. Yan and X. Zhao, Uncertain mean-variance model for dynamic project portfolio selection problem with divisibility, Fuzzy Optim. Decis. Mak., 18 (2019), 37-56.  doi: 10.1007/s10700-018-9283-6.  Google Scholar

[33]

D. Lozovanu and S. Pickl, Algorithms for solving multiobjective discrete control problems and dynamic c-games on networks, Discrete Appl. Math., 155 (2007), 1846-1857.  doi: 10.1016/j.dam.2007.03.012.  Google Scholar

[34]

V. MohagheghiS. M. MousaviB. Vahdani and M. R. Shahriari, R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach, Neural Compu. Appl., 28 (2017), 3869-3888.  doi: 10.1007/s00521-016-2262-3.  Google Scholar

[35]

V. MohagheghiS. M. Mousavi and M. Mojtahedi, Project portfolio selection problems: Two decades review from 1999 to 2019, J. Intelligent & Fuzzy Systems, 38 (2020), 1675-1689.  doi: 10.3233/JIFS-182847.  Google Scholar

[36]

A. MoheimaniR. SheikhS. M. H. Hosseini and S. S. Sana, Assessing the preparedness of hospitals facing disasters using the rough set theory: Guidelines for more preparedness to cope with the COVID-19, Inter. J. Systems Science: Operations & Logistics, (2021), 1-16.  doi: 10.1080/23302674.2021.1904301.  Google Scholar

[37]

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Figure 1.  Relationships between four synergy types
Figure 2.  Relationships between four synergy types (type II)
Figure 3.  Benefit synergy; lower triangular matrix
Figure 4.  Technology diffusion relationships
Figure 5.  Three strategic contribution solution scenarios
Figure 6.  Technology diffusion relationship
Table 1.  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
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)
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)
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)
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)
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
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
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)
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)
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
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
Table 7.  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
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
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
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
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
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
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
Table 11.  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
Table 12.  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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