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Project Portfolio Selection Considering Uncertainty: Stochastic Dominance-Based Fuzzy Ranking

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Abstract

This paper proposes a method for project selection based on stochastic dominance (SD) and fuzzy theory. Using fuzzy theory and stochastic dominance, the method is tested using data from real-world projects. The findings show the importance of the proposed methodology improved existing methods in two ways: (1) This research alleviates the subjective bias in risk assessment in estimating the expected value hidden in the project portfolio (2) Adding the stochastic dominance rule to the fuzzy ranking process contributes to efficiency in project portfolio selection. The study contributes to the literature by exploring the combination of both fuzzy theory and stochastic dominance. For practitioner significance, managers can identify key uncertainty factors and estimate value in managing project portfolios.

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Authors and Affiliations

  1. Department of Statistics, Feng Chia University, 100, Wenhwa Rd, Seatwen, Taichung, 40724, Taiwan, ROC

    Liang-Hong Wu

  2. Institute of Technology Management, National Chung Hsing University, 250, Kuo Kuang Rd, Taichung, 402, Taiwan, ROC

    Liangchuan Wu

  3. Department of Business Economics, Tokyo University of Science, 1-11-2 Fujimi, Chiyoda-ku, Tokyo, 102-0071, Japan

    Jianming Shi

  4. Corporate Banking, Far Eastern International Bank, 207, Sect. 2, Tunhua South Road, Taipei, 106, Taiwan, ROC

    Yang-Tai Chou

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Appendix

Appendix

1.1 Illustrative Real-World Case. Staff Authorization System (Project Code C2015-11)

Under the work breakdown structure (WBS), a project consists of five major activities and 13 sub-activities, as shown in Table 13. Using the connections between activities in the Gantt chart, the relationships are shown clearly (Fig. 6). The baseline schedule is used to modify and execute the project on time.

Table 13 Baseline schedule
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Fig. 6
figure 6

Source OR-AS Database: Staff Authorization System Data (C2015-11)

Gantt chart of the baseline schedule.

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Because activities may not complete in a pre-defined duration, the uncertainty should be given as a fuzzy characteristic. Generally, managers define activities using different uncertainties in three scenarios: optimistic, most probable, and pessimistic. For convenience of analysis, this paper defines a symmetric triangular fuzzy number for each activity with uncertainty, as shown in Fig. 7.

Fig. 7
figure 7

Source OR-AS Database: Staff Authorization System Data (C2015-11)

Schedule risk analysis specification.

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After constructing the baseline schedule and estimating the uncertainty in the activity durations, manager performs the schedule risk analysis (SRA). The SRA analysis is based on the CPM, which calculates the longest path of the planned activities. The importance of CPM is that it identifies the critical activities in the project. If the activity is marked critical, its total float should be zero and it should not delay the termination of the project (Table 14). Finally, after 1000 Monte Carlo simulation runs, the average number of the critical indicator is about 30.3%. This metric helps managers to quantify the schedule risk (endogenous risk) and is useful in defining the fuzzy number of the expected value.

Table 14 Calculation in CI
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Wu, LH., Wu, L., Shi, J. et al. Project Portfolio Selection Considering Uncertainty: Stochastic Dominance-Based Fuzzy Ranking. Int. J. Fuzzy Syst. 23, 2048–2066 (2021). https://doi.org/10.1007/s40815-021-01069-y

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