Multi-objective project portfolio scheduling with multi-skilled and inter-project dependency based on NSGA-Ⅱ: Case study

Heng Zhang; Yanfei Ma; Yixuan Qin; Heng Zhang; Yanfei Ma; Yixuan Qin

doi:10.3934/jimo.2026054

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 3: 1464-1490. doi: 10.3934/jimo.2026054

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Case report Special Issues

Multi-objective project portfolio scheduling with multi-skilled and inter-project dependency based on NSGA-Ⅱ: Case study

School of Mechanical Engineering, Guizhou University, Guiyang 550025, China

Received: 03 November 2025 Revised: 28 January 2026 Accepted: 10 February 2026 Published: 27 February 2026
90B50, 68U35

This study addresses the complex resource-constrained scheduling problem for software project portfolios, where baseline and customized projects with inter-dependencies are developed in parallel. We formulated a nonlinear integer programming model that simultaneously minimizes total duration, optimizes software quality, and balances engineer workload, explicitly incorporating multi-skilled human resources and cross-project dependencies. To solve this problem, we developed an improved Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) algorithm featuring localized coding, heuristic population initialization, and Pareto-based local search. A real-world case study from an AI-powered voice technology enterprise demonstrates the method's efficacy: the final population significantly outperforms the initial one, and our algorithm surpasses classic NSGA-Ⅱ, Ant Lion Optimization (ALO), and Simulated Annealing (SA) in convergence and diversity. Crucially, our approach achieves remarkable improvements—reducing duration by 16%, enhancing quality by 21.6%, and improving workload balance by 94.4% compared to skill-homogenized scenarios. Similarly, inter-project dependency-aware scheduling improves duration, quality, and workload balance by 5.2%, 3.9%, and 53.9%, respectively, compared to inter-project dependency-unaware scenarios. Managers can utilize the decoded Pareto optimal solutions to formulate detailed allocation plans, thereby achieving contextually optimized resource management.
- project portfolio scheduling,
- multi-skilled,
- inter-project dependency,
- NSGA-Ⅱ,
- multi-objective optimization
Citation: Heng Zhang, Yanfei Ma, Yixuan Qin. Multi-objective project portfolio scheduling with multi-skilled and inter-project dependency based on NSGA-Ⅱ: Case study[J]. Journal of Industrial and Management Optimization, 2026, 22(3): 1464-1490. doi: 10.3934/jimo.2026054

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Abstract

This study addresses the complex resource-constrained scheduling problem for software project portfolios, where baseline and customized projects with inter-dependencies are developed in parallel. We formulated a nonlinear integer programming model that simultaneously minimizes total duration, optimizes software quality, and balances engineer workload, explicitly incorporating multi-skilled human resources and cross-project dependencies. To solve this problem, we developed an improved Non-dominated Sorting Genetic Algorithm Ⅱ (NSGA-Ⅱ) algorithm featuring localized coding, heuristic population initialization, and Pareto-based local search. A real-world case study from an AI-powered voice technology enterprise demonstrates the method's efficacy: the final population significantly outperforms the initial one, and our algorithm surpasses classic NSGA-Ⅱ, Ant Lion Optimization (ALO), and Simulated Annealing (SA) in convergence and diversity. Crucially, our approach achieves remarkable improvements—reducing duration by 16%, enhancing quality by 21.6%, and improving workload balance by 94.4% compared to skill-homogenized scenarios. Similarly, inter-project dependency-aware scheduling improves duration, quality, and workload balance by 5.2%, 3.9%, and 53.9%, respectively, compared to inter-project dependency-unaware scenarios. Managers can utilize the decoded Pareto optimal solutions to formulate detailed allocation plans, thereby achieving contextually optimized resource management.

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