A Stochastic Knapsack Model for Sustainable Safety Resource Allocation Under Interdependent Safety Measures

Gökhan Özkan (), Burak Birgören and Ümit Sami Sakallı
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Gökhan Özkan: Industrial Engineering Department, Engineering Faculty, Kırıkkale University, Yahsihan Campus, Kırıkkale 71450, Türkiye
Burak Birgören: Industrial Engineering Department, TOBB ETU University of Economics and Technology, Ankara 06510, Türkiye
Ümit Sami Sakallı: Industrial Engineering Department, Engineering Faculty, Kırıkkale University, Yahsihan Campus, Kırıkkale 71450, Türkiye

Sustainability, 2025, vol. 17, issue 12, 1-23

Abstract: The optimum choice of safety measures (SMs) within constraints is necessary for effective risk management in occupational health and safety (OHS). The stochastic nature of safety interventions is frequently overlooked by traditional approaches such as deterministic models and risk matrices. This study presents a novel stochastic knapsack model that maximizes the overall expected benefit during a risk assessment period considering budgetary constraints and the interdependencies between risks and safety measures. Two models are developed as follows: a one-to-one relationship model assuming independent risks and a multiple-relationship model accounting for interdependent safety measures. The suggested model’s real-world implementation is illustrated through a case study in the retail industry. The results demonstrate the model’s ability to efficiently prioritize SMs, showing an 18% reduction in objective function value and an average risk reduction of 29.5 per monetary unit invested, compared to 26.2 for the deterministic model. A more realistic and flexible framework for safety investment planning is offered by the analysis, which emphasizes the benefits of including stochastic components and interdependencies in decision-making. By addressing the significant drawbacks of deterministic models and providing a flexible, data-driven framework for safety optimization, this study adds to the body of literature. The suggested model is in line with the United Nations Sustainable Development Goals (SDGs), specifically SDGs 3, 8, 9, and 12. Its adaptability contributes to achieving SDG 13, emphasizing possible uses in risk management for climate change. This study shows how decision-making that is structured and aware of uncertainty can support safer, more sustainable industrial processes.

Keywords: stochastic programming; knapsack model; risk matrix; expert judgment; occupational health and safety; sustainable development; risk-informed decision-making; resilient infrastructure (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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