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Showing 2 results for Mathematical Modeling
Forouzesh Ghambari, Mahdi Ahangari,
Volume 17, Issue 2 (9-2026)
Abstract
Cooperative game theory is an important tool for analyzing cooperation and benefit allocation among coalition members, but classical models usually do not consider the existence of a minimum capacity required for cooperation to be activated. In this study, “threshold coalition games” are introduced, in which the formation of an effective coalition requires crossing a certain threshold of collective capacity. Also, a coalition activation index and a new rule called “threshold allocation value” are presented to determine the players’ shares, and their properties, including efficiency, symmetry, and uniqueness, are proven. Finally, a numerical example shows that the proposed model can model threshold-based cooperation structures coherently and provides a suitable framework for future research in cooperative game theory.
Maedeh Alinasab, Mohammad Fallah, Iraj Mahdavi, Ghasem Tohidi,
Volume 17, Issue 2 (9-2026)
Abstract
This study develops a multi-objective mathematical model for planning and optimizing patrol operations in surveillance networks using an integrated truck–quadrotor system. The proposed model simultaneously considers five conflicting objectives: maximizing network coverage, minimizing operational costs, operational risks, mission duration and environmental emission. To balance these objectives, the LP-metric distance-to-ideal-point approach is employed to transform the multi-objective formulation into an equivalent single-objective model. Benders decomposition is subsequently applied to efficiently solve larger-scale instances and reduce computational complexity. The performance of the proposed approach is evaluated through numerical experiments and sensitivity analyses. Results show that network coverage reaches approximately 89% in the baseline scenario and increases to 96% under a coverage-oriented strategy. Meanwhile, total operational cost decreases from approximately 47800 to 39900 cost units under a cost-focused strategy, while operation time varies between 590 and 710 minutes across different scenarios. Sensitivity analysis indicates that a 20% increase in truck deployment cost reduces network coverage by 22% and increases operational cost by 10%, whereas a 30% increase in quadrotor energy consumption increases operation time by 18% and cost by 7%. The findings demonstrate that the proposed integrated framework provides an effective decision-support tool for patrol planning and resource allocation.
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