en Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR كاربردي Applicable <span style="font-size:11pt"><span style="line-height:normal"><span style="text-autospace:none"><span new="" roman="" style="font-family:" times=""><i><span style="font-size:10.0pt"><span style="letter-spacing:-.25pt">This study develops a multi-objective mathematical model for planning and optimizing patrol operations in surveillance networks using an integrated truck&ndash;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.</span></span></i></span></span></span></span><br> &nbsp; Keywords: Optimal patrol, mathematical modeling, quadrotor, truck, multi-objective optimization, operations planning. 99 116 http://iors.ir/journal/browse.php?a_code=A-10-6118-1&slc_lang=en&sid=1 Maedeh Alinasab maedehalinasab@gmail.com 00031947532846003225 00031947532846003225 Yes Department of Industrial Engineering.CT.C.Islamic Azad University, Teharan,Iran Mohammad Fallah mohammad.fallah43@yahoo.com 00031947532846003226 00031947532846003226 No Department of Industrial Engineering.CT.C.Islamic Azad University, Teharan,Iran Iraj Mahdavi irajustmb@gmail.com 00031947532846003227 00031947532846003227 No Department of Industrial Engineering,Mazandaran University of Science and Technology, babol, iran Ghasem Tohidi gh_tohidi@iauctb.ac.ir 00031947532846003228 00031947532846003228 No Department of Mathematics.CT.C.Islamic Azad University, Teharan,Iran,