en زنجیره تامین و لجستیک Logistic & Apply Chain پژوهشي Research <div style="text-align: justify;"><span style="font-size:11pt"><span new="" roman="" style="font-family:" times=""><a name="_Hlk165224034"></a></span><span new="" roman="" style="font-family:" times=""><span style="font-size:11.5pt">The increasing demand for food delivery services driven by technological innovations has led to a surge in online shopping and food ordering. Efficient logistics play a crucial role in connecting customers with restaurants seamlessly. In this context, the practical application of graphical networks is explored in this article to streamline food delivery operations. We introduce a novel parameter eternal m-certified domination number denoted by </span><m:omath><m:ssubsup><m:ssubsuppr><span style="font-size:11.5pt"><span cambria="" math="" style="font-family:"><span style="font-style:italic"><m:ctrlpr></m:ctrlpr></span></span></span></m:ssubsuppr><m:e><span style="font-size:11.5pt"><span cambria="" math="" style="font-family:"><m:r>&gamma;</m:r></span></span></m:e><m:sub><span style="font-size:11.5pt"><span cambria="" math="" style="font-family:"><m:r>mcer</m:r></span></span></m:sub><m:sup><span style="font-size:11.5pt"><span cambria="" math="" style="font-family:"><m:r>&infin;</m:r></span></span></m:sup></m:ssubsup><span style="font-size:11.5pt"><span cambria="" math="" style="font-family:"><m:r>(</m:r><m:r>G</m:r><m:r>)</m:r></span></span></m:omath><span style="font-size:11.0pt"><span new="" roman="" style="font-family:" times=""><span style="position:relative"><span style="top:2.5pt"> </span></span></span></span><span style="font-size:11.5pt">, which represents the minimum number of guards needed to handle any sequence of single orders using multiple-guard movements, ensures that the guard arrangement consistently constitutes a certified dominating set. A case study is presented, illustrating how this concept can be employed to de-crease human resources in a food delivery start-up. This research contributes to optimizing food delivery logistics and reducing operational costs, thereby enhancing the efficiency of the food delivery industry.</span></span></span></div> Domination number, Eternal m-domination number, Certified domination number, Online food delivery, Business logistics 33 43 http://ijiepr.iust.ac.ir/browse.php?a_code=A-10-2023-2&slc_lang=en&sid=1 Mary Jiny D maryjinymaths@gmail.com 1800319475328460012022 1800319475328460012022 No Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai-602105, Tamilnadu, India G Navamani g_navamani@yahoo.co.in 1800319475328460012023 1800319475328460012023 No Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai-602105, Tamilnadu, India Raman Kumar sehgal91@yahoo.co.in 1800319475328460012024 1800319475328460012024 No Department of Mechanical and Production Engineering, Guru Nanak Dev Engineering College, Ludhiana, Punjab, 141006, India Željko Stević zeljkostevic88@yahoo.com 1800319475328460012025 1800319475328460012025 Yes University of East Sarajevo, Faculty of Transport and Traffic Engineering, Vojvode Mišića 52, 74000 Doboj, Bosnia and HerzegovinaSchool of Industrial Management Engineering, Korea University, 145 Anam-Ro, Seongbuk-Gu, Seoul 02841, Korea, Darjan Karabašević darjan.karabasevic@mef.edu.rs 1800319475328460012026 1800319475328460012026 No Faculty of Applied Management, Economics and Finance, University Businesses Academy in Novi Sad, 11000 Belgrade, Serbia Rajender Kumar rajender.set@mriu.edu.in 1800319475328460012027 1800319475328460012027 No School of Engineering and Technology, Manav Rachna International Institute of Research and Studies, Faridabad, India & Chitkara Center for Research and Development, Chitkara University, Pinjore, Himachal Pradesh-174103 India