<p>In this study, a cold supply chain logistics model is developed for mixed-integer nonlinear programming with vaccine distribution in post-disaster scenarios. In this non-linear programming model, the transportation costs, capacity constraints, and time windows are formulated to optimize the mixed-integer non-linear programming. Moreover, the MATLAB simulations are addressed to optimize the non-linear programming. This work also addressed various issues related to defective locations, insecure road conditions, and restricted resources. The capacity constraint is used to solve the shortest path optimization, secure and quality area for storage, and reduce the delivery time (lead time) for vaccine distribution. Further, the case study was implemented to address the usages of constraints in non-linear programming for cold supply chain logistics. Also, the highlights and necessity of cold supply chain logistical optimization with controlling the vaccine temperature are presented to improve vaccine distribution in post-disaster situations. Cold supply chain transportation delivers fresh and perishable goods from production, processing, or warehouse to consumption under controlled temperature settings. As consumers demand improved food safety and quality, the cold chain logistics industry has grown significantly. The originality of this study is that it comprehensively explores cold storage technology for more rapid and comprehensive vaccine distribution, therefore it is expected to serve as a reference and inspiration for stakeholders. Further, the sensitivity analysis is employed to enhance the visibility of the proposed cold supply chain logistics in mixed integer programming with non-linear cases. This present study is mainly implemented to enhance simulation methodologies for reducing total costs, accurate delivery in vaccine distribution, and ensuring protective supplies in the cold supply chain logistics model.</p>