Time-dependent integrated production and outbound distribution scheduling with multiple cold chain products considering carbon emissions

Sustainable urban development urgently requires the implementation of advanced low-carbon transportation strategies, with emissions from cold chain product transportation being particularly significant. Cold chain products are essential to modern society, their perishable nature greatly increases the complexity of production and distribution planning. Enterprises typically organize production around order-defined delivery dates to ensure product freshness and customer satisfaction, distributing products immediately to minimize value loss and energy waste. These challenges are further amplified under time-varying operational conditions. To address this issue, we propose a three-objective mathematical optimisation model for low-carbon operations that maximize product freshness and customer satisfaction while minimizing costs. This model integrates various factors such as employee time-varying processing efficiency during the production stage, the time-varying vehicle speed during the distribution stage, and the influence of dynamic speed and load on carbon emissions. Given the NP-hard nature of the proposed model, a hybrid algorithm based on variable neighbourhood search (VNS) and non-dominated sorting genetic algorithm-III (NSGA-III) is designed to solve it. Numerical experiments and analyses demonstrate that the proposed model and algorithm substantially improve scheduling efficiency and reduce carbon emissions. The research results not only deepen and extend the theory of integrated production and outbound distribution scheduling under time-varying condition but also provide a scientific and reasonable approach for guiding cold chain enterprises toward net-zero emissions and promoting the sustainable development of production–delivery systems.