Development of vector models and methods for their solution for optimization of logistics problems in e-commerce

The object of research is the logistics processes of delivering goods in a digital environment (e-commerce), which require optimization using mathematical models. One of the most problematic areas is taking into account dynamic changes and unpredictable factors: seasonal and daily fluctuations in demand, delays in deliveries, fluctuations in delivery costs, changes in routes, etc. This necessitates the creation of adaptive mathematical models that can quickly respond to changing conditions and ensure high efficiency of logistics processes in real time. The study used a comprehensive approach that includes: mathematical modeling, linear programming methods (in particular, the potential method, the simplex method), the unloading cycle method, as well as multi-criteria analysis and decision-making methods. The experiments were performed using the MATLAB and Python computing environments based on both real and synthetic data that simulate e-commerce conditions. The main results of the study are as follows. First, it was established that classical scalar models of the transport problem (TP) are insufficient for describing multi-criteria logistics conditions in e-commerce, where it is important to simultaneously take into account several performance indicators. Second, the feasibility of using vector models that allow optimizing delivery processes according to several criteria – in particular, minimizing total costs, transportation time or loading time – was demonstrated. Such models reflect the real conditions and requirements of e-commerce much more accurately. Third, it was proven that the use of vector models allows achieving a balanced distribution of resources between competing criteria, which makes it possible to find compromise, but strategically more effective solutions at the moment. The possibility of using normalization methods, as well as methods of multi-criteria selection, was also demonstrated. As a result, two-criteria and three-criteria models of the transport problem were developed, implemented and tested, adapted to the conditions of digital logistics. It is shown that, taking into account the priorities of the criteria, these models provide a more flexible and adequate solution to optimization problems, compared to classical approaches.