Optimisation of Management of Multi-Component Transport Operations With Application in Modern Logistics Using a Flexible Mathematical Model for Cost Minimisation

The effective management of transport and logistics issues is a critical component of contemporary supply chain management. In the context of a globalised economy and increasing demands for speed and quality of service, the optimisation of transport processes is becoming a strategic priority for achieving economic sustainability and enhancing the competitiveness of enterprises. In view of this, the aim of this study is to develop an innovative mathematical model that will minimise the total costs of organising complex, multi-component transport operations. The proposed model framework is characterised by a high degree of realism, as it takes into account key practical constraints. These include the limited capacity of transport vehicles, the specific requirements for personnel qualifications and availability, and the detailed conditions for servicing final destinations. This approach offers flexibility and adaptability when modelling a variety of logistics scenarios, including those involving dynamic changes in consumer demand, resource availability, and infrastructure constraints. It is particularly well-suited to urban logistics and inter-platform delivery management, as well as other sectors requiring a high degree of coordination and precision in resource allocation. The mathematical formulation transforms the transport problem into an integer programming optimisation model. In this model, binary variables play a key role in representing discrete solutions for allocating tasks and resources. The model ensures compliance with operational, logistical and regulatory requirements by incorporating precisely defined constraints. Due to the problem's high combinatorial complexity, the solution is implemented using a combined approach that includes both exact (e.g., branch-and-bound) and heuristic (e.g., greedy algorithms and local search) optimisation methods. This hybrid methodological approach enables the discovery of solutions that are close to optimal within an acceptable computational time, which is critically important for real-world applications. The empirical part of the study comprises simulations and quantitative analyses demonstrating the model’s ability to efficiently allocate transport tasks while reducing costs. This is achieved by making balanced use of different types of transport vehicle, engaging qualified drivers optimally, and providing an adequate service to geographically diverse destinations. This work's scientific contribution is demonstrated through the creation of a compact, applicable optimisation framework that integrates multidimensional, practically significant constraints, and through the demonstration of its effectiveness and applicability in real scenarios. The main achievements of the study can be summarised as follows: development of a detailed optimisation model for multi-component transport processes; formulation of the problem as an integer model with multiple constraints; application of a hybrid approach combining exact and heuristic methods for finding solutions; demonstration of practical applicability through simulations and quantitative evaluation of the results. All models and calculations are implemented in the MATLAB programming environment, which offers the computing power and flexibility required for the real-time simulation and analysis of transport scenarios.