Vaihtoehtoinen kokonaisluku optimointiongelman muotoilu vyöhykkeisiin perustuvalle hinnoittelusuunnittelulle

This thesis focuses on the optimization problem of zone-based tariff design in public transportation networks, as originally formulated by Otto and Boysen. The original model (ZTDP) integrates both the determination of zone structures and the assignment of tariffs into a single integer programming formulation. This approach suffers from scalability issues: the number of feasible zone configurations grows exponentially with the size of the transport network, making real-world instances practically unsolvable within reasonable time limits. In this work, the original ZTDP model is modified to improve its computational efficiency. The key modification lies in decoupling the zone formation process from the optimization problem by introducing a predefined pool of feasible zone candidates. This restricted zone-pool is provided as input to the model, allowing the solver to focus solely on selecting the best combination of these zones and setting appropriate tariffs. This change transforms the original formulation into a more scalable solution, suitable for larger problem instances. The performance and behavior of the modified model are evaluated using numerical experiments with Gurobi, a mixed-integer programming solver, in the LinTimenvironment. Multiple zone-pools of varying sizes and levels of structural restriction are tested to assess the impact on both solving times and objective value. The results show that the restricted model significantly reduces solving times without notable losses in solution quality. When the zone-pool is limited to connected subgraphs of a given size range, solving time decreases significantly for moderate zone budgets. Additionally, the model demonstrates stable behavior across different customer population sizes, while retaining revenue outcomes compared to the original approach. The simplified zone selection strategy thus enables practical application of the ZTDP concept to more realistic transport networks. In conclusion, the proposed reformulation offers a scalable and computationally efficient alternative to the original ZTDP model, without compromising key economic objectives. Future work may focus on heuristic zone-pool generation and integration of further pricing schemes.