The thesis studies the application of cooperative game theory and network flow optimization to Public Bicycle Sharing Systems (PBSS). The work combines several theoretical areas, including linear programming, network flow models, and cooperative game theory, to evaluate the contributions of individual stations in a bicycle-sharing network using concepts such as the Shapley value and the nucleolus.

The theoretical part of the thesis provides an overview of the relevant mathematical concepts, including linear programming, time–space networks, and cooperative game solution concepts. The student demonstrates a basic understanding of these topics and presents the necessary definitions and background. However, the overall structure of the thesis would benefit from a clearer logical flow. The theoretical sections are relatively extensive but are not always sufficiently connected to the subsequent modelling and application parts. As a result, the transition from the general theoretical framework to the specific PBSS model is sometimes not fully articulated, and the thesis's overall narrative could be more cohesive.

The practical part of the thesis implements a computational framework using Python and Pyomo to simulate cooperative interactions between stations in a PBSS network. The implementation demonstrates effort and basic technical competence in the use of optimization models and numerical experimentation.

A methodological limitation arises in the estimation of the Shapley value. In the larger scenario with 30 stations, the Shapley value is estimated using only ten random permutations. Given the extremely large number of permutations in such games, a small sample cannot provide a reliable estimate, limiting the interpretability and robustness of the reported results. In addition, the thesis presents the resulting Shapley allocations mainly in numerical form but provides only limited discussion of the structural properties of the underlying network that might influence these values. A deeper analysis of how specific network characteristics—such as connectivity patterns, station positioning, or flow structure—affect the resulting contributions of individual stations would have strengthened the interpretation of the results.

From a scientific perspective, the thesis primarily summarizes existing theoretical concepts and demonstrates their application in a simplified simulated setting. The independent research component is therefore somewhat limited, and several modelling aspects and conceptual formulations were developed with substantial guidance from the supervisor.

Despite these limitations, the student demonstrates familiarity with the studied mathematical concepts and the ability to implement optimization models and computational experiments. Overall, the thesis meets the basic requirements for a master’s thesis, although several conceptual and methodological aspects could be further developed.

Proposed final grade: C

The submitted master's thesis addresses the optimization and fair evaluation of Public Bicycle Sharing Systems (PBSS) using Time-Space Networks and cooperative game theory. The author formulates the PBSS optimization as a maximum flow problem and utilizes the Shapley value and the Nucleolus to assess the marginal contributions of individual stations.

While the mathematical formulation and the general methodology are logically structured, the thesis lacks sufficient depth in its analytical part. The experimental evaluation is somewhat limited and superficial. The author evaluates the framework on synthetic scenarios involving 10 and 30 stations. However, to truly demonstrate the robustness and practical applicability of the proposed model, the study should have explored multiple diverse scenarios and applied the framework to a more realistic, large-scale network size typical for actual urban environments. Furthermore, the evaluation of the 30-station scenario relies on a Monte Carlo approximation using only m=10 permutations. This extremely small sample size raises concerns about the statistical reliability of the resulting Shapley values and limits the depth of the subsequent interpretation.

Additionally, the document contains occasional formatting issues and typographic inconsistencies that detract from the overall professional presentation of the text. For example, the inclusion of unformatted code snippets disrupts the academic flow. The main text would benefit from replacing raw source code with clear pseudocode to outline the methodology, reserving the actual implementation for the appendices or supplementary attachments. Despite these shortcomings, the author has demonstrated a solid understanding of operations research and game theory concepts. The work provides a functional foundational framework, but it would greatly benefit from a more rigorous experimental design and a deeper, more comprehensive evaluation of the results. Taking these factors into consideration, I recommend the thesis for defence with an overall grade of C. Topics for thesis defence:

1. There is a potential issue where the system might intentionally hoard bicycles to benefit their circulation later, rather than satisfying immediate demand. How could you prevent this behaviour in your model (for instance, by introducing constraints that prioritize immediate demand satisfaction)?
2. The current Time-Space Network model utilizes deterministic capacities. How would the introduction of stochastic or highly fluctuating user demands alter the cooperative game formulation and the stability of the grand coalition?
3. You used m=10 permutations to estimate the Shapley value for the 30-station network. How adequate is this sample size, and how could you establish some statistical guarantees or confidence intervals for the resulting approximation?
4. Since the exact computation of the Nucleolus for 30 stations is computationally infeasible, are there any heuristic approaches, relaxations, or alternative stability concepts you would suggest for large-scale networks?