The Problem of Constructing Specialized Routes: a Case Study of the Vienna – Venice "Wine Route"

"Wine routes" serve as one of the strategic mechanisms for shaping and strengthening regional reputation, acting as a form of collective action to promote both products and territories. Therefore, the problem of constructing optimal specialized routes for both tourists and travel agencies is highly relevant and serves as an illustrative application of optimization methods. The purpose of this work is to develop a mathematical model for constructing a specialized route with the minimum travel time, as well as routes maximizing winery ratings or the number of reviews, and to validate the model's correctness through computational experiments. The paper presents a substantive problem formulation for constructing specialized routes, using the Vienna–Venice "wine route" as a case study. The route is divided into three segments: Vienna – Maribor, Maribor – Gorizia, and Gorizia – Venice. The association between wineries and segments is defined (each winery belongs to a specific segment). For each segment, the number of wineries that must be visited is specified. Two mathematical models are proposed to solve the problem: a model for the minimum-time route, based on the k-vertex cycle search for the Traveling Salesman Problem (TSP) with Miller – Tucker – Zemlin constraints and a model based on the method of sequential concessions for routes with the maximum winery rating or the highest number of reviews. The proposed models were tested on an instance containing 23 wineries, with 11 belonging to the first segment and 7 to each of the second and third segments. For each segment, the number of mandatory wineries to visit is set to one. The results obtained confirm the correctness of the models and the potential for their further practical application. Future work plans include identifying all optimal routes regarding minimum time, maximum rating, and the highest number of reviews; extending the mathematical model with constraints on wine quality and time windows (winery operating hours); constructing specialized routes using artificial intelligence (e.g., Gemini, Copilot, etc.) and comparing them with the mathematically optimal solutions. Keywords: wine routes, traveling salesman problem, k-vertex cycle, Miller – Tucker – Zemlin constraint, method of successive concessions.