Budget-conscious tourists are travellers electing to plan their vacations by taking advantage of pricing variability to minimize the total cost of their desired multi-city vacation. This paper presents the formulation and analysis of a time-discretized linear integer programming (LIP) model to optimize total travel costs for travellers vacationing between major European cities by considering dynamic flight costs and accommodation expenses. The proposed time-discretized network flow model presented is an extension of classical Shortest-Route-Problems (SRP) and is solved using Excel’s SIMPLEX LP algorithm. Flight data collected from the online travel agency Kiwi.com between May 1^st, 2022, and May 30^th was found to show significant daily price fluctuation, whereas accommodation prices collected from Airbnb.com between May 1^st, 2023, and May 13^th, 2023, remained stable. This paper includes the model formulation, assumptions, and cost analysis of varying travel instances by rotating the origin city and altering the stay duration at each destination. Three solutions, the generous, greedy, and cost-minimized solutions, were calculated for each travel trip instance. By optimizing the route, the cost can be reduced by upwards of 20.3% and 6.7% relative to the generous and greedy solutions. The model evaluated the impact of varying staying durations on the optimal travel order and was found to be very robust in terms of stay durations such that the optimized cost remained constant. The results of this paper have implications for the global travel industry by lowering the barrier of entry for budget-friendly consumers.