Minimum-cost flow optimization of road freight delivery in a mountainous transport network: a case study of Kyrgyzstan

This paper presents a minimum-cost flow model for optimizing road freight delivery in a mountainous transport network, using Kyrgyzstan as a representative case of a landlocked Central Asian economy. The proposed approach integrates transportation cost, handling cost, and time-delay penalties into a unified linear programming framework in order to evaluate both domestic and cross-border freight movements under capacity and delivery-time constraints. The freight system is represented as a directed transport graph whose nodes correspond to logistics hubs and demand points, while arcs describe road corridors with different operational characteristics. The model was implemented in Python using a linear programming solver and calibrated with recent transport statistics and corridor data. For the domestic scenario with a balanced freight demand of 500 tons, the optimized total logistics cost reached 18,750 USD, of which 68 % corresponded to transportation, 17 % to handling, and 15 % to delay-related costs. For the extended cross-border scenario with a total volume of 800 tons, the optimized cost increased to 32,400 USD, while delivery time rose to 36-42 hours due to border-related delays. The results demonstrate that, in mountainous freight systems, time-dependent factors substantially affect route efficiency and total logistics cost. The study shows that minimum-cost flow optimization can support engineering decision-making in freight transport planning, corridor modernization, and customs process improvement in Central Asia.