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These days customers expect the lowest price of postal services but still they look forward to its’ wide availability, security and delivery of mail items on time. The most important in generating the total costs in these services is transport cost of postal items. Transport costs depend on many factors- purchase price of the vehicle, labor costs of the drivers, costs of maintenance and repairs, fuel costs etc. Hence, it is so important to find organizational solutions that can reduce the costs associated with the transportation of postal shipments, thereby reducing the total cost of postal services. An excellent way for doing it is to minimize the length of postal transportation routes, what means finding the shortest ways between post offices in selected area. This article presents the results of analysis and researches on existing postal network, which were based on the graph theory, in order to optimize actual network. Realized computer simulations were oriented to find a new location of the local distribution center. The relocation of local distribution center leads to minimize of the transport costs for delivery postal items “from point to point” of Polish Post SA network in the selected area of the Lublin province.