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This paper models a logistics network as a multi-distribution multi-state flow network (MFN) in which each arc has a random capacity characterized by more than one probability distribution under different budget allocations. An optimization model is constructed to minimize the total budget required for the network to achieve a given reliability level. By integrating a novel budget vector method with the well-known binary search method, an effective and efficient algorithm is developed to solve the optimization model, together with analyses on the computational complexity. A practical implementation on a simple network is presented to illustrate the proposed method, and the computational efficiency is explored via numerical examples. Finally, a real case study is provided to showcase the application of the proposed model and method.

Budget optimization for a multi-distribution multi-state logistics network with reliability consideration