A reliability-related optimization problem in multidistribution multi-state logistics network

Logistics networks, as the fundamental infrastructure, play a critical role in boosting economic prosperity. In this paper, we model a logistics network as a multidistribution multi-state flow network (MFN) in which each arc has random capacity characterized by more than one probability distribution under different budget allocations. Accordingly, we construct an optimization model to minimize the total budget required for the network to achieve a given reliability value. To address this challenging reliability-related optimization problem, an effective method is developed by integrating the well-known binary-search method and an existing method that solves the budget-allocation multi-distribution MFN reliability problem. The effectiveness and time complexity of the proposed algorithm are analyzed, and a benchmark example is provided to demonstrate how to minimize the total budget under the condition that the network reliability is not below a specific threshold.