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Controlling and maintaining public health in the face of diseases necessitates the effective implementation of response strategies, including the distribution of vaccines. By distributing vaccines, vulnerable populations can be targeted, individuals can be protected, and the spread of diseases can be minimized. However, managing vaccine distribution poses challenges that require careful consideration of various factors, including the location of distribution facilities. This paper proposes a novel model that combines location-allocation problems with queueing systems methodologies to optimize the efficiency of vaccine distribution. The proposed model considers factors such as uncertain demand, varying service rates, depending on the system state. Its primary objective is to minimize total costs, which encompass the establishment and adjustment of the service mechanism, travel times, and customer waiting time. To forecast customer demand rates, the model utilizes time series techniques, specifically the seasonal Autoregressive Integrated Moving Average (ARIMA) model. In order to tackle large-scale problems, a total of 16 newly developed Metaheuristic algorithms are employed, and their performance is thoroughly evaluated. This approach facilitates the generation of solutions that are nearly optimal within a reasonable timeframe. The effectiveness of the model is evaluated through a real case study focused on vaccination distribution in Iran. Furthermore, a comprehensive sensitivity analysis is conducted to demonstrate the practical applicability of the proposed model. The study contributes to the advancement of robust decision-making frameworks and provides valuable insights for addressing location-related challenges in health systems.

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We propose an approach to constructing metrics of network resilience, where resilience is understood as the network's amenability to restoring its optimal or near‐optimal operations subsequent to unforeseen (stochastic) disruptions of its topology or operational parameters, and illustrated it on the examples of the resilient maximum network flow problem and the resilient minimum cost network problem. Specifically, the network flows in these problems are designed for resilience against unpredictable losses of network carrying capacity, and the mechanism of attaining a degree of resilience is through preallocation of resources toward (at least partial) restoration of the capacities of the arcs. The obtained formulations of resilient network flow problems possess a number of useful properties, for example, similarly to the standard network flow problems, the network flow is integral if the arc capacities, costs, and so forth, are integral. It is also shown that the proposed formulations of resilient network flow problems can be viewed as “network measures of risk”, similar in properties and behavior to convex measures of risk. Efficient decomposition algorithms have been proposed for both the resilient maximum network flow problem and the resilient minimum cost network flow problem, and a study of the network flow resilience as a function of network's structure has been conducted on networks with three types of topology: that of uniform random graphs, scale‐free graphs, and grid graphs.