Under the backdrop of frequent emergencies, the rational layout of emergency service facilities (ESF) and the effective allocation of emergency supplies have emerged as crucial in determining the timeliness of post-disaster response. By adequately accounting for potential uncertainties and carrying out comprehensive pre-planning, the robustness of location-allocation decisions can be significantly improved. This paper delves into the ESF network design problem under demand uncertainty and formulates this problem as a two-stage robust optimization model. The presented model defines a generalized budget uncertainty set to capture victims’ uncertain demand and minimizes the sum of the costs involved in the two stages. The objective function integrates the input cost in the preparedness phase, the deprivation cost from the victims’ perspective and the environmental impact cost responding to sustainable development in the response phase, which respectively correspond to the comprehensive optimization of the deployment of ESF, the distribution of emergency supplies and the implementation of sustainable measures. Subsequently, we employ the column and constraint generation (C&CG) algorithm to solve the proposed model and take the COVID-19 epidemic in Wuhan as a case to verify the effectiveness of the model and algorithm. Finally, we examine the influence of demand uncertainty and environmental impact cost on the optimal solution, yielding valuable managerial insights.

Zeroing neural networks (ZNNs) play a crucial role in efficiently solving time-varying problems. Recently, ZNNs are integrated with many advanced control theories with a certain convergence time to enhance their performance. On account of the convergence time of the prescribed-time convergence is precise, it is of great significance to investigate ZNN with prescribed-time convergence. In addition, delay is unavoidable in circuit implementation, not only impacting the prescribed-time convergence but also inducing instability and oscillation in ZNN. To evaluate the effectiveness of prescribed-time ZNN under delay environment, prescribed-time delayed zeroing neural network (PTDZNN) is proposed for solving time-varying equations in this article. It is concluded that PTDZNN can obtain the correct real-time solution in prescribed time and the convergence time of PTDZNN is independent of initial conditions. Furthermore, PTDZNN exhibits notable tolerance to delay and distinguishes itself from existing delayed zeroing neural networks by its independence from linear matrix inequality (LMI). Moreover, the LMI-independent stability proof of ZNN under delay environment is also proved. Numerical simulations are presented to demonstrate the prescribed-time convergence and delay tolerance of PTDZNN. Ultimately, PTDZNN is successfully applied in dynamic positioning algorithms and image fusion problems. Notably, PTDZNN stands out as the first ZNN to incorporate both prescribed-time convergence and delay.