Abstract:

Natural disasters have inflicted significant casualties and economic losses on society， with earthquakes being the most devastating. From 1993 to 2017， earthquakes in China resulted in 74，000 fatalities， 474，000 injuries， and economic losses amounting to 1.1 trillion yuan. After disasters， it is critical to strategically establish a network consisting of material supply centers and temporary distribution centers near affected areas， along with implementing timely material allocation to meet the demands of disaster-stricken regions. Furthermore， as post-disaster information evolves dynamically， emergency relief decisions must be continuously adapted to enhance operational efficiency. Efficient material transportation through both direct and indirect modes can ensure timely delivery to disaster sites. To manage risks and address uncertain demand for emergency supplies， a hybrid transportation strategy combining both modes is critical. Direct transport involves using vehicles to deliver materials directly from the supply center to the disaster site， while indirect transport first utilizes vehicles to transfer supplies to a temporary distribution center， from which helicopters transport them to the disaster area. Given the dynamic nature of available emergency resources， such as vehicles， helicopters， and material stocks， it is imperative to divide the emergency response into multiple decision-making cycles. Addressing this integrated optimization problem—encompassing the location of emergency facilities and multi-cycle distribution of materials—is vital for enhancing post-disaster relief efforts. The uncertain demand for commodities in affected areas and the changes in the availability of emergency resources are addressed. A robust optimization model is proposed for the location of emergency facilities and commodity distribution using both direct and indirect transportation modes， including vehicles and helicopters. The objective is to determine the location of supply centers and temporary distribution centers， as well as the distribution plan for each period， to maximize the fulfillment of needs at disaster sites while minimizing transportation time. The model utilizes an affine adjustable robust optimization method， where decision variables and state variables are expressed as affine functions of demand. Affine tunable robust optimization is a branch of tunable robust optimization in which uncertain parameters are represented by uncertain sets. To maintain the model's integrity， the uncertainty of material demand is described using polyhedral sets. Some variables， called “unadjustable variables”， must be determined before the implementation of uncertain parameters， while others， referred to as “adjustable variables”， can be adjusted after the uncertainty is revealed. According to affine rules， the adjustable variables are expressed as affine functions of uncertain parameters and substituted into the original model for strong dual transformation， facilitating solution computation. Case studies of the Wenchuan earthquake are conducted， and CPLEX is used to simulate and solve the model after preprocessing. The main findings of this study are as follows： （1） The affine adjustable robust optimization model outperforms both deterministic models and sample-based stochastic programming models in terms of resilience； （2） Predicting and reducing the uncertainty of information can better meet the supply demands in the disaster area； （3） Increasing the number of decision-making cycles improves the ability to meet material demand effectively； and （4） Increasing the number of rescue transport vehicles， distribution center capacity， and overall cost budget enhances material availability， though excessive quantities may lead to waste. Multiple sources of uncertainty are considered， including demand， supply， and transportation time， but the casualty evacuation problem is not addressed. Future studies will integrate the location of emergency facilities， multi-cycle casualty transport， and multi-cycle material distribution under uncertain conditions.

Key words: emergency logistics, facilities location-supplies allocation, multi-objective optimization, demand uncertainty, affine adjustable robust optimization