A Bi-level Programming Approach for Pre-positioning Emergency Warehouses

In some countries, regional authorities may attempt to rebalance the allocation of national facilities in benefit of their own region which, in turn, may cause disturbances in the central government’s decision-making proces. Regarding the hierarchical nature of these types of decisions, classical optimization models are not effective in decision-making and the use of multi-level programming can increase the efficiency of planning. Our paper aims to address the issue of a bi-level programming model to conduct the location analysis of emergency warehouses. A three-echelon relief supply chain is considered in which the relief network involves national and regional warehouses and demand cities. The upper-level model decides on the location of national warehouses, allocating them to regional warehouses. The lower-level model determines the location of regional warehouses and allocates them to demand points. The structure of both levels is based on the median location-allocation problem. Three solution approaches are presented based on the full enumeration and two types of nested evolutionarymethods (genetic and heuristic local search algorithms). For the model to be used in Iran, the efficiency of algorithms is analyzed for two sizes of problems. The obtained results show the proper functioning of the solution approaches.