Flexible Districting Policy for the Multiperiod Emergency Resource Allocation Problem With Demand Priority

To address responsiveness, time-dependence, and limited emergency supply issues, we introduce a new flexible districting policy, aiming to improve satisfaction in multiperiod emergency resource allocation (MPERA), and set demand priorities to guarantee allocation balance in resource-limited scenarios. The modeling and solution process involves the following: 1) formulating a mixed-integer programming (MILP) model for MPERA with demand priority (MPERA-DP), aiming to maximize utility considering the transportation cost, districting change, and penalty for unsatisfied demand and 2) incorporating the justifiable granularity principle (JGP) and particle swarm optimization (PSO) into the brand-and-price (B&P) algorithm for initial districting and allocating decisions to improve the solution quality and calculation speed. The results of the experiments show that 1) the JGP-PSO-B&P algorithm achieves superior efficiency in terms of optimality and convergence for large-scale cases. This algorithm could improve the optimality by 13.42% compared with that of the JGP-PSO algorithm, 13.15% compared with that of the B&P algorithm, and 28.18% compared with that of the PSO algorithm, on average; 2) the MPERA-DP model with flexible districting policy outperforms flexible MPERA without demand priority, emergency resource allocation with rescheduling (ERAR) and fixed emergency resource allocation with demand priority (FERA-DP), improving the utility by 20.56%, 5.14% and 41.84%, respectively; and 3) the scheme efficiency is influenced by the desirable satisfaction deviation, and when set to 0.6, it allows for the optimization of both demand satisfaction and utility.