Nested logic-based Benders decomposition for disaster preparedness planning with horizontal coordination

Disaster preparedness planning includes capacity building, delivery planning, and requirements estimation. Uncertainties of disaster make it challenging to place the proper amount of relief resources at the right locations. This paper develops a two-stage stochastic preparedness planning problem for stockpiling and distributing relief items. The model allows horizontal coordination to rebalance inventory from relief facilities in surplus to where in shortage by a new vehicle routing problem variant with inter-facility routes. This paper also proposes the concept of service level, by defining it as the lowest proportion of satisfied demand for all the affected communities, which not only helps with humanitarian equity but also makes the model a tool for comprehending the value of budgets. Under certain service levels, cost requirements are estimated by the objective function. A nested logic-based Benders decomposition algorithm with optimality and feasibility cuts is designed to solve the problem exactly. In contrast with the classical implementation that builds a new branch-and-bound tree in each iteration, the branch-and-check, which searches on a single branch-and-bound tree, is implemented as an alternative. Based on the numerical study instances, extensive experiments validate the efficiency of the algorithm, the value of horizontal coordination, and the impact of integrating vehicle routing.