Capacity reservation for humanitarian relief: A logic-based Benders decomposition method with subgradient cut
针对人道主义救援中仅靠预置物资成本高、品类有限且易受损的问题，提出结合预置、物理能力预留和生产能力预留的两阶段随机模型，并开发了带次梯度割的基于逻辑的Benders分解方法高效求解，案例验证了方法的有效性。
Prepositioning of relief supplies has been widely addressed to cover the demands of humanitarian emergencies. However, cost inefficiency, item type limitation, and damage risk make solely relying on prepositioning unrealistic. We develop two-stage stochastic models that incorporate prepositioning, physical capacity reservation, and production capacity reservation for reactive procurement. As an alternative to the traditional physical capacity reservation, the production capacity reservation is inspired by the practice of the automotive industry, garment industry, etc. for manufacturing personal protective equipment during the pandemic. Our models minimize the supply-side monetary costs and the demand-side social impacts, i.e., deprivation costs. The discretized deprivation cost function is introduced to handle the nonlinear deprivation cost function. The hierarchical nature of our stochastic models motivates us to utilize the logic-based Benders decomposition (LBBD). Our Benders master problem contains one set of nonbinary integer variables for prepositioning inventory and another set of continuous variables for estimating the second-stage costs, which differs from the existing LBBD works that typically contain binary and continuous variables in the master problem. Hence, a new type of logic-based Benders optimality cut, namely logic-based subgradient cut, is first introduced. To compute the cutting coefficients efficiently, heuristics that can lead to almost optimal solutions is developed. We also develop warm-start cutting planes, namely wait-and-see cuts and expected-value cuts, to help with better upper bounds and lower bounds. Extensive numerical results followed by a case study validate the efficiency of the solution method, the value of incorporating stochasticity, and the superiority of the capacity reservation.