A novel min-max robust model for post-disaster relief kit assembly and distribution

In disaster response phase, different types of emergency relief materials are prepared simultaneously. Assorting and packing a proportion of relief items into relief kits will benefit in improving relief distribution agility and efficiency. This study focuses on the relief kit assembly and distribution problem, which includes two stages. The first stage solves the facility location and relief kit assembly problem with the minimum operation cost. The second stage optimizes the relief kit distribution plan with the minimum distribution cost and maximum demand satisfaction, in which an epsilon-constraint method is adopted to transfer the bi-objective model into a single one with the minimum total cost. Then, a min-max robust model is developed to cope with the uncertain demand and travel time. Computational experiments are provided to validate the effectiveness of the min-max robust model compared with deterministic model and two-stage stochastic model. A realistic case study based on earthquakes in Yunnan Province is provided to illustrate the applicability of the proposed min-max robust model. Some managerial insights are obtained by sensitivity analyses as follows. Assembling relief kits in the distribution centers is more effective than that in the demand points. Specifically, the average cost and 95% percentile of the former are 19.45% and 20.52% lower than those of the latter respectively. The vehicle loading capacity has a greater influence on the optimal solution than that of the available working time. Decision makers can balance the total cost and uncertainty budget by adjusting the conservatism level under expected demand satisfaction.