In this paper, we describe a matheuristic to solve the stochastic facility location problem which determines the location and size of storage facilities, the quantities of various types of supplies stored in each facility, and the assignment of demand locations to the open facilities, which minimize unmet demand and response time in lexicographic order. We assume uncertainties about demands, inventory spoilage, and transportation network availability. A good example where such a formulation makes sense is the the problem of pre-positioning emergency supplies, which aims to increase disaster preparedness by making the relief items readily available to people in need. The matheuristic employs iterated local search techniques to look for good location and inventory configurations, and uses CPLEX to optimize the assignments. Numerical experiments on a number of case studies and random instances for the pre-positioning problem demonstrate the effectiveness and efficiency of the matheuristic, which is shown to be particularly useful for tackling larger instances that are intractable for exact solvers. The matheuristic is therefore a contribution to the literature on heuristic approaches to solving facility location under uncertainties, can be used to further study the particular variant of the facility location problem, and can also support humanitarian logisticians in their planning of pre-positioning strategies.

在本文中，我们描述了一种数学方法来解决随机设施的位置问题，该问题确定了存储设施的位置和大小，每个设施中存储的各种供应品的数量以及对开放设施的需求位置的分配，从而最大程度地减少了按字典顺序未满足的需求和响应时间。我们假设有关需求，库存损坏和运输网络可用性的不确定性。这种措辞有意义的一个很好的例子是预先安置应急物资的问题，该问题旨在通过使有需要的人容易获得的救济物资来提高备灾能力。该数学家使用迭代的本地搜索技术来寻找良好的位置和库存配置，并使用CPLEX来优化分配。针对大量案例研究和针对预定位问题的随机实例的数值实验证明了数学方法的有效性和效率，这对于解决精确求解器难以解决的较大实例特别有用。因此，数学是对在不确定条件下求解设施位置的启发式方法文献的一种贡献，可以用于进一步研究设施位置问题的特定变体，还可以支持人道主义后勤人员规划预定位策略。