Abstract In this paper a stochastic districting problem is investigated. Demand is assumed to be represented by a random vector with a given joint probability distribution function. A two-stage mixed-integer stochastic programming model is proposed. The first stage comprises the decision about the initial territory design: the districts are defined and all the territory units assigned to one and exactly one of them. In the second stage, i.e., after demand becomes known, balancing requirements are to be met. This is ensured by means of two recourse actions: outsourcing and reassignment of territory units. The objective function accounts for the total expected cost that includes the cost for the first-stage territory design plus the expected cost incurred at the second stage by outsourcing and reassignment. The (re)assignment costs are associated with the distances between territory units, i.e., the focus is put on the compactness of the solution. The model is then extended in different ways to account for aspects of practical relevance such as a maximum desirable dispersion, reallocation constraints, or similarity of the second-stage solution w.r.t. the first-stage one. The new modeling framework proposed is tested computationally using instances built using real geographical data.

中文翻译：

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走向用于分区的随机编程建模框架

摘要 本文研究了一个随机分区问题。假设需求由具有给定联合概率分布函数的随机向量表示。提出了一种两阶段混合整数随机规划模型。第一阶段包括关于初始领土设计的决定：定义地区并将所有领土单位分配给一个，而且恰好是其中一个。在第二阶段，即在知道需求之后，要满足平衡要求。这是通过两种追索行动来确保的：外包和领土单位的重新分配。目标函数计算总预期成本，包括第一阶段区域设计的成本加上第二阶段外包和重新分配产生的预期成本。（重新）分配成本与领土单位之间的距离相关，即重点放在解决方案的紧凑性上。然后以不同的方式扩展模型以考虑实际相关的方面，例如最大期望分散、重新分配约束或第二阶段解决方案与第一阶段解决方案的相似性。提出的新建模框架使用使用真实地理数据构建的实例进行计算测试。