设施选址及其规模选择优化对供应链的长期战略成本和运营成本有着重要影响, 是提高企业利润和竞争力的关键决策之一, 也是运筹优化领域研究的热点与难点. 针对已有的两阶段设施选址问题,(two-stage facility location problem, TSFLP),研究中缺乏对设施容量选择的优化, 在设施选址问题基础上引入了设施容量选择的优化, 同时确定了工厂的位置、仓库的位置和容量、从工厂到仓库的产品流以及客户到仓库的分配, 建立了以最小化总成本为目标的混合整数规划模型, 并基于模型特点设计了适合求解此问题的拉格朗日松弛(Lagrangean relaxation, LR)方法和混合变邻域禁忌搜索,(hybrid variable neighborhood tabu search, HVNTS)算法. 基于随机生成的大量具有不同参数的实例, 验证了所提出的算法可有效求解大规模的、且需同时优化设施选址及容量选择的问题.

Facility location is a problematic point in modern enterprise production and operation management. Further, it is a decisive factor affecting enterprises' efficiency because of the shortage of facility capacity selection in the existing two-stage facility location study. This study introduced the optimisation decision technology of facility capacity selection simultaneously. The problem was predominately in opening plants and depots, selecting the size of depots, determining the product flows from the opened plants to the opened depots, and the customers' assignments to the opened depots to satisfy the customers' demands. A mixed-integer programming model to minimise the total cost was proposed. The Lagrangean relaxation (LR) approach and hybrid variable neighbourhood tabu search (HVNTS) algorithm were designed to solve this problem. A large number of instances were randomly generated and tested to evaluate the effectiveness of the proposed method. The results verified that this method could solve the problem of large-scale facility location with depot size selection.