物资保障网络防卫力量分配的最大覆盖模型

Maximal Covering Model for Allocating Defense Forces in Material Support Network

针对后勤防卫中的防卫力量部署问题,根据物资保障网络的结构特点,建立了防卫力量分配的最大覆盖模型.模型表示为双层规划形式,采用保障基地能够覆盖的需求量衡量敌我双方的攻击效果与防护效果.上层规划的目标是最大化己方保护q个保障基地的防护效果,下层规划的目标是最大化敌方攻击r个保障基地的攻击破坏效果.根据模型的特点,采用隐式枚举算法对模型进行了求解.算例应用表明,模型所得分配方案的防护效果优于传统的以网络元素脆弱性为决策依据所得分配方案的防护效果.

In order to resolve the problem of deploying defense forces in material support network,a maximal covering model was designed to allocate defense forces based on the characteristic of material support network structure.The model was a bilevel programming whose upper level programming was to maximize the extent of facilities covering customers when enemy had destroyed r unprotected facilities and lower level programming was to maximize the loss that should be made by the enemy.Based on the feature in the decision making,implicit enumeration algorithm was adopted to get optimal solution to the model.Numerical example shows that the result of the model is better than the one of traditional method which takes the vulnerability of element in the network as the decision rule.