Abstract: The maximal coverage model has two assumptions: ‘all or nothing coverage' and ‘individual coverage'. Each demand point within the coverage radius of a facility is completely covered, otherwise, not covered at all. The demand point can be covered by only one facility, namely the closest one. It is not hard to think of settings where the two assumptions may be unrealistic. This research relaxes the two assumptions and studies the gradual coverage and the cooperative coverage. Firstly, we propose a cooperative coverage model to maximum the effectiveness of the location, on the condition that every demand can receive the given lowest service level. The objective function contains a fraction. The nonlinear programming is transformed to an equivalent linear programming by introducing some auxiliary variables. Finally, a numerical example is used to illustrate the effects of the lowest service level on the optimal facility location scheme. Moreover, we obtain how the location cost, total service level and the service level per cost change with the lowest service level. In addition, the sensitivity analyses with the important parameters that influence the model are also analyzed.

Key words: cooperative coverage, the lowest service level, the effectiveness of the location

摘要： 传统的覆盖模型含有“全有全无”和“单一覆盖”两个假设,即假设需求点在设施的服务半径内才被覆盖,否则不被覆盖;需求点只能被最近的设施覆盖。这两条假设在实际应用中均存在不合理之处。松弛了这两条假设,研究逐渐覆盖和联合覆盖。在保证每个需求点都享受到最低服务水平的情况下,提出了选址效益最大化的联合覆盖模型。由于目标函数中含有分式,通过引入辅助变量的方法,将含有分式目标函数的非线性规划转化成等价的线性规划。最后,通过数值算例分析了最低服务水平限制对最佳选址方案的影响,并得到选址成本、总服务水平和单位成本服务水平随最低服务水平限制的变化,同时对影响模型的重要参数做了敏感性分析。

关键词: 联合覆盖, 最低服务水平, 选址效益