Table 1 Relevant parameters and variables.
From: Hierarchical optimal configuration model and algorithm for counterterrorism resource allocation
parameters | Â |
|---|---|
\(i\) | city node index, \(i=1,\cdots ,I\). |
\(j\) | alternative counterterrorism facility node index, \(j=1,\cdots ,J\). |
\(j\left(i,k\right)\) | the nearest facility \(j\) providing class \(k\) resources for city \(i\). |
\(h,k\) | type, level index, \(h,k=1,\cdots ,H\). |
\(\alpha\) | the delay loss of resource transfer per unit distance and type. |
\(\gamma\) | the benefit per unit distance and type. |
\(B\) | total budget limitation. |
\({w}_{i}\) | demand of city i after the attack. |
\({\eta }_{i}\) | the negative impact caused by the attacking unit demand. |
\({{\rm{C}}}_{h}\) | cost of h-level facility. |
\({\delta }_{i}\) | the benefit obtained by attacking unit demand. |
\({d}_{{ij}}\) | distance from city i to facility \(j\). |
\(M1\) | a sufficiently large constant. |
\(d\left(i,j\left(i,k\right)\right)\) | distance from city i to facility \(j\left(i,k\right)\); if \({y}_{{ijk}}=1\), then \(d\left(i,j\left(i,k\right)\right)={d}_{{ij}}\), and otherwise, \(d\left(i,j\left(i,k\right)\right)=M\). |
variables | Â |
\({x}_{{jh}}\) | if h-level facility j is established, then \({x}_{{jh}}=1\); otherwise, \({x}_{{jh}}=0\). |
\({y}_{{ijh}}\) | if the type h requirement of city i is allocated to facility j, then \({y}_{{ijh}}=1\); otherwise, \({y}_{{ijh}}=0\). |
\({p}_{i}\) | if the city node is attacked, then \({p}_{i}=1\); otherwise, \({p}_{i}=0\). |
