Table 2 Notation of multistage stochastic programming model
Symbol | Definition |
|---|---|
Indices and sets | |
\(\,i \in {{\mathcal {I}}}\) | Node |
\(\,k \in {{\mathcal {K}}}\) | Message |
\(\,t \in {{\mathcal {T}}}\) | Time |
\(\,s \in {{\mathcal {S}}}\) | Scenario |
Parameters | |
\(\,a^{t,s}_{ij}\) | The directed arc from node i to node j |
\(\,b_{ki}\) | The information preference of node i with respect to message k |
\(\,c_{ki}\) | The pre-activation, that node i has known or has not known the message k before the seed selection |
\(\,w_k\) | The influence weight of message k |
Decision variable | |
\(\,x^t_{ki}\) | Binary variable, seed selection, whether the node i is selected as the seed node of message k at time t |
\(\,y^{t,s}_{ki}\) | Binary variable, node activation, whether the node i is activated by message k at time t and scenario s |
\(\,z^{t,s}_{ki}\) | Binary variable, message transmission, whether the node i decide to transmit message k to its neighbor at time t and scenario s |
Other | |
\(\,Q(x)\) | The total cost of seed selection x |
\(\,R(y)\) | The total reward of node activation y |
\(\,P(a)\) | The network topology probability of all the arcs a |