I'm working on an optimization problem, but I'm not sure how to write this constraint correctly.
I have several servers (e.g., S1, S2, S3, S4...) and some Virtual Network Functions (e.g., V1, V2, V3...). Each server and VNF have a security level. So each VNF should only be allocated to the corresponding server with the same security level.
$\alpha_k = 0,1,0,2...$ -> Security level for servers
$\beta^i = 0,0,1...$ -> Security level for VNFs
$\sigma_k^i \in {0,1}$ -> Indicates the assignment of VNF to a server (decision variable)
If there is a valid assignment then $\sigma_k^i$ will be 1 otherwise 0. For instance, if V1 is assigned to S1 then $\sigma_k^i$ will be 1
Example:
Server --> $\alpha_k$ ::::: VNF --> $\beta^i$
S1 --> 1 ::::::::::::: V1 --> 0
S2 --> 0 ::::::::::::: V2 --> 2
S3 --> 2 ::::::::::::: V3 --> 1
S4 --> 0
Possible assignment:
V1 to either S2 or S4
V2 to S3 and
V3 to S1
I have an objective function and many other constraints that decision is based on, but I want to add this specific constraint (defined above) as well. I tried writing it as follows, but it didn't work.
$\alpha_k \sigma_k^i = \beta^i$ where k and i are iteration variables for servers and VNFs, respectively.
If anyone can please help write this constraint in a proper mathematical equation, that would be great.