• Gurobi Staff

Hi Bahri,

I think we will need to bridge this gap in order for anybody to be able to help.  Feel free to post your formulation and a brief description of the problem, variables, and constraints, and illustrate where the issue is with a small example.

- Riley

let be K=[k1,k2,k3..km] a set of commodities of demand D=[d1..dm]  to be migrated from thier old path Pold=[Po1,Po2..Pom] to thier final Path Pf=[Pf1,Pf2..Pfm]

y[k,t]  binary denote that flow k is migrated at step t

A set of arcs

C=[ Cij  i j   in A ] set of capacities on arc ij

the objective is to find minimal flow management plan such that  transition do not create overload on arcs

contraints :

on capacity on each arc  at each step t on each arcs ij : sum( not migrated flow) + sum( of migrated flow) < C(i;j)

each flow is migrated once. for each k sum of (y[k,t]  over t) = 1

• Gurobi Staff

I think some details are still missing, but I'd guess you could introduce continuous variables: z_{k,i,j,t} to represent the flow of commodity k along arc (i,j) at timestep t.

Then you could link it to y with
$z_{k,i,j,t} \leq \min\{F_k, C_{i,j}\} y_{k,t} \quad \quad \forall k,i,j,t: (i,j) \in A_k$
where F_k is the total flow required by F, and A_k is the arcs that can be used by commodity k.

Then to observe capacity constraints at each t:
$\sum_{k : (i,j) \in A_k} z_{k,i,j,t} \leq C_{i,j} \quad \quad \forall (i,j) \in A, t$

- Riley