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modeling flow management problem




  • Riley Clement
    Gurobi Staff Gurobi Staff

    Hi Bahri,

    Your question reads as if the audience is familiar with your problem, and your model formulation (but they are not).

    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

  • jamal bahri
    First Comment
    First Question

    let be K=[k1,k2,] a set of commodities of demand D=[]  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



  • Riley Clement
    Gurobi Staff 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


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