modeling flow management problem

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jamal bahri

2024年05月10日 15:01

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thanks to help me encode variable dependency  for flow management problem:

i' have constraints on capacity on each arcs

at each step some flow should be migrated ; but i need to express non violation at transition during a \delta(t)

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  Simranjit Kaur

  • Gurobi Staff

  2026年11月13日 01:25

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  Riley Clement

  • Gurobi Staff

  2024年05月14日 03:04

  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

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  jamal bahri

  2024年05月14日 07:05

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  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

   

   

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  Riley Clement

  • Gurobi Staff

  2024年05月15日 05:03 編集済み

  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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