Multiobjective Uncapacitated Facility Location Problems (UFLP)

Definition (0/1 case)

The 0/1 uncapacitated facility location problem with p objectives is defined as follow:

Min  z^k(x,s) = sum{i=1,...,nI; j=1,…,nJ} c^k(i,j) x(i,j) + sum{j=1,…,nJ} r^k(j) s(j)    for k=1,…,p
s/t sum{j=1,…,nJ} x(i,j) = 1     for i=1,…,nI
    x(i,j) <= s(j)               for i=1,…,nI; j=1,…,nJ
    x(i,j) = 0 or 1              for i=1,…,nI; j=1,…,nJ
    s(j) = 0 or 1                for j=1,…,nJ  

Definition (Mixed integer case)

The mixed integer uncapacitated facility location problem with p objectives is defined as follow:

Min  z^k(x,s) = sum{i=1,...,nI; j=1,…,nJ} c^k(i,j) x(i,j) + sum{j=1,…,nJ} r^k(j) s(j)    for k=1,…,p
s/t sum{j=1,…,nJ} x(i,j) = 1     for i=1,…,nI
    x(i,j) <= s(j)               for i=1,…,nI; j=1,…,nJ
    x(i,j) >= 0                  for i=1,…,nI; j=1,…,nJ
    s(j) = 0 or 1                for j=1,…,nJ                

Datasets

• 0/1 case with p=2 objectives:

  • dataDidactic
  • dataFernandez
  • dataHarris
  • dataBeasley

• Mixed integer case with p=2 objectives:

  • Gadegaard
  • Delmaire
  • FernandezEasy
  • FernandezHard
  • Real