#      
#      0 1 2 3 5
#      1 0 1 2 3
#      2 1 0 1 2
#      3 2 1 0 1
#      4 3 2 1 0
#      
#      0 1 0 0 0
#      0 0 1 0 0
#      1 0 0 0 0
#      0 0 0 0 1
#      0 0 0 1 0
#      
#      0 0 0 1 0
#      0 0 1 0 0
#      0 0 0 0 1
#      0 1 0 0 0
#      1 0 0 0 0
#      
#      4 2 3 5 1
#      

#  GLPK model file created by SUN for RO teaching


###############################  Model ###############################


###############################  Sets  ###############################

set POSITIONS; 	

###################  Variables  ###################

var cycle{i in POSITIONS, j in POSITIONS}, binary; 

###################  Constants: Data to load  #########################

param Distances{i in POSITIONS, j in POSITIONS}; 

###################  Constraints  ###################

# Matrice de permutation
s.t. RespectUnTravailParPersonne{i in POSITIONS}:
  sum{j in POSITIONS} cycle[i, j] = 1;
s.t. RespectUnePersonneParTravail{j in POSITIONS}:
  sum{i in POSITIONS} cycle[i, j] = 1;

# Pas de sous cycle
s.t. SousCycle1{(i in POSITIONS, j in POSITIONS):(i <= j and i < 4)}:
  sum{k in POSITIONS, l in POSITIONS: i <= k <= j, i <= l <= j} cycle[k, l] <= (j - i + 1);
  

###### Objective ######

minimize CoutTotal:
	sum{i in TRAVAUX, j in PERSONNELS} Cout[i, j] * cycle[i, j];

end;