% arg - solver glpk

parameters:

	# Number of pilots
	pilots:=8;	
	no_pil:= 1..pilots;
	# Number of languages  		
	no_lan:= 1..4;	 
	# Number of plane type		
	no_pl_type:= 1..5;
	
	# Matrix of language ratings of pilots
	R_lan[no_pil,no_lan]:= ((20,12,0,0),(14,0,20,0),(0,0,12,0),(13,10,0,0),(0,15,8,17), (0,20,11,0),(8,8,14,0),(8,9,12,16));

	# Matrix of ratings of pilots of experience of two seater aircraft 
	R_planetype[no_pil,no_pl_type]:= (( 18,10,0,0,0),(12,0,17,0,0),(15,9,0,14,0),(0,14,11,0,0),(0,15,13,0,12),(0,8,10,12,18),(8,12,0,16,0),(0,13,0,0,18));
	
			
variables:
	
	x[no_pil,no_pil] : binary ;
		
	
objectives:
	 
	 sum {i in no_pil, j in no_pil: x[i,j] } -> max ; # Objective for answer1

constraints:

	
	con1 {i in no_pil, j in no_pil,i<j: 
				    {k in no_lan : 
					      x[i,j] * R_lan[i,k] >= 10 ;        # valid crew has to  meet the language requirement score ( pilot1)
				              x[i,j] * R_lan[j,k] >= 10 ;        # valid crew has to  meet the language requirement score ( pilot2)
				    } 
	   		    	    { m in no_pl_type : 
					      x[i,j] * R_planetype[i,m] >= 10 ;  # valid crew has to  meet the flight exp. score ( pilot1)
					      x[i,j] * R_planetype[j,m] >= 10 ;  # valid crew has to  meet the flight exp. score ( pilot2)
				     } 
					
	     }
					      
	# Assumption taken that every pilot is a member of at most single crew
	con2 {i in no_pil: 
			sum{ j in no_pil, i!=j:x[i,j] } <= 1 ;
	     }
	
	# Assumption taken that every pilot is a member of at most single crew
	con3 {j in no_pil: 
			sum{ i in no_pil, i!=j :x[i,j] } <= 1 ;
	     }
	
	con4 {i in no_pil: sum{j in no_pil:x[i,j]+x[j,i] } <=1 ; }