# ABC-comp.mod
# Original AMPL coding by Sven Leyffer, Argonne Natl. Lab.
#
# A simple multi-objective optimization problem (p. 79f):
# C.-L. Hwang & A. S. Md. Masud, Multiple Objective
# Decision Making - Methods and Applications, No. 164 in 
# Lecture Notes in Economics and Mathematical Systems,
# Springer, 1979.
#
# ... model modified to give meaningful MOOP.

# ... variables
var x1 >= 0.0;		# product 1 in tons/day
var x2 >= 0.0;		# product 2 in tons/day

# ... objective functions
minimize  f1: (x1-4)^2 + x2^2 + 5*x1 + 4*x2 - x1*x2;	# ... total cost
minimize  f2: - x1 - 2*x2;				# ... production

# ... constraints
subject to

   # ... achieve profit min & limit labor cost
   profit: x1*x2 >= 3;
   labor:  5*x1 + 4*x2 <= 25;

   # ... daily production goal
   product: x1 + 2*x2 >= 5;