# 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;