# This is a file that builds a few different objectives for a 5x4 sched LP
#   (1) first we give no objective (so Gurobi just solves the feasibility
#       problem)
#   (2) 

# import the Gurobi tools if you are running python
from gurobipy import *

######################

# Set some parameters
n = 5
d = 4

jf_model = Model('scheduler')

vars = jf_model.addVars(n,d, vtype=GRB.BINARY, name='sched')

vars   # type this to examine the variables

# Each group must take one day

jf_model.addConstrs(  (vars.sum(i,'*') == 1
	for i in range(n)
	), name='Group')

# Each day has at most three presentations

jf_model.addConstrs(  (vars.sum('*',j) <= 3
	for j in range(d)
	), name='Days')


# End of setting up variables and constraints
# ########################################################

# ######################################################## 
# First LP: we do not specify an objective

jf_model.optimize()

#     (If you really want to see all the variables in the optimal solution)
for v in jf_model.getVars():
    print('%s %g' % (v.varName, v.x))

#     (If you only want to see the nonzero variables)
jf_model.printAttr("X")

# ######################################################## 
# Second LP: the objective is 0.1 times the index of the variable

my_obj = LinExpr()
i = 0.0
for v in jf_model.getVars():
	i = i + 0.1
	my_obj.addTerms( i , v )

#          Now poke around a bit
my_obj
jf_model.setObjective( my_obj, GRB.MAXIMIZE)

#          Optimize and examine the optimal solution 
jf_model.optimize()
jf_model.printAttr("X")

# ######################################################## 
# A third toy example: the objective coefficient is the square of
# the index

my_obj.clear()
i = 0.0
for v in jf_model.getVars():
	i = i + 0.1
	my_obj.addTerms( i * i , v )

# Now examine the objective and optimize
my_obj
jf_model.setObjective( my_obj, GRB.MAXIMIZE)
jf_model.optimize()
jf_model.printAttr("X")

# ######################################################## 
# A fourth toy example

my_obj.clear()
for i in range(n):
	for j in range(d):
 		my_obj.addTerms( i * j * 1.0, vars[i,j] )
# the line below is equivalent
#		my_obj.addTerms( i * j * 1.0, a[i*d+j] )

# Now examine the objective and optimize
my_obj
jf_model.setObjective( my_obj, GRB.MAXIMIZE)
jf_model.optimize()
jf_model.printAttr("X")