From:	ADVAX::"kerr@eniac.seas.upenn.edu" "David E. Kerr"
Subject: simplex
 
I'm sending a makefile first which will tell you that
as a stand-alone pgm, you run "sim"
   sim gets problem file specification and calls subroutine "simplx"
 
simplx calls bldtab to build a tableau and returns the answer in 
argument X and RAY (if solution is unbounded, RAY is a direction 
along which the objective function can be minimized without limit
and without violating constraints...
 
incidently, the program assumes that problems are all minimization
problems... to maximize an objective function, minimize its negative
and change the sign of the final objective function value.
 
in input file, as read by "sim"
* starts a comment
the first numbers are NVar (number of variables) and M (# of constraints)
 
the next numbers are NVar coefficients of the linear objective
function
 
the next M lines are constraints with <=, >=, or = relations to
right-hand-side
 
the last line is up to NVar >= signs designating which of the
problem variables are non-negative (usually, they all are)
 
i'll send sample input files too.
 
the makefile:
 
 
CC=fort
RM=/bin/rm -rf
all: sim
sim: sim.o smplx.o simrpt.o bldtab.o
	$(CC) -O -o sim sim.o smplx.o simrpt.o bldtab.o
sim.o: sim.f
	$(CC) -O -c sim.f
smplx.o: smplx.f
	$(CC) -O -c smplx.f
simrpt.o: simrpt.f
	$(CC) -O -c simrpt.f
bldtab.o: bldtab.f
	$(CC) -O -c bldtab.f
clean:
	$(RM) *.o core sim
 
 
sample inputs:
 
* Nvar, M
* Bazaraa & Jarvis p. 143
2, 3
* objective function
1, -2
* M=1 - 1st constraint, relation, rhs
1, 1 >= 2
* M=2 - 2nd constraint, relation, rhs
-1, 1 >= 1
* M=3 - 2nd constraint, relation, rhs
, 1 <= 3
* non-negativity of variables (relation wrt 0)
>=, >=
** end
 
 
 
* Bazaraa & Jarvis p. 166 : Beale's example of a degenerate, cycling problem
* Nvar, M
7, 3
* objective function
,,,-0.75, 20, -0.5, 6
* M=1 - 1st constraint, relation, rhs
1, 0, 0, 0.25, -8, -1, 9 = 0
* M=2 - 2nd constraint, relation, rhs
0, -1, 0, -0.5, 12, 0.5, -3 = 0
* M=3 - 3rd constraint, relation, rhs
,, -1, , , -1, = -1
* non-negativity of variables (relation wrt 0)
>=, >=, >=, >=, >=, >=, >=
** end
 
 
 
* Nvar, M
3, 2
* objective function
1, 1, 4
* M=1 - 1st constraint, relation, rhs
3, 2, 3 <= 2
* M=2 - 2nd constraint, relation, rhs
-2, 1, 5 >= 4
* non-negativity of variables (relation wrt 0)
, >=, >=
** end