HP50G SIMPLEX Version14b Max Min Pivot Algorithm, multiple/unbounded, unfeasible sol

[Gil]

Version 12

- In some very special cases, the program could be sometimes "stuck" at the end and chose the wrong row, returning then the second solution — but possibly an unfeasible one.
A special "artificial" test was duly included in subprogram CHECK. 2SOL to fix up that issue.
- The NOTE Var was changed : explanations now only regarding the "pivoting" (outside the program) & no more explanations relative to roundings.
- Lines of explanations in —>PIVOT¦&COL.ROW subprogram suppressed for speed purpose.

[Gil]

New Version 12

- In some very special cases, the program could be sometimes "stuck" at the end and chose the wrong row, returning then the second solution — but possibly an unfeasible one.
A special "artificial" test was duly included in subprogram CHECK.2SOL to fix up that issue.
- The NOTE Var was changed : explanations now only regarding the "pivoting" (outside the program) & no more explanations relative to roundings.
- Lines of explanations in —>PIVOT¦&COL.ROW subprogram suppressed for speed purpose.

[Gil]

Version 13d

Handling of "unfeasible" problem.
For visual outlook, deletion of no more used SAME.SOL.

Just look at the following problem (input Matrix) :
[[ 1 1 'L' 5 ]*
[ 0 1 'G' 8 ]**
[ 6 4 0 'Max' ]]

According to usual SIMPLEX convention (in this program), if nothing is said about xi (here x1 and x2), it is assumed to be >=0.
If x2 >= 8 according to **, then * cannot be <0 as said in *, unless breaking the above rule and accepting that x1 might be <= 0 (x1=-3).

Put
[[ 1 1 'L' 5]
[ 0 1 'G' 8 ]
[ 6 4 0 'Max' ]]
on the stack and launch —>GO.

You get then, with the new version 13d:

{ Var 2¦Steps 4 Time1¦s :

Z-Max: 14 :x1: -3 :x2: 8 :
Sign { x1 }
not allowed: UNFEASIBLE.problem}.

Then, pressing afterwards the variable S.1-­N, you get also the reminder:
:Unfeasible problem
Sign incompatibility
of { x1 },
[x1 x2... ]:
[ -3 8 ]

Of course, if you specify that x1 is <= 0

[[ 1 1 'L' 5 ]
[ 1 0 'L' 0 ]
[ 0 1 'G' 8 ]
[ 6 4 0 'Max' ]]

and launch —>GO
with the new above Matrix, you will get:

{ Var 2¦Steps 5 Time1¦s :
Z-Max: 14 :x1: -3 :x2: 8 },
with no special message.

The same applies to

[[ 1 1 'L' 5 ]
[ 1 0 'F' 0 ]
[ 0 1 'G' 8 ]
[ 6 4 0 'Max' ]],
supposing x1 Free (of unknown sign).

[Gil]

Version 14
- Linear Combination of xi in prior versions supposed all xi to be >= 0 (default case), or free.
Now, in the linear combination of the xi, besides the free case of xi being free, the default case respects the real signs of the xi.
- Programs variables S.1­N, S.LIN & d.LIN, when called, give more details about the solution (multiple/unbounded/unfeasible solution).

[Gil]

New Version 14b

Slight change in output for RESULT¦Ci.rows in case of unfeasible problem.