LINDO Interactive Execution

! There are three commands, ALTER, RANGE, and PARARHS for studying the 
! effect of various parameters on the optimal solution.
!
! The ALTER command allows one to alter any coefficient of the problem, 
! including ones which are currently zero.  A subsequent optimization tries 
! to use the last solution as a starting point for solving the altered 
! problem.  ALTER can be used to change a rhs or the direction of a row.
!
! The RANGE command causes a standard range report to be printed.  This 
! report specifies the allowable changes for objective function and 
! right-hand-side coefficients which will not cause a change in basis.
: max x + y + z
 ?subject to
 ?2) 4 x + y <= 5
 ?3) 5 y - z >= 4
 ?4) x + 6 z  = 7
 ?end

: ! Alter a constraint coefficient:
: alter
ROW:
4
VAR:
y
VARIABLE NOT IN THIS ROW.  WANT IT INCLUDED?
 ?y
NEW COEFFICIENT:
 ?3

: ! Alter the direction of an inequality:
: alter 3 dir
NEW DIRECTION:
 ?<
: ! Alter the name of a row:
: alter 2 name
NEW NAME=
two
: ! The following is the net result of all the above alterations
: look all
MAX     X + Y + Z
SUBJECT TO
     TWO)   4 X + Y <=   5
       3)   5 Y - Z <=   4
       4)   X + 3 Y + 6 Z =    7
END
: ! This is the end of ALTER section.
! The PARARHS command allows the user to automatically trace out the effect 
! of varying a right-hand-side over a wide range.  Its use is illustrated 
! with the following example session.
: help para
 
PARA COMMAND:
 
TYPE  "PARA row-id new-rhs" TO DO PARAMETRIC RHS ANALYSIS ON
ROW "row-id".  "PARA" VARIES THE RHS OF THIS  ROW  FROM  ITS
CURRENT  VALUE  TO  THE  NEW VALUE "new-rhs", DISPLAYING THE
OPTIMAL OBJECTIVE VALUE AT EACH BASIS CHANGE ALONG THE  WAY.
THE PROBLEM MUST BE OPTIMIZED BEFORE CALLING PARA.

: help range

RANGE COMMAND:

PRINTS RANGE REPORT ON THE RHS AND OBJ COEFFICIENTS.

: ! Let us try an example problem for PARA
: max 20 astro + 30 cosmo
 ?subject to
 ?2) astro <= 60
 ?3) cosmo <= 70
 ?4) astro + 2 cosmo <= 210
 ?end

: terse
: go
LP OPTIMUM FOUND AT STEP      2
OBJECTIVE VALUE =   3300.00000

: solution
 
       OBJECTIVE FUNCTION VALUE
 
       1)     3300.0000
 
 VARIABLE        VALUE          REDUCED COST
    ASTRO        60.000000          0.000000
    COSMO        70.000000          0.000000
 
 
      ROW   SLACK OR SURPLUS     DUAL PRICES
       2)         0.000000         20.000000
       3)         0.000000         30.000000
       4)        10.000000          0.000000

NO. ITERATIONS=       2

: ! Now illustrate the RANGE commnad
: range
 
RANGES IN WHICH THE BASIS IS UNCHANGED:
 
                          OBJ COEFFICIENT RANGES
VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE
                  COEF          INCREASE         DECREASE
   ASTRO       20.000000         INFINITY        20.000000
   COSMO       30.000000         INFINITY        30.000000
 
                          RIGHTHAND SIDE RANGES
     ROW         CURRENT        ALLOWABLE        ALLOWABLE
                   RHS          INCREASE         DECREASE
       2       60.000000        10.000000        60.000000
       3       70.000000         5.000000        70.000000
       4      210.000000         INFINITY        10.000000

: ! Now illustrate the PARA command on row 4:
: para
ROW:
4
NEW RHS VAL=
-1.
 
   VAR       VAR    PIVOT    RHS       DUAL PRICE      OBJ
   OUT       IN      ROW     VAL      BEFORE PIVOT     VAL
 
                           210.000      0.000000E+00   3300.00
SLK    4  SLK    3     4   200.000      0.000000E+00   3300.00
   COSMO  SLK    2     3   60.0000       15.0000       1200.00
   ASTRO  ART          2  0.000000E+00   20.0000      0.000000E+00
                          -1.00000       +INFINITY   INFEASIBLE