There are many commercial linear programming packages that can be used to solve linear programming problems. Lindo is one such package. If the special command
//+L
is included in an "LPSolves" program, then Lindo compatible output is generated in the "
Trace" output window. The following is the Lindo output generated by "LPSolves" for the house construction problem.
! (clear the lindo screen)
! This is a batch lindo program
! DOS command: lindo.exe < cbars-01.lpi > cbars-01.lpo
! where: cbars-01.lpi is the input file
! cbars-01.lpo is the output file
! (do not forget the paths for the files)
PAGE 0 ! (do not pause after each screen)
! Title: Chocolate bars
! Author: Robin Snyder
! Source: Robin Snyder
! Generated: 1997/11/22 10:20
! Variables:
! x1 = "Galaxy bars (lots)"
! x2 = "Continental bars (lots)"
MAX 2 x1 + 3 x2
! z = "profit ($)"
SUBJECT TO
! "milk (tons)"
2) 3 x1 + x2 < 18
! "cocoa (tons)"
3) x1 + 2 x2 < 12
! "sugar (tons)"
4) 3 x1 + 3 x2 < 21
END
GO
SOLUTION
RANGE
QUIT
This can be run through Lindo in batch mode with the following DOS command-line command which, for convenience, is provided as part of the "LPSolves" output.
lindo.exe < cbars-01.lpi > cbars-01.lpo
The "
<" is the input redirection specifier and "
>" is the output redirection specifier. In this case, input is taken from file
cbars-01.lpi and output is generated to file
cbars-01.lpo. The output file
cbars-01.lpo appears as follows.
LINDO/PC 5.01 (27 JULY 91)
COPYRIGHT (C) 1991 LINDO SYSTEMS INC, CHICAGO, IL.
LICENSED MATERIAL, ALL RIGHTS RESERVED. COPYING
EXCEPT AS AUTHORIZED IS PROHIBITED.
STUDENT VERSION - FOR EDUCATIONAL USE ONLY
DISTRIBUTED BY WEST PUBLISHING COMPANY
LP OPTIMUM FOUND AT STEP 2
OBJECTIVE FUNCTION VALUE
1) 19.000000
VARIABLE VALUE REDUCED COST
X1 2.000000 .000000
X2 5.000000 .000000
ROW SLACK OR SURPLUS DUAL PRICES
2) 7.000000 .000000
3) .000000 1.000000
4) .000000 .333333
NO. ITERATIONS= 2
DO RANGE(SENSITIVITY) ANALYSIS?
? :
RANGES IN WHICH THE BASIS IS UNCHANGED:
OBJ COEFFICIENT RANGES
VARIABLE CURRENT ALLOWABLE ALLOWABLE
COEF INCREASE DECREASE
X1 2.000000 1.000000 .500000
X2 3.000000 1.000000 1.000000
RIGHTHAND SIDE RANGES
ROW CURRENT ALLOWABLE ALLOWABLE
RHS INCREASE DECREASE
2 18.000000 INFINITY 7.000000
3 12.000000 2.000000 3.500000
4 21.000000 4.200000 3.000000
Note the following.
The line of ":" and "?" characters is a feature of Lindo in batch mode when reading (and ignoring) comment lines.
The answers are the same as for "LPSolves".
Stripped of comments, the minimal Lindo batch program to solve the problem is as follows.
PAGE 0
MAX 2 x1 + 3 x2
SUBJECT TO
2) 3 x1 + x2 < 18
3) x1 + 2 x2 < 12
4) 3 x1 + 3 x2 < 21
END
GO
SOLUTION
RANGE
QUIT
Which is easier and/or better? It depends on your needs, resources, etc.
