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Modify problem: add an extra variable within an additional constraint

Description
We take the trimloss problem described in trimloss.mat, in which each integer variable x(p) represents the number of rolls cut to pattern p. We define a new integer variable y=SUM(p)x(p) and add the associated constraint
            x(1)+x(2)+...+x(N)-y = 0
We do this by first adding a row containing the (unitary) coefficients of the x(p), and then a column corresponding to y. We output the revised matrix to a file and then solve the revised MIP, giving y the highest branching priority. Finally, we output the solution, both to the screen and to an ASCII solution file.


Source Files

Data Files





trimloss.mat

NAME          TRIMLOSS
ROWS
 N  Trimloss
 G  Demand01
 G  Demand02
 G  Demand03
COLUMNS
    x_____01  Trimloss     10.000000   Demand01      5.000000
    x_____02  Trimloss      2.000000   Demand01      4.000000
    x_____02  Demand02      1.000000
    x_____03  Demand01      4.000000   Demand03      1.000000
    x_____04  Trimloss      6.000000   Demand01      2.000000
    x_____04  Demand02      2.000000
    x_____05  Trimloss      4.000000   Demand01      2.000000
    x_____05  Demand02      1.000000   Demand03      1.000000
    x_____06  Trimloss      2.000000   Demand01      2.000000
    x_____06  Demand03      2.000000
    x_____07  Trimloss     10.000000   Demand02      3.000000
    x_____08  Trimloss      8.000000   Demand02      2.000000
    x_____08  Demand03      1.000000
    x_____09  Trimloss      6.000000   Demand02      1.000000
    x_____09  Demand03      2.000000
    x_____10  Trimloss      4.000000   Demand03      3.000000
RHS
    RHS00001  Demand01      8.000000   Demand02     13.000000
    RHS00001  Demand03     10.000000
BOUNDS
 UI BOUND001  x_____01      9.000000
 UI BOUND001  x_____02      9.000000
 UI BOUND001  x_____03      9.000000
 UI BOUND001  x_____04      9.000000
 UI BOUND001  x_____05      9.000000
 UI BOUND001  x_____06      9.000000
 UI BOUND001  x_____07      9.000000
 UI BOUND001  x_____08      9.000000
 UI BOUND001  x_____09      9.000000
 UI BOUND001  x_____10      9.000000
ENDATA

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