# ----------------------------------------
# CUTTING STOCK PROBLEM
# ----------------------------------------

set WIDTHS;                   # set of widths to be cut

param roll_width > 0;         # width of raw rolls
 
param orders {WIDTHS} > 0;    # number of each width to be cut

param nPAT integer >= 0;      # number of patterns

set PATTERNS := 1..nPAT;      # set of patterns

param nbr {WIDTHS,PATTERNS} integer >= 0;

var Cut {PATTERNS} integer >= 0;   # rolls cut using each pattern

minimize Number:                   # minimize total raw rolls cut
   sum {j in PATTERNS} Cut[j];   

subject to Fill {i in WIDTHS}:
   sum {j in PATTERNS} nbr[i,j] * Cut[j] >= orders[i];

                                   # for each width, total
                                   # rolls cut meets total orders