# ----------------------------------------
# CUTTING STOCK USING PATTERNS
# ----------------------------------------

param nPAT integer >= 0, default 0;
param roll_width;

set PATTERNS := 1..nPAT;
set WIDTHS;

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

   check {j in PATTERNS}: sum {i in WIDTHS} i * nbr[i,j] <= roll_width;

var Cut {PATTERNS} integer >= 0;

minimize Number: sum {j in PATTERNS} Cut[j];

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


# ----------------------------------------
# KNAPSACK SUBPROBLEM FOR CUTTING STOCK
# ----------------------------------------

param price {WIDTHS};

var Use {WIDTHS} integer >= 0;

minimize Reduced_Cost:
   1 - sum {i in WIDTHS} price[i] * Use[i];

subj to Width_Limit:
   sum {i in WIDTHS} i * Use[i] <= roll_width;