Let x j be the number of times the j th pattern is used. Of course, this set of patterns is probably not adequate for solving the problem. The main linear program and the knapsack problem are solved consecutively until there are no more patterns to include in the main problem. In solving the cutting stock problem using the delayed column generation method, we solve a subproblem called the Knapsack problem. W i to include in the pattern.
L is the length of the rolls.
Once the knapsack problem has been solved, the integer variables z i represent the number of required widths to include in the new pattern. Otherwise, this new pattern will be added to the first linear program. Procedure Select a set of patterns for the linear program. Solve the linear program. Using the dual prices, solve the knapsack problem.