Wastage reduction in wood cutting (Q1820679)

The problem of cutting planks from sleepers is basically a three- dimensional cutting stock problem but due to practical constraints, it has been formulated and solved as a two-dimensional cutting problem. The resulting linear programming problem cannot be solved by using standard LP packages available as the number of columns of the matrix A runs into millions and are unknown. The columns of matrix A represent the cutting patterns. A special computer package has been developed which generates the cutting patterns as and when required by solving a knapsack problem. Computational experience with a large problem is mentioned. The original problem was finally split up into four subproblems and each solved separately. This study helped in reducing the avoidable wastage by about 50\% of the avoidable wastage earlier.