Generating optimal cutting patterns for rectangular blanks of a single size

This paper deals with the problem of minimizing trim loss in cutting rectangular blanks of a single size from a rectangular sheet using orthogonal guillotine cuts. First we prove that we can obtain the unconstrained optimal layout by searching among normal multi-section layouts. Next we present an unconstrained algorithm to search for it. The unconstrained algorithm uses a branch-and-bound method with a tight upper bound. Later we discuss the algorithm for the constrained problem where the blank demand must be met exactly. Finally, the unconstrained algorithm is extended to cope with the blade length constraint. Experimental computations show that the algorithms are extremely efficient.