Summary: Best-first search is a widely used problem solving technique in the field of artificial intelligence. The method has useful applications in operations research as well. Here we describe an application to constrained two-dimensional cutting stock problems of the following type: A stock rectangle \(S\) of dimensions \((L,W)\) is supplied. There are \(n\) types of demanded rectangles \(r_ 1,r_ 2,\dots,r_ n\) with the \(i\)th type having length \(l_ i\), width \(w_ i\), valued \(v_ i\), and demand constraint \(b_ i\). It is required to produce, from the stock rectangle \(S\), \(a_ i\) copies of \(r_ i\), \(1\leq i\leq n\), to maximize \(a_ 1v_ 1+a_ 2v_ 2+\dots+a_ nv_ n\) subject to the constraints \(a_ i\leq b_ i\). Only orthogonal guillotine cuts are permitted. All parameters are integers. A best-first tree search algorithm based on Wang’s bottom-up approach is described that guarantees optimal solutions and is more efficient than existing methods.