Solving the Assortment and Trim Loss Problem with Branch-and-Price-and-Cut

In this paper, we address the combined assortment and trim loss minimization problem. In real settings, when different stock lengths are available, a common problem is to select a subset of stock lengths from which to cut the ordered items. In the cutting and packing literature, this problem is known as the assortment problem. Solving the assortment and trim loss minimization problem in a single stage yields better cutting plans since one takes into account the whole set of stock lengths while computing the best set of cutting patterns. Here, we present an exact branch-and-price-and-cut algorithm to solve both the assortment and the trim loss minimization problem in a single stage. We use an integrated Integer Linear Programming model to compute lower bounds at the nodes of the branch-and-bound tree, and we derive a robust branching scheme to find the integer optimal solution. We report on an extensive set of computational experiments for random instances. Keywords—Cutting Stock Problem; Assortment Problem; Branch-and-Price-and-Cut.