The cutting stock problem is one of the six basic types of Cutting and Packing problems and belongs to the input minimization problems category. In these problems, there is a set of orders to be cut and enough stock of raw-material from where to cut all of them. Therefore, the goal is to minimize the total raw-material consumed or, equivalently, to minimize the waste, i.e. the raw-material parts that are not used to satisfy demand. In the one-dimensional form of the problem, only the length of both the raw-material and the ordered pieces is relevant for the problem, i.e. the other two dimensions are common to raw-material and orders and don’t have to be cut. This is the case of cutting paper rolls, wooden torus, or metal frames and bars. A small example of such a problem would be to decide how to cut 100 sets of frames of a length 2.9 m, 2.1 m, and 1.5 m, respectively, from stock objects 7.4 m long. The simplest solution is to make one set from each stock object, since 7.4 = 2.9 + 2.1 + 1.5 + 0.9, and to let the end pieces 0.9 m long be wasted. However, optimization methods allow us to show that the best solution is to cut 30 stock objects according to cutting pattern 1 x 2.9 + 3 x 1.5, 10 stock objects according to cutting pattern 2x2.9 + 1 x 1.5, and 50 stock objects according to cutting pattern 1 x 2,9 + 2 x 2.1. The total number of stock objects required will be 90, as against 100 trunks needed according to the simplest solution. Wastage will be only 10 x 0.1 + 50 x 0.3 = 16 m, that is 2.4 %, and this is the minimum value that can be achieved.

In the multi-period problem, small pieces from orders that are not due in the current period of time (day/week/month) may be cut in advance if this decreases the overall waste. These problems are naturally larger and more complex, but lead to a globally better solution, even when inventory and holding costs are taken into consideration.

However, when dealing with future orders uncertainty arises. In fact, orders many times change before their due date, and in these kind of industries, the change may mainly occur on the quantities to cut and on the due date (orders may be both anticipated or delayed). These unexpected changes not only question the optimality of the generated solutions but also may require replanning and modifying production orders. The goal of this task is to incorporate this type of uncertainty in the multi-period one-dimensional cutting-stock problem so that solutions are more robust regarding the variability induced by uncertainty and, when needed, the changes in the already defined cutting plans are minimized: robust planning and optimized replanning.