Setup and Open-Stacks Minimization in One-Dimensional Stock Cutting

Abstract

The primary objective in cutting and packing problems is trim loss or material input minimization (in stock cutting) or value maximization (in knapsack-type problems). However, in real-life production we usually have many other objectives (costs) and constraints. Probably the most complex auxiliary criteria of a solution are the number of different cutting patterns (setups) and the maximum number of open stacks during the cutting process. There are applications where the number of stacks is restricted to two. We design a sequential heuristic to minimize material input while restricting the number of open stacks to any given limit. Then, the heuristic is simplified and integrated into a setup minimization approach in order to combine setup and open stacks minimization. To get a smaller number of open stacks, we may split up the problem into several parts of smaller size. Different solutions are evaluated in relation to the multiple objectives using the PARETO criterion.

An effective solution for a real cutting stock problem in manufacturing plastic rolls

“…Basic ideas of these and other algorithms are summarized in Haessler (1991). Recently, in Belov and Scheithauer (2007) an adaptive sequential heuristic, termed sequential value correction (SVC), is proposed that aims at minimizing not only the number of setups but also the number of open stacks. However they consider a simplified model in which an order is packed into only one stack, while in real situations it is usual that more than one stack is required for each order.…”

“…Moreover, the repairing mechanism may be implemented by strategies other than local search, such as greedy or even an evolutionary algorithm. The simplified problem is solved by means of a Sequential Heuristic Randomized Procedure (SHRP) very similar to the Sequential Value Correction (SVC) proposed in Belov and Scheithauer (2007). These procedures construct a solution pattern after pattern and assign a frequency to each one.…”

“…So, in general, it is better not to select the best patterns at the beginning, in order to have the chance to obtain good patterns at the end as well. In order to do so, in Belov and Scheithauer (2007) the SVC procedure is proposed, which is based on the concept of pseudo-price. The idea is quite simple; at the beginning each roll has a price equal to its width li.…”

“…To do this, we have chosen the Sequential Value Correction (SVC) procedure and the benchmark problems proposed in Belov and Scheithauer (2007). These problems can be downloaded from http://www.math.tu-dresden.de/˜capad/.…”

“…By varying one of the parameters, all 9 classes are obtained. In the first set of experiments, we have considered only the classes 1, 4 and 9 (as was done in Belov and Scheithauer (2007) for some preliminary experiments) that correspond to the parame-…”