The Cutting-Stock Approach to Bin Packing: Theory and Experiments
نویسندگان
چکیده
We report on an experimental study of the Gilmore-Gomory cutting-stock heuristic and related LP-based approaches to bin packing, as applied to instances generated according to discrete distributions. No polynomial running time bound is known to hold for the Gilmore-Gomory approach, and empirical operation counts suggest that no straightforward implementation can have average running time O(m), where m is the number of distinct item sizes. Our experiments suggest that by using dynamic programming to solve the unbounded knapsack problems that arise in this approach, we can robustly obtain average running times that are o(m) and feasible for m well in excess of 1,000. This makes a variant on the previously un-implemented asymptotic approximation scheme of Fernandez de la Vega and Lueker practical for arbitrarily large values of m and quite small values of †. We also observed two interesting anomalies in our experimental results: (1) running time decreasing as the number n of items increases and (2) solution quality improving as running time is reduced and an approximation guarantee is weakened. We provide explanations for these phenomena and characterize the situations in which they occur.
منابع مشابه
Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints
The paper examines a new problem in the irregular packing literature that has existed in industry for decades; two-dimensional irregular (convex) bin packing with guillotine constraints. Due to the cutting process of certain materials, cuts are restricted to extend from one edge of the stock-sheet to another, called guillotine cutting. This constraint is common place in glass cutting and is an ...
متن کاملTwo-stage two-dimensional guillotine cutting stock problems with usable leftover
In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...
متن کاملTwo-stage two-dimensional guillotine cutting problems with usable leftovers∗
In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...
متن کاملAnt Colony Optimisation and Local Search for Bin Packing and Cutting Stock Problems
The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for real-world problems we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary ...
متن کاملAbstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...
متن کامل