{"title":"A two-phase heuristic for strip packing: Algorithm and probabilistic analysis","authors":"F. Chauny, R. Loulou, S. Sadones, F. Soumis","doi":"10.1016/0167-6377(87)90006-X","DOIUrl":null,"url":null,"abstract":"<div><p>The strip packing problem consists in laying out a specified list of rectangular pieces on a rectangular strip of fixed width but infinite length, in such a way as to minimized the length of strip used. We present a novel heuristic algorithm for this problem, based on a two-phase approach: the strategic and the tactical; the former has a global view of the problem and proposes a list of patterns to the latter, which in turn is in charge of actually laying out these patterns. The strategic module is based on a linear programming relaxation of the problem, whereas the tactical module is a recursive algorithm based on repeated knapsack operations. The performance of the algorithm is analyzed through a probabilitic analysis on its relative deviation from the (unknown) optimal solution; the deviation is found to converge to zero as problem size increases under some conditions on the problem data.</p></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"6 1","pages":"Pages 25-33"},"PeriodicalIF":0.9000,"publicationDate":"1987-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0167-6377(87)90006-X","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/016763778790006X","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 12
Abstract
The strip packing problem consists in laying out a specified list of rectangular pieces on a rectangular strip of fixed width but infinite length, in such a way as to minimized the length of strip used. We present a novel heuristic algorithm for this problem, based on a two-phase approach: the strategic and the tactical; the former has a global view of the problem and proposes a list of patterns to the latter, which in turn is in charge of actually laying out these patterns. The strategic module is based on a linear programming relaxation of the problem, whereas the tactical module is a recursive algorithm based on repeated knapsack operations. The performance of the algorithm is analyzed through a probabilitic analysis on its relative deviation from the (unknown) optimal solution; the deviation is found to converge to zero as problem size increases under some conditions on the problem data.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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