A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem
Computers and Operations Research
Heuristics for the variable sized bin-packing problem
Computers and Operations Research
Grouping genetic algorithm for solving the serverconsolidation problem with conflicts
Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation
Hybrid algorithms for the variable sized bin packing problem
HM'10 Proceedings of the 7th international conference on Hybrid metaheuristics
Relaxations and exact solution of the variable sized bin packing problem
Computational Optimization and Applications
Variable neighbourhood search for the variable sized bin packing problem
Computers and Operations Research
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In this paper we consider a one-dimensional bin packing problem where the bins do not have identical sizes, or a variable-sized bin packing problem, to minimize the bin consumption, i.e., the total size of the opened bins. The identical size problem has been extensively studied in the literature both for static and dynamic settings. The worst-case or average-case performance has been analyzed. Our problem setting particularly arises in metal cutting industries. Therefore, it presents a great practical relevance. Four greedy approximation algorithms based on a construction approach called largest object first with least absolute waste (LFLAW), largest object first with least relative waste (LFLRW), least absolute waste (LAW), and least relative waste (LRW) are examined. Their absolute worst-case performances are analyzed. The worst case bounds are 2 for LFLAW and LFLRW, 3 for LAW, and 2+ln 2 for LRW. We also show that these worst-case bounds are tight.