Towards Bin Packing (preliminary problem survey, models with multiset estimates)

Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items

In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...

Best-fit Bin-packing with Random Order Ecole Normale Supérieure De Lyon Best-fit Bin-packing with Random Order Best-fit Bin-packing with Random Order

Best t is the best known algorithm for on line bin packing in the sense that no algorithm is known to behave better both in the worst case and in the average uniform case In practice Best t appears to perform within a few percent of optimal In this paper we study the expected performance ratio taking the worst case multiset of items L and assuming that the elements of L are inserted in random o...

Improved Bin Completion for Optimal Bin Packing and Number Partitioning

The bin-packing problem is to partition a multiset of n numbers into as few bins of capacity C as possible, such that the sum of the numbers in each bin does not exceed C. We compare two existing algorithms for solving this problem: bin completion (BC) and branch-and-cut-and-price (BCP). We show experimentally that the problem difficulty and dominant algorithm are a function of n, the precision...

 Abstract: 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...

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  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 objective fu...