# BIN-PACKING

**DOI:**https://doi.org/10.1007/1-4020-0611-X_75

## PROBLEM DEFINITION

The bin-packing problem is concerned with the determination of the minimum number of bins that are needed to pack a given set of input data items. The problem has numerous applications in operations research, computer science, and engineering, where the items and bins to be packed can be multi-dimensional. These applications include industrial manufacturing, stock cutting, military vehicle loading, television commercial scheduling, job scheduling on multiple processors, integrated circuit manufacturing and fault detection, location testing in linear circuits, and vehicle routing. Since the bin-packing problem is known to be NP-hard, it is of interest to find efficient heuristics that obtain near-optimal solutions to the problem (Garey and Johnson, 1981).

The classical one-dimensional bin-packing problem is defined as follows: Given a positive bin capacity *C* and a list of items *L* = (*p*_{1}, *p*_{2}, ..., *p*_{n}), where *p*_{i} has size *s*(*p*_{i}) satisfying 0 ≤ *s*(*p*_{i}) ≤ *C*, determine the...

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