Article ID: | iaor1995257 |
Country: | United States |
Volume: | 42 |
Issue: | 2 |
Start Page Number: | 287 |
End Page Number: | 299 |
Publication Date: | Mar 1994 |
Journal: | Operations Research |
Authors: | Simchi-Levi David, Anily Shoshana, Bramel Julien |
Keywords: | heuristics |
The authors consider the famous bin packing problem where a set of items must be stored in bins of equal capacity. In the classical version, the objective is to minimize the number of bins used. Motivated by several optimization problems that occur in the context of the storage of items, the authors study a more general cost structure where the cost of a bin is a concave function of the number of items in the bin. The objective is to store the items in such a way that total cost is minimized. Such cost functions can greatly alter the way the items should be assigned to the bins. The authors show that some of the best heuristics developed for the classical bin packing problem can perform poorly under the general cost structure. On the other hand, the so-called next-fit increasing heuristic has an absolute worst-case bound of no more than 1.75 and an asymptotic worst-case bound of 1.691 for any concave and monotone cost function. The present analysis also provides a new worst-case bound for the well studied next-fit decreasing heuristic when the objective is to minimize the number of bins used.