1994/04/01 by Shoshana Anily, Julien Bramel, David Simchi‐Levi · 1 citation
Engineering · Computer Science · Mathematics · #Optimization and Packing Problems #Advanced Manufacturing and Logistics Optimization #Optimization and Search Problems #Bin packing problem #Bin #Heuristics #Mathematical optimization #Upper and lower bounds #Heuristic #Context (archaeology) #Set (abstract data type) #Mathematics #Function (biology) #Computer science #Algorithm
paper · doi:10.1287/opre.42.2.287
openalex publication_date 1994/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
We 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, we 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. We 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. Our analysis also provides a new worst-case bound for the well studied next-tit decreasing heuristic when the objective is to minimize the number of bins used.