Online variable-sized bin packing

AbstractThe classical bin packing problem is one of the best-known and most widely studied problems of combinatorial optimization. Efficient offline approximation algorithms have recently been designed and analyzed for the more general and realistic model in which bins of differing capacities are allowed (Friesen and Langston (1986)). In this paper, we consider fast online algorithms for this challenging model. Selecting either the smallest or the largest available bin size to begin a new bin as pieces arrive turns out to yield a tight worst-case ratio of 2. We devise a slightly more complicated scheme that uses the largest available bin size for small pieces, and selects bin sizes for large pieces based on a user-specified fill factor ƒ≥12, and prove that this strategy guarantees a worst-case bound not exceeding 1.5+ƒ2