The generalized bin packing problem under uncertainty
ICACM'11 Proceedings of the 2011 international conference on Applied & computational mathematics
A bounded item bin packing problem over discrete distribution
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Expected performance of the shelf heuristic for 2-dimensional packing
Operations Research Letters
Largest-first sequential selection with a sum constraint
Operations Research Letters
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We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an excellent agreement between the two. We also explain a certain empirically observed anomaly in the behaviour of the algorithm. Finally we establish that asymptotically perfect packing is possible when input items are drawn from a monotonically decreasing density function.