Abstract
The stochastic bin packing problem (SBPP) is an extension of the well-studied classical bin packing problem with respect to imperfect information on the item sizes. From a practical point of view, the latter are typically represented by (stochastically independent) normally distributed random variables with given means and variances. In this scenario, the SBPP requires to determine the minimum number of bins needed to pack all the items, with the risk of overloading a bin not exceeding a certain tolerable limit. Such computations are of high relevance in server consolidation applications, where decisions have to be made before witnessing the true item characteristics. The resulting integer optimization problems are generally nonlinear and therefore difficult to solve. For this reason, previous approaches from the literature can only handle small instance sizes exactly. In this work, we present a column generation algorithm using heuristic information and near-optimal solutions of the associated (challenging) pricing problems. Based on numerical tests, we show that in most cases this heuristic approach already leads to an optimal solution, so that much larger instance sizes can now be dealt with in reasonable time.
This work does not relate to the author’s position at Amazon.
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References
Chen, M., Zhang, H., Su, Y.-Y., Wang, X., Jiang, G., Yoshihira, K. (2011). Effective VM sizing in virtualized data centers. In Proceedings of the 12th IFIP/IEEE International Symposium on Integrated Network Management and Workshops, 594–601.
Cohen, M. C., Keller, P. W., Mirrokni, V., & Zadimoghaddam, M. (2019). Overcommitment in Cloud Services: Bin Packing with Chance Constraints. Management Science, 65(7), 3255–3271.
Delorme, M., Iori, M., & Martello, S. (2016). Bin packing and Cutting Stock Problems: Mathematical Models and Exact Algorithms. European Journal of Operational Research, 255, 1–20.
Goyal, V., & Ravi, R. (2010). A PTAS for the chance-constrained knapsack problem with random item sizes. Operations Research Letters, 38(3), 161–164.
Klopfenstein, O., & Nace, D. (2008). A robust approach to the chance-constrained knapsack problem. Operations Research Letters, 36, 628–632.
Martinovic, J., Hähnel, M., Scheithauer, G., Dargie, W., Fischer, A. (2019). Cutting stock problems with nondeterministic item lengths: A new approach to server consolidation. 4OR 17(2), 173–200.
Martinovic, J., Selch, M. (2022). Mathematical models and approximate solution approaches for the stochastic bin packing problem. Computers and Operations Research 135, Article 105439.
Perboli, G., Tadei, R., & Baldi, M. (2012). The Stochastic Generalized Bin Packing Problem. Discrete Applied Mathematics, 160(7–8), 1291–1297.
Wang, M., Meng, X., Zhang, L. (2011). Consolidating virtual machines with dynamic bandwidth demand in data centers. In Proceedings IEEE INFOCOM, pp. 71–75.
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Martinovic, J., Strasdat, N., Côté, JF., de Lima, V.L. (2023). A Heuristic Column Generation Approach for the Stochastic Bin Packing Problem. In: Grothe, O., Nickel, S., Rebennack, S., Stein, O. (eds) Operations Research Proceedings 2022. OR 2022. Lecture Notes in Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-24907-5_16
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