Article Dans Une Revue INFORMS Journal on Computing Année : 2020

Branch and Price for Chance-Constrained Bin Packing

Résumé

This article describes two versions of the chance-constrained stochastic bin-packing (CCSBP) problem that consider item-to-bin allocation decisions in the context of chance constraints on the total item size within the bins. The first version is a stochastic CCSBP (SP-CCSBP) problem, which assumes that the distributions of item sizes are known. We present a two-stage stochastic mixed-integer program (SMIP) for this problem and a Dantzig–Wolfe formulation suited to a branch-and-price (B&P) algorithm. We further enhance the formulation using coefficient strengthening and reformulations based on probabilistic packs and covers. The second version is a distributionally robust CCSBP (DR-CCSBP) problem, which assumes that the distributions of item sizes are ambiguous. Based on a closed-form expression for the DR chance constraints, we approximate the DR-CCSBP problem as a mixed-integer program that has significantly fewer integer variables than the SMIP of the SP-CCSBP problem, and our proposed B&P algorithm can directly solve its Dantzig–Wolfe formulation. We also show that the approach for the DR-CCSBP problem, in addition to providing robust solutions, can obtain near-optimal solutions to the SP-CCSBP problem. We implement a series of numerical experiments based on real data in the context of surgery scheduling, and the results demonstrate that our proposed B&P algorithm is computationally more efficient than a standard branch-and-cut algorithm, and it significantly improves upon the performance of a well-known bin-packing heuristic.

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Dates et versions

hal-04941861 , version 1 (12-02-2025)

Identifiants

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Zheng Zhang, Brian Denton, Xiaolan Xie. Branch and Price for Chance-Constrained Bin Packing. INFORMS Journal on Computing, 2020, 32 (3), pp.547-564. ⟨10.1287/ijoc.2019.0894⟩. ⟨hal-04941861⟩
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