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Solving a class of stochastic mixed-integer programs with branch and price

机译:用分支和价格求解一类随机混合整数程序

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We begin this paper by identifying a class of stochastic mixed-integer programs that have column-oriented formulations suitable for solution by a branch-and-price algorithm (B&P). We then survey a number of examples, and use a stochastic facility-location problem (SFLP) for a detailed demonstration of the relevant modeling and solution techniques. Computational results with a scenario representation of uncertain costs, demands and capacities show that B&P can be orders of magnitude faster than solving the standard formulation by branch and bound. We also demonstrate how B&P can solve SFLP exactly – as exactly as a deterministic mixed-integer program – when demands and other parameters can be represented as certain types of independent, random variables, e.g., independent, normal random variables with integer means and variances.
机译:我们从确定一类随机混合整数程序开始,该程序具有适用于分支价格算法(B&P)求解的面向列的公式。然后,我们调查了许多示例,并使用随机设施位置问题(SFLP)来详细演示相关的建模和解决方案技术。具有不确定成本,需求和容量的情景表示的计算结果表明,与按分支定界法求解标准公式相比,B&P可以快几个数量级。当需求和其他参数可以表示为某些类型的独立,随机变量(例如具有整数均值和方差的独立,正常随机变量)时,我们还将展示B&P如何精确地解决SFLP(就像确定性混合整数程序一样)。

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