考虑车辆和设施容量的选址路径双因子近似
Bifactor Approximation for Location Routing with Vehicle and Facility Capacities
摘要：
选址-路径选择是物流中的一个基本规划问题，在这个问题中，关于设施（仓库、配送中心、仓库等）的位置的战略性选址决策。是基于对运营路由成本的准确估计而采取的。我们提出了一种近似算法，对于该问题的一般容量限制版本，具有已证明的最坏情况的算法在运行时间和解决方案质量方面都有保证，其中车辆和设施都是容量限制的。在此之前，这种算法只知道在特殊情况下，设施是uncapacitated或他们的能力可以任意扩展的线性成本。以前建立的下限，已知近似的最优解值以及在无能力的情况下，可以由一个任意的因素，在一般情况下。我们表明，这个问题可以克服的双因子近似算法，可能会稍微超过设施容量的可调，任意小的利润率，而近似的最佳成本由一个常数因子。除了这些已被证明的最坏情况下的保证，我们还评估了我们的算法在一个全面的计算研究的实际性能，表明该方法允许有效的计算的实例大小超出了目前的国家的最先进的算法的接近最优的解决方案。
英文摘要：
Location Routing is a fundamental planning problem in logistics, in which strategic location decisions on the placement of facilities (depots, distribution centers, warehouses etc.) are taken based on accurate estimates of operational routing costs. We present an approximation algorithm, i.e., an algorithm with proven worst-case guarantees both in terms of running time and solution quality, for the general capacitated version of this problem, in which both vehicles and facilities are capacitated. Before, such algorithms were only known for the special case where facilities are uncapacitated or where their capacities can be extended arbitrarily at linear cost. Previously established lower bounds that are known to approximate the optimal solution value well in the uncapacitated case can be off by an arbitrary factor in the general case. We show that this issue can be overcome by a bifactor approximation algorithm that may slightly exceed facility capacities by an adjustable, arbitrarily small margin while approximating the optimal cost by a constant factor. In addition to these proven worst-case guarantees, we also assess the practical performance of our algorithm in a comprehensive computational study, showing that the approach allows efficient computation of near-optimal solutions for instance sizes beyond the reach of current state-of-the-art heuristics.
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