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A tractable two-stage robust winner determination model for truckload service procurement via combinatorial auctions

机译：通过组合拍卖的卡车服务采购的易于处理的两阶段稳健赢家确定模型

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摘要

A combinatorial auction is one of the adopted mechanisms for truckload (TL) service procurement. In such an auction, the shipper faces a well-known winner determination problem (WDP): the shipper, as the auctioneer, is given bids submitted by a group of carriers. In most literature, WDP is modeled as a deterministic mixed-integer program (MIP) and is solved by standard MIP algorithms. However, in practice, the exact shipping demand is unavailable until after the auction. This shipment volume uncertainty has a significant impact on the solution to WDP. Therefore, a deterministic winner determination model with an estimate of shipment volume may not provide solutions that attain low procurement costs. This paper proposes a new tractable two-stage robust optimization (RO) approach to solve WDP for TL service procurement under shipment volume uncertainty. Assuming that only historical data is available, we propose a data-driven approach based on the central limit theorem (CLT) to construct polyhedral uncertainty sets. In particular, we consider two random cases: independent shipment volume and correlated shipment volume. A two-stage RO model with integer first-stage decision variables and continuous recourse variables is then formulated. We develop a reformulation solution method and use numerical tests to demonstrate that it is much more computationally efficient than the widely adopted Benders' type constraint generation algorithm. We demonstrate by numerical tests that real-world sized instances of TL service procurement problems can be solved by our proposed robust method. Moreover, we compare our robust approach with benchmark and show that it is more tractable and robust to uncertainty. (C) 2015 Elsevier Ltd. All rights reserved.
机译：组合拍卖是采用的卡车运输（TL）服务采购机制之一。在这样的拍卖中，托运人面临着一个众所周知的获胜者确定问题（WDP）：作为拍卖人，托运人被一组承运人提交了投标书。在大多数文献中，WDP被建模为确定性混合整数程序（MIP），并通过标准MIP算法求解。但是，实际上，要到拍卖后才能获得确切的运输需求。这种装运量的不确定性对WDP解决方案有重大影响。因此，具有估计装运量的确定性获胜者确定模型可能无法提供获得较低采购成本的解决方案。本文提出了一种新的可处理的两阶段鲁棒优化（RO）方法，以解决在装运量不确定的情况下用于TL服务采购的WDP。假设只有历史数据可用，我们建议基于中心极限定理（CLT）的数据驱动方法来构造多面体不确定性集。特别是，我们考虑两种随机情况：独立的发货量和相关的发货量。然后建立具有整数第一阶段决策变量和连续追索变量的两阶段RO模型。我们开发了一种重新制定解决方案的方法，并通过数值测试证明了它比广泛采用的Benders类型约束生成算法具有更高的计算效率。我们通过数值测试证明，通过我们提出的健壮方法可以解决TL服务采购问题的实际规模实例。此外，我们将稳健的方法与基准进行了比较，并表明它对不确定性更易处理且更可靠。 （C）2015 Elsevier Ltd.保留所有权利。

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