The multiple vehicle traveling purchaser problem (MVTPP) consists of simultaneously selecting suppliers and routing a fleet of homogeneous vehicles to purchase different products at the selected suppliers so that all product demands are fulfilled and traveling and purchasing costs are minimized. We consider variants of the MVTPP in which the capacity of the vehicles can become binding and the demand for each product is one unit. Corresponding solution algorithms from the literature are either branch-and-cut or branch-and-price algorithms, where in the latter case the route-generation subproblem is solved on an expanded graph by applying standard dynamic-programming techniques. Our branch-price-and-cut algorithm employs a novel labeling algorithm that works directly on the original network and postpones the purchasing decisions until the route has been completely defined. Moreover, we define a new branching rule generally applicable in case of unitary product demands, introduce a new family of valid inequalities to apply when suppliers can be visited at most once, and show how product incompatibilities can be handled without considering additional resources in the pricing problem. In comprehensive computational experiments with standard benchmark sets we prove that the new branch-price-and-cut approach is highly competitive.

中文翻译：

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需求单一的多车出行购买者问题的分行砍价算法

多车辆旅行购买者问题（MVTPP）包括同时选择供应商并安排同质车辆车队在选定的供应商处购买不同的产品，以便满足所有产品需求并最小化旅行和采购成本。我们考虑 MVTPP 的变体，其中车辆的容量可以成为约束并且对每种产品的需求是一个单位。文献中相应的解决方案算法是分支和切割算法或分支和价格算法，在后一种情况下，路线生成子问题通过应用标准动态规划技术在扩展图上解决。我们的分支价格和切割算法采用了一种新颖的标记算法，该算法直接在原始网络上工作，并将购买决策推迟到完全定义路线。此外，我们定义了一个新的分支规则，在单一产品需求的情况下普遍适用，引入了一个新的有效不等式系列，以在最多可以访问一次供应商时应用，并展示如何在不考虑定价中的额外资源的情况下处理产品不兼容性问题。在标准基准集的综合计算实验中，我们证明了新的分支价格和削减方法具有很强的竞争力。引入一系列新的有效不等式，以在最多可访问一次供应商时应用，并展示如何在不考虑定价问题中的额外资源的情况下处理产品不兼容性。在标准基准集的综合计算实验中，我们证明了新的分支价格和削减方法具有很强的竞争力。引入一系列新的有效不等式，以在最多可访问一次供应商时应用，并展示如何在不考虑定价问题中的额外资源的情况下处理产品不兼容性。在标准基准集的综合计算实验中，我们证明了新的分支价格和削减方法具有很强的竞争力。