In this paper, we investigate the vehicle routing problem with release and due dates (VRPRD), which is a new variant of vehicle routing problem (VRP). In the problem, the order required by a customer is available for delivery later than its release date. A penalty cost, called tardiness cost, will be imposed if a customer is served after its due date. The objective of the VRPRD is to minimize the total routing and weighted tardiness costs. To address the problem, we develop an exact branch-price-and-cut algorithm based on the set-partitioning formulation. An effective bidirectional labeling algorithm is proposed to deal with the pricing problem. Numerical studies have verified that the proposed algorithm can obtain the exact optimal solutions for more than 75$\%$ of benchmark instances within approximately six minutes on average.

在本文中，我们研究了具有发布和到期日（VRPRD）的车辆路径问题，这是车辆路径问题（VRP）的新变体。在问题中，客户所需的订单可在其下达日期之后交付。如果在到期日之后送达客户，将收取称为拖延费的罚款。VRPRD的目标是最大程度地减少总布线和加权拖延成本。为了解决该问题，我们基于集合划分公式开发了一种精确的分支价格削减算法。提出了一种有效的双向标注算法来解决定价问题。数值研究证明，该算法可以为超过75种算法获得精确的最优解。$％$ 平均约六分钟之内的基准实例。