Fuel cost contributes to a significant portion of operating cost in cargo transportation. Though classic routing models usually treat fuel cost as input data, fuel consumption heavily depends on the travel speed, which has led to the study of optimizing speeds over a given fixed route. In this paper, we propose a joint routing and speed optimization problem to minimize the total cost, which includes the fuel consumption cost. The only assumption made on the dependence between the fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set partitioning formulation and a branch-cut-and-price algorithm to solve this problem. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time.
Improved formulations of the joint order batching and picker routing problem
订单拣选是从仓库的存储位置检索订购产品的过程。在拣货员到零件的订单拣货系统中，两个或多个客户订单可以被分组并分配给单个拣货员。然后，必须做出关于拣货行程期间物品的访问顺序的路由决策。（J.Won和S.Olafsson 2005）发现，与单独和顺序解决这两个问题相比，解决配送和路由的集成问题使仓库管理员能够更有效地组织订单拣选操作。因此，我们调查的数学规划制定这一综合问题。我们根据Valle，Beasley和da Cunha 2017的发现提出了几种改进的公式，可以显着改善计算结果。更具体地说，我们重建的连接约束，并产生新的切割平面在我们的分支和切割框架。我们还讨论了一些问题的性质，通过研究的图形表示的结构，我们提出了两种类型的附加约束。我们还考虑了这个问题的无逆转的情况。我们提出了有效的配方，通过建立不同的辅助图。最后，我们提出了计算结果公开可用的测试问题，单块和多块仓库配置
A bin packing formulation for the joint batching, routing and sequencing problem
CNRS, Grenoble INP, G-SCOP, University of Grenoble Alpes（法国国家科学研究中心，格勒诺布尔理工学院，G-SCOP，格勒诺布尔阿尔卑斯大学）；Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL（里尔大学，法国国家科学研究中心，法国国家信息与自动化研究所，里尔中央理工学院，CRIStAL联合研究实验室）；Department of Mathematics, Computer Science and Physics, University of Udine（乌迪内大学数学、计算机与物理系）；INSA Lyon, Université Lumière Lyon 2, Université Claude Bernard Lyon 1, Université Jean Monnet Saint-Etienne, DISP UR4570（里昂国立应用科学学院，里昂第二大学，里昂第一大学，圣艾蒂安让·莫奈大学，DISP联合研究实验室）
