分支定价方法求解带二维装箱约束的车辆路径问题EI北大核心CSCD

面向家具、电器等货物的物流配送场景,研究带二维装箱约束的车辆路径问题(2L–CVRP),构建了2L–CVRP的混合整数线性规划模型.为求解大规模2L–CVRP,构建了该问题集合划分模型,提出基于分支定价的方法.针对分支节点的松弛模型,基于列生成策略将其分解为线性规划主问题、带资源和二维装箱约束的最短路径子问题,并提出基于ng-route松弛策略的标签算法和基于禁忌搜索的装箱算法有效求解复杂子问题.仿真结果表明,提出的方法可高效求解大规模2L–CVRP,其中ng-route松弛策略能有效提升算法求解效率,研究成果为装箱约束下大规模车辆路径问题的高效求解提供了有效途径.     

基于列生成算法求解动态库存板坯分配问题

针对钢铁企业中遇到的动态库存板坯分配问题进行了研究。建立了一个0-1整数规划数学模型,该模型的目标是最小化板坯与合同规格差异费用以及板坯在库停留所产生的库存成本费用之和。根据问题特点,使用Danzig-Wolfe策略将这个模型分解为一个带有集划分约束的主问题和一个具有背包特征约束的价格子问题,开发了分支价格算法进行求解。计算结果表明所开发的分支价格算法能够最优求解生产实际问题。     

钢铁企业全流程物流优化问题的建模及分支——定价算法

研究了钢铁企业的全流程物流优化问题, 该问题在确保全流程各个工序机组产能和库存能力限制以及满足客户需求的前提下, 决策炼钢、连铸、热轧及冷轧工序间的物料流向和流量, 最小化物流成本、产能损失及库存费用. 为该问题建立了混合整数规划(Mixed integer programming, MIP)模型. 在问题求解中, 首先对MIP模型进行了Dantzig-Wolfe分解, 得到一个结构相对简单但列变量数目非常多的主问题和四个描述列向量空间的子问题. 然后, 从一个包含部分列变量的限制主问题出发, 通过子问题和主问题之间的迭代来获取主问题线性松弛的最优解. 最后, 将列生成同分支—定界相结合, 即分支—定价算法, 以获取原问题的整数最优解. 对某钢铁企业的实际生产数据扩展的随机算例进行仿真实验, 结果显示所提出的算法能够在合理计算时间内获得最优解或次优解.     

Daily scheduling of caregivers with stochastic times

This paper addresses a daily caregiver scheduling and routing problem arising in home health care or home care service providers. The problem is quite challenging due to its uncertainties in terms of travel and service times derived from changes in road traffic conditions and customer health status in practice. We first model the problem as a stochastic programme with recourse, where the recourse action is to skip customers without services if the caregiver arrives later than their latest starting service time (i.e. hard time window requirements). Then, we formulate the problem as a set partitioning model and solve it with a branch-and-price (B&P) algorithm. Specifically, we devise an effective discrete approximation method to calculate the arrival time distribution of caregivers, incorporate it into a problem-specific label algorithm, and use a removal-and-insertion-based heuristic and the decremental state-space relaxation technique to accelerate the pricing process. Finally, we conduct numerical experiments on randomly generated instances to validate the effectiveness of the discrete approximation method and the proposed B&P algorithm.     

Mathematical model and exact algorithm for the home care worker scheduling and routing problem with lunch break requirements

Home health care or home care (HHC/HC) refers to the delivery of social, medical and paramedical services to clients in their own homes. Each day, care workers start from the HHC/HC centre, visit some clients and return to the centre. During the service delivery process, there is usually a lunch break for each worker. In this paper, we address a real-life home care worker scheduling and routing problem with the consideration of lunch break requirements. A three-index mathematical model is constructed for the problem. The problem is decomposed into a master problem and several pricing sub-problems, and is optimally solved by a branch-and-price (B&P) algorithm. Specifically, a sophisticated label-correcting algorithm is designed to address lunch break constraints in pricing sub-problems; some cutting-edge acceleration strategies are applied during the column generation process. Experimental results show that the proposed B&P algorithm is able to produce satisfied solutions within an acceptable runtime and outperforms the mixed integer programming solver CPLEX.     

Hierarchical Ring Network Design Using Branch-and-Price

We consider the problem of designing hierarchical two layer ring networks. The top layer consists of a federal-ring which establishes connection between a number of node disjoint metro-rings in a bottom layer. The objective is to minimize the costs of links in the network, taking both the fixed link establishment costs and the link capacity costs into account.Hierarchical ring network design problems combines the following optimization problems: Clustering, hub selection, metro ring design, federal ring design and routing problems. In this paper a branch-and-price algorithm is presented for jointly solving the clustering problem, the metro ring design problem and the routing problem. Computational results are given for networks with up to 36 nodes.     

基于分支定价算法的双层轿运车运输问题

整车物流中双层轿运车运输问题属于一类需要考虑乘用车装载(vehicle filling problem, VFP)及轿运车路径规划(vehicle routing problem, VRP)的组合优化问题,称此类问题为VFRP(vehicle filling and routing problem).由于VFP和VRP的问题复杂性均为NP完全问题(non-deterministic polynomial complete problem, NPC),且VFRP等组合优化问题模型的目标函数及约束往往具有非凸结构,使得该类问题的线性化处理、精确算法的设计及求解效率的提升一直是该领域的研究难点.对此,以轿运车使用成本最低为目标,构建双层轿运车的VFRP模型,在此基础上提出两种线性化方法并设计改进分支定价算法(branch-and-price algorithm)以求解:在分支定价算法的基础上,提出结合最为分数策略(most-infeasible-branching strategy)和强分支策略(strong-branching strategy)的分支策略,以及在分支过程中降低可行域维度的...     

连铸-轧制混流生产模式下轧批调度问题的分支-定价算法

研究了连铸——轧制在热装、温装和冷装混流生产模式下的一类新型轧批调度问题.以最小化温装钢坯（热钢锭）缓冷（等待）导致的热能损失和连轧机架切换带来的产能损失为目标,建立了整数规划模型.由于商业优化软件难以在有限时间内直接求得模型的最优解甚至可行解,提出利用Dantzig-Wolfe分解技术将原模型分解为主问题和子问题,采用列生成算法对主问题和子问题进行迭代求解得到原问题的紧下界,最后以列生成算法作为定界机制嵌入分支——定界框架中形成分支——定价算法,执行分支搜索过程以获得整数最优解.本文还从影响分支——定价算法性能的要素出发提出改进策略.针对主问题,提出列生成和拉格朗日松弛混合求解策略来抑制单一列生成算法的尾效应.针对价格子问题,在动态规划算法中提出了基于占优规则和标号下界计算方法来及早消除无效状态空间,加速求解过程.以钢铁企业的实际生产数据和扩展的随机算例进行了数值实验,结果显示所提出改进策略能够突破求解能力的限制,使分支——定价算法在可接受计算时间内求得工业规模问题的最优解.     

单向航道下连续泊位分配与船舶调度集成优化

为改善单向航道连续泊位港口的运营效率,研究泊位分配与船舶进出港调度集成优化.考虑潮汐、进出港时段交替与偏好泊位的影响,建立0-1整数线性规划模型,以船舶偏离偏好泊位成本和滞期成本为优化目标,确定各艘船舶的靠泊位置与进出港时刻.针对问题情境和其特有的约束条件,将原数学模型通过Dantzig-Wolfe分解方法分成主问题模...