Branch and price for the vehicle routing problem with discrete split deliveries and time windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles’ capacity and customer time windows. Each customer can be visited by more than one vehicle since each customer’s demand, discretized in items, can be split in orders, i.e., feasible combinations of items. In this work, we model the DSDVRPTW assuming that all feasible orders are known in advance. Remarkably, service time at customer’s location depends on the delivered combination of items, which is a modeling feature rarely found in literature. We present a flow-based mixed integer program for the DSDVRPTW, we reformulate it via Dantzig-Wolfe and we apply column generation. The proposed branch-and-price algorithm largely outperforms a commercial solver, as shown by computational experiments on Solomon-based instances. A comparison in terms of complexity between constant service time vs delivery-dependent service time is presented and potential savings are discussed.     

On a Theorem of Van de Ven

A result by Van de Ven characterizes linear subspaces as the only closed submanifolds X ? ? ^N for which the normal bundle exact sequence splits. We show that X is linear assuming only the splitting of the same exact sequence when restricted to some curve contained in X .     

混凝土动态直接拉伸实验技术研究

霍普金森压杆(Split Hopkinson Pressure Bar,简称为SHPB)实验装置越来越多地被应用于混凝土等脆性材料动态压缩力学性能的研究之中。由于种种原因,混凝土动态拉伸的实验研究一般还是通过SHPB实验装置间接进行(例如层裂实验和巴西圆盘实验等)。本文以C30混凝土材料为例,根据霍普金森实验技术的两个基本假定(一维假定和均匀假定),探讨了利用大直径(Φ75mm)霍普金森拉杆(Split Hopkinson Tension Bar,简称为SHTB)实验装置对混凝土类试件进行动态直接拉伸的实验技术问题,提出了一种可行的对混凝土类材料进行直接动态拉伸实验的方法。     

Homogeneous varieties under split solvable algebraic groups

We present a modern proof of a theorem of Rosenlicht, asserting that every variety as in the title is isomorphic to a product of affine lines and punctured affine lines.     

准三维针刺C_f/SiC复合材料室温层向动态压缩力学行为的实验研究

为了研究应变率对准三维针刺碳纤维增韧的碳化硅复合材料(Cf/SiC)层向压缩力学性能的影响,本文利用分离式Hopkinson压杆装置对三维针刺Cf/SiC复合材料进行了应变率为10-4至6.5×103s-1的单轴压缩力学性能测试。实验结果表明,由于材料缺陷,其动态压缩强度分布遵循Weibull分布。破坏时,材料并未表现出典型的脆性破坏,而是在应力达到压缩强度后经历了较大的伪塑性变形才最终破坏。这表明三维针刺Cf/SiC复合材料沿厚度方向针刺的碳纤维有助于提高材料的韧性。同时,材料的压缩强度随应变率的升高显著增大,并与对数应变率近似成线性关系。借助光学显微镜和扫描电镜对压缩断口的观察表明:材料的失效模式随着应变率变化而发生改变。在准静态下,材料主要表现为剪切和分层破坏,而在高应变率下,则主要表现为劈裂。     

冲击载荷下盐岩的力学性能和本构关系研究

利用直径75mm的大尺寸SHPB实验装置开展盐岩的动态压缩性能实验研究,得到了其动态应力应变曲线。分析表明,在冲击压缩载荷作用下,盐岩材料有明显的损伤软化现象和应变率效应。针对实验曲线,通过引入描述材料强度随应变率强化的应变率增强因子和随不可逆变形发展而弱化的损伤因子,提出了含损伤率的相关动态本构模型,拟合得到的本构方程形式比较简单,能够较好地反映盐岩动态实验加载过程的主要特征,具有一定的工程应用价值。     

Scatter search for a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries in Brazil

In this paper, we consider a real-life heterogeneous fleet vehicle routing problem with time windows and split deliveries that occurs in a major Brazilian retail group. A single depot attends 519 stores of the group distributed in 11 Brazilian states. To find good solutions to this problem, we propose heuristics as initial solutions and a scatter search (SS) approach. Next, the produced solutions are compared with the routes actually covered by the company. Our results show that the total distribution cost can be reduced significantly when such methods are used. Experimental testing with benchmark instances is used to assess the merit of our proposed procedure.     

Hessenberg pairs of linear transformations

Let denote a field and V denote a nonzero finite-dimensional vector space over . We consider an ordered pair of linear transformations A:V→V and A^*:V→V that satisfy (i)–(iii) below.

1. [(i)]Each of A,A^* is diagonalizable on V.

2. [(ii)]There exists an ordering of the eigenspaces of A such that

where V_-1=0, V_d+1=0.

3. [(iii)]There exists an ordering of the eigenspaces of A^* such that

where , .

We call such a pair a Hessenberg pair on V. In this paper we obtain some characterizations of Hessenberg pairs. We also explain how Hessenberg pairs are related to tridiagonal pairs.

Treelike comparability graphs

An undirected graph is a treelike comparability graph if it admits a transitive orientation such that its transitive reduction is a tree. We show that treelike comparability graphs are distance hereditary. Utilizing this property, we give a linear time recognition algorithm. We then characterize permutation graphs that are treelike. Finally, we consider the Partitioning into Bounded Cliques problem on special subgraphs of treelike permutation graphs.