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The Capacitated Arc Routing Problem. A heuristic algorithm.

Enrique. Benavent, V. Campos, Angel Corberán, Enrique Mota (1990)

Qüestiió

In this paper we consider the Capacitated Arc Routing Problem, in which a fleet of K vehicles, all of them based on a specific vertex (the depot) and with a known capacity Q, must service a subset of the edges of the graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity.A heuristic algorithm for this problem is proposed consisting of: the selection of K centers, the construction of K connected graphs with associated loads not exceeding the vehicle...

The complexity of short schedules for uet bipartite graphs

Evripidis Bampis (2010)

RAIRO - Operations Research

We show that the problem of deciding if there is a schedule of length three for the multiprocessor scheduling problem on identical machines and unit execution time tasks in -complete even for bipartite graphs, i.e. for precedence graphs of depth one. This complexity result extends a classical result of Lenstra and Rinnoy Kan [5].

The formation of a tree leaf

Qinglan Xia (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...

The inverse carrier problem

Grant B. Gustafson, Miroslav Laitoch (2002)

Czechoslovak Mathematical Journal

The problem was motivated by Borůvka’s definitions of the carrier and the associated carrier. The inverse carrier problem is precisely defined and partially solved. Examples are given.

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