We study a continuous version of the capacity and flow assignment problem (CFA) where the design cost is combined with an average delay measure to yield a non convex objective function coupled with multicommodity flow constraints. A separable convexification of each arc cost function is proposed to obtain approximate feasible solutions within easily computable gaps from optimality. On the other hand, DC (difference of convex functions) programming can be used to compute accurate upper bounds and...

We study a continuous version of the capacity and flow assignment problem (CFA) where the design cost is combined with an average delay measure to yield a non convex objective function coupled with multicommodity flow constraints. A separable convexification of each arc cost function is proposed to obtain approximate feasible solutions within easily computable gaps from optimality. On the other hand, DC (difference of convex functions) programming can be used to compute accurate upper bounds and...

This paper aims at developing efficient solving methods for an original service network design problem imbued with sustainable issues. Indeed the network has to be designed for short and local supply chain and for fresh food products. The original features of the problem are the seasonality of supply, the limitation of transshipments for a product and no possibility of storage between consecutive periods. Decisions at strategic and tactical level are (1) decisions on a subset of hubs to open among...

By a ternary system we mean an ordered pair $(W,R)$, where $W$ is a finite nonempty set and $R\subseteq W\times W\times W$. By a signpost system we mean a ternary system $(W,R)$ satisfying the following conditions for all $x,y,z\in W$: if $(x,y,z)\in R$, then $(y,x,x)\in R$ and $(y,x,z)\notin R$; if $x\ne y$, then there exists $t\in W$ such that $(x,t,y)\in R$. In this paper, a signpost system is used as a common description of a connected graph and a spanning tree of the graph. By a ct-pair we mean an ordered pair $(G,T)$, where $G$ is a connected graph and $T$ is a spanning tree of $G$. If $(G,T)$ is a ct-pair, then by the guide to...

In this paper, we propose a method which enables to construct almost optimal broadcast schemes on an $n$-dimensional hypercube in the circuit switched, $\Delta$-port model. In this model, an initiator must inform all the nodes of the network in a sequence of rounds. During a round, vertices communicate along arc-disjoint dipaths. Our construction is based on particular sequences of nested binary codes having the property that each code can inform the next one in a single round. This last property is insured...

The irrigation problem is the problem of finding an efficient way to transport a measure μ+ onto a measure μ-. By efficient, we mean that a structure that achieves the transport (which, following [Bernot, Caselles and Morel, Publ. Mat.49 (2005) 417–451], we call traffic plan) is better if it carries the mass in a grouped way rather than in a separate way. This is formalized by considering costs functionals that favorize this property. The aim of this paper is to introduce a dynamical cost functional...