We present here a pricing model which is an extension of the cooperative game concept and which includes a notion of elastic demand. We present some existence results as well as an algorithm, and we conclude by discussing a specific problem related to network pricing.

It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i,j,k,l.

We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient of the regularized function, instead of using ϵ-subgradients of the original objective function. Quadratic convergence for LP is also proved using a more stringent error criterion.

Minimizing shutterings assembling time on construction sites can yield significant savings in labor costs and crane moves. It requires solving a pairing problem that optimizes the ability for the crane to move chains of shutterings as a whole when they can be later reused together to frame another wall of the site. In this paper, we show that this problem is NP-hard in the strong sense as well as both its multiflow and ordering aspects. We also introduce a linear relaxation that computes reasonably good lower bounds of the objective, and describe a Tabu Search based on pairings insertion and ejection that builds promising solutions.

In this paper we, firstly, present a recursive formula of theempirical estimator of the semi-Markov kernel. Then a non-parametricestimator of the expected cumulative operational time forsemi-Markov systems is proposed. The asymptotic properties of thisestimator, as the uniform strongly consistency and normality aregiven. As an illustration example, we give a numerical application.

In telecommunications network design, one of the most frequentproblems is to adjust the capacity on the links of the network in order to satisfy a set of requirements. In the past, theserequirements were demands based on historical data and/or demographic predictions. Nowadays, because of new technologydevelopment and customer movement due to competitiveness, thedemands present considerable variability. Thus, network robustness w.r.t demand uncertainty is now regarded as a majorconsideration. In this work, we propose a min-max-min formulation and a methodology to cope with this uncertainty. We model the uncertainty as the convex hull of certain scenarios and show thatcutting plane methods can be applied to solve the underlying problems. We will compare Kelley, Elzinga-Moore and bundle methods.

The recourse to operation research solutions has strongly increasedthe performances of scheduling task in the High-Level Synthesis(called hardware compilation). Scheduling a whole program is notpossible as too many constraints and objectives interact. We decomposehigh-level scheduling in three steps. Step 1: Coarse-grain schedulingtries to exploit parallelism and locality of the whole program (inparticular in loops, possibly imperfectly nested) with a rough view ofthe target architecture. This produces a sequence of logical steps,each of which contains a pool of macro-tasks. Step 2: Micro-schedulingmaps and schedules each macro-task independently taking into accountall peculiarities of the target architecture. This produces areservation table for each macro-task. Step 3: Fine-grain schedulingrefines each logical step by scheduling all its macro-tasks. Thispaper focuses on the third step.As tasks are modeled as reservation tables, we can express resourceconstraints using dis-equations (i.e., negations of equations). Asmost scheduling problems, scheduling tasks with reservation tables tominimize the total duration is NP-complete. Our goal here is todesign different strategies and to evaluate them, on practicalexamples, to see if it is possible to find optimal solution inreasonable time. The first algorithm is based on integer linearprogramming techniques for scheduling, which we adapt to our specificproblem. Our main algorithmic contribution is an exactbranch-and-bound algorithm, where each evaluation is accelerated byvariant of Dijkstra's algorithm. A simple greedy heuristic is alsoproposed for comparisons. The evaluation and comparison are done onpieces of scientific applications from the PerfectClub and theHLSynth95 benchmarks. The results demonstrate the suitability of thesesolutions for high-level synthesis scheduling.

Most systems are characterized by uncertainties that cause throughput to be highly variable, for example, many modern production processes and services are substantially affected by random yields. When yield is random, not only is the usable quantity uncertain, but the random yield reduces usable capacity and throughput in the system. For these reasons, strategies are needed that incorporate random yield. This paper presents the analysis of the newsvendor model with a general random yield distribution, including the derivation of the optimal order quantity. Results are shown to converge to the basic newsvendor model for the case of perfect yield, and are further demonstrated using the case of general multiplicative random yield. Results have significant impact on both manufacturing and service sectors since the newsvendor model applies to many real-world situations.


The Progressive Second Price mechanism (PSP), recently introduced byLazar and Semret to share aninfinitely-divisible resource among users through pricing, has been shown to verifyvery interesting properties. Indeed, the incentive compatibilityproperty of that scheme, and the convergence toan efficient resource allocation where established, using the frameworkof Game Theory.Therefore, that auction-based allocation and pricing scheme seemsparticularly well-suited to solve congestion problems intelecommunication networks, where the resource to share is theavailable bandwidth on a link.This paper aims atsupplementing the existing results by highlighting some properties of thedifferent equilibria that can be reached. We precisely characterize the possible outcomes of thePSP auction game in terms of players bid price: when the bid fee (cost of a bid update) tends to zero then the bid price of all users at equilibrium gets close to the so-called market clearing price of the resource. Therefore, observing an equilibrium of the PSP auction game gives some accurate information about the market clearing price of the resource.