Existence of local strong solutions to fluid–beam and fluid–rod interaction systems

We study an unsteady nonlinear fluid–structure interaction problem. We consider a Newtonian incompressible two-dimensional flow described by the Navier–Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear wave equation or a linear beam equation. The fluid and the structure systems are coupled via interface conditions prescribing the continuity of the velocities at the fluid–structure interface and the action-reaction principle. Considering three different structure models, we prove existence of a unique local-in-time strong solution, for which there is no gap between the regularity of the initial data and the regularity of the solution enabling to obtain a blow up alternative. In the case of a damped beam this is an alternative proof (and a generalization to non zero initial displacement) of the result that can be found in [20]. In the case of the wave equation or a beam equation with inertia of rotation, this is, to our knowledge the first result of existence of strong solutions for which no viscosity is added. The key points consist in studying the coupled system without decoupling the fluid from the structure and to use the fluid dissipation to control, in appropriate function spaces, the structure velocity.     

Interval availability analysis of a two-echelon,multi-item system

In this paper we analyze the interval availability of a two-echelon, multi-item spare part inventory system. We consider a scenario inspired by a situation that we encountered at Thales Netherlands, a manufacturer of naval sensors and naval command and control systems. Modeling the complete system as a Markov chain we analyze the interval availability and we compute in closed and exact form the expectation and the variance of the availability during a finite time interval [0, T]. We use these characteristics to approximate the survival function using a Beta distribution, together with the probability that the interval availability is equal to one. Comparison of our approximation with simulation shows excellent accuracy, especially for points of the distribution function below the mean value. The latter points are practically most relevant.     

Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature

We investigate the singular limit, as ${\varepsilon \to 0}$ , of the Allen-Cahn equation ${u^\varepsilon_t=\Delta u^\varepsilon+\varepsilon^{-2}f(u^\varepsilon)}$ , with f a balanced bistable nonlinearity. We consider rather general initial data u ₀ that is independent of ${{\varepsilon}}$ . It is known that this equation converges to the generalized motion by mean curvature ?? in the sense of viscosity solutions??defined by Evans, Spruck and Chen, Giga, Goto. However, the convergence rate has not been known. We prove that the transition layers of the solutions ${u^{\varepsilon}}$ are sandwiched between two sharp ??interfaces?? moving by mean curvature, provided that these ??interfaces?? sandwich at t?=?0 an ${\mathcal O({\varepsilon}|\,{\rm ln}\,{\varepsilon}|)}$ neighborhood of the initial layer. In some special cases, which allow both extinction and pinches off phenomenon, this enables to obtain an ${\mathcal O({\varepsilon}|\,{\rm ln}\,{\varepsilon}|)}$ estimate of the location and the thickness measured in space-time of the transition layers. A result on the regularity of the generalized motion by mean curvature is also provided in the Appendix.     

Last time buy decisions for products sold under warranty

Manufacturers supplying products under warranty need a strategy to deal with failures during the warranty period: repair the product or replace it by a new one, depending on e.g. age and/or usage of the failed product. An (implicit) assumption in virtually all models is that new products to replace the failed ones are immediately available at given replacement costs. Because of the short life cycles of many products, manufacturing may be discontinued before the end of the warranty period. At that point in time, the supplier has to decide how many products to put on the shelf to replace failed products under warranty that will be returned from the field (the last time buy decision). This is a trade-off between product availability for replacement and costs of product obsolescence. In this paper, we consider the joint optimization of repair-replacement decisions and the last time buy quantity for products sold under warranty. We develop approximations to estimate the total relevant costs and service levels for this problem, and show that we can easily find near-optimal last time buy quantities using a numerical search. Comparison to discrete event simulation results shows an excellent performance of our methods.     

Variable space search for graph coloring

Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,…,k}) to each vertex of G so that no edge has both endpoints with the same color. We propose a new local search methodology, called Variable Space Search, which we apply to the k-coloring problem. The main idea is to consider several search spaces, with various neighborhoods and objective functions, and to move from one to another when the search is blocked at a local optimum in a given search space. The k-coloring problem is thus solved by combining different formulations of the problem which are not equivalent, in the sense that some constraints are possibly relaxed in one search space and always satisfied in another. We show that the proposed algorithm improves on every local search used independently (i.e., with a unique search space), and is competitive with the currently best coloring methods, which are complex hybrid evolutionary algorithms.     

Markov-modulated Brownian motions perturbed by catastrophes

ABSTRACT

We consider a one-sided Markov-modulated Brownian motion perturbed by catastrophes that occur at some rates depending on the modulating process. When a catastrophe occurs, the level drops to zero for a random recovery period. Then the process evolves normally until the next catastrophe. We use a semi-regenerative approach to obtain the stationary distribution of this perturbed MMBM. Next, we determine the stationary distribution of two extensions: we consider the case of a temporary change of regime after each recovery period and the case where the catastrophes can only happen above a fixed threshold. We provide some simple numerical illustrations.     

Markov-Modulated Brownian Motion with Temporary Change of Regime at Level Zero

We determine the stationary distribution of a one-sided Markov-Modulated Brownian Motion (MMBM) of which the behaviour is modified during the intervals between a visit to level zero and the next visit to a fixed positive level b. We use the semi-regenerative structure of the process, and we also use the fluid approximation for MMBMs introduced by Latouche and Nguyen in 2015. Finally, we show how the expressions can be simplified in some interesting special cases and we conclude by providing some numerical illustrations.     

Comparison of agent-based scheduling to look-ahead heuristics for real-time transportation problems

We consider the real-time scheduling of full truckload transportation orders with time windows that arrive during schedule execution. Because a fast scheduling method is required, look-ahead heuristics are traditionally used to solve these kinds of problems. As an alternative, we introduce an agent-based approach where intelligent vehicle agents schedule their own routes. They interact with job agents, who strive for minimum transportation costs, using a Vickrey auction for each incoming order. This approach offers several advantages: it is fast, requires relatively little information and facilitates easy schedule adjustments in reaction to information updates. We compare the agent-based approach to more traditional hierarchical heuristics in an extensive simulation experiment. We find that a properly designed multi-agent approach performs as good as or even better than traditional methods. Particularly, the multi-agent approach yields less empty miles and a more stable service level.