In recent years, balanced network optimization problems play an important role in practice, especially in information transmission, industry production and logistics management. In this paper, we consider some logistics optimization problems related to the optimal tree structures in a network. We show that the most optimal subtree problem is NP-hard by transforming the connected dominating set problem into this model. By constructing the network models of the most balanced spanning tree problem with edge set restrictions, and by finding the optimal subtrees in special networks, we present efficient computational methods for solving some logistics problems.

The canonical configuration of a solid particle bouncing on a wall in a viscous fluid is considered here, focusing on rough particles as encountered in most of the laboratory experiments or applications. In that case, the particle deformation is not expected to be significant prior to solid contact. An immersed boundary method (IBM) allowing the fluid flow around the solid particle to be numerically described is combined with a discrete element method (DEM) in order to numerically investigate the dynamics of the system. Particular attention is paid to modelling the lubrication force added in the discrete element method, which is not captured by the fluid solver at very small scale. Specifically, the proposed numerical model accounts for the surface roughness of real particles through an effective roughness length in the contact model, and considers that the time scale of the contact is small compared to that of the fluid. The present coupled method is shown to quantitatively reproduce available experimental data and in particular is in very good agreement with recent measurement of the dynamics of a particle approaching very close to a wall in the viscous regime $St \le {O}(10)$, where $St$ is the Stokes number which represents the balance between particle inertia and viscous dissipation. Finally, based on the reliability of the numerical results, two predictive models are proposed, namely for the dynamics of the particle close to the wall and the effective coefficient of restitution. Both models use the effective roughness height and assume the particle remains rigid prior to solid contact. They are shown to be pertinent to describe experimental and numerical data for the whole range of investigated parameters.

This paper presents a simple and computationally tractable method which recursively computes the stationary probabilities of the queue size in an M/G/1 queueing system with variable service rate. For each service two possible service types are available and the service rule is characterized by two switch-over levels. The computational approach discussed in this paper can be applied to a variety of queueing problems.