Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems.     

New heuristics for over-constrained flight to gate assignments

We consider the over-constrained Airport Gate Assignment Problem where the number of flights exceed the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distances. The problem is formulated as a binary quadratic programming problem. We design a greedy algorithm and use a Tabu Search meta-heuristic to solve the problem. The greedy algorithm minimizes ungated flights while we devise a new neighbourhood search technique, the Interval Exchange Move, which allows us flexibility in seeking good solutions, especially when flight schedules are dense in time. Experiments conducted give good results.     

A flexible and generic approach to dynamic modelling of supply chains

In this paper, we present a new modelling approach for realistic supply chain simulation. The model provides an experimental environment for informed comparison between different supply chain policies. A basic simulation model for a generic node, from which a supply chain network can be built, has been developed using an object-oriented approach. This generic model allows the incorporation of the information and physical systems and decision-making policies used by each node. The object-oriented approach gives the flexibility in specifying the supply chain configuration and operation decisions, and policies. Stochastic simulations are achieved by applying Latin Supercube Sampling to the uncertain variables in descending order of importance, which reduces the number of simulations required. We also present a case study to show that the model is applicable to a real-life situation for dynamic stochastic studies.     

On a class of preconditioners for solving the Helmholtz equation

In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called “shifted Laplace” preconditioners of the form Δφ−k²φ with . Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR.     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

Dissipative Nonlinear Evolution Equations and Chaos

In this article we have studied the nonlinear interaction between ellipticity and dissipation in a set of model equations (1.1) and established the relation between this interaction and chaos. In addition to theoretical investigations, extensive numerical simulations with these equations have been made, and different routes to chaos have been found. The numerical studies have revealed the chaotic nature of the solutions.     

Rarefied Flow Computations Using Nonlinear Model Boltzmann Equations

High resolution finite difference schemes for solving the nonlinear model Boltzmann equations are presented for the computations of rarefied gas flows. The discrete ordinate method is first applied to remove the velocity space dependency of the distribution function which renders the model Boltzmann equation in phase space to a set of hyperbolic conservation laws with source terms in physical space. Then a high order essentially nonoscillatory method due to Harten et al. (J. Comput. Phys. 71, 231, 1987) is adapted and extended to solve them. Explicit methods using operator splitting and implicit methods using the lower-upper factorization are described to treat multidimensional problems. The methods are tested for both steady and unsteady rarefied gas flows to illustrate its potential use. The computed results using model Boltzmann equations are found to compare well both with those using the direct simulation Monte Carlo results in the transitional regime flows and those with the continuum Navier-Stokes calculations in near continuum regime flows.