A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

A hybrid technique using constraint programming and linear programming is applied to the problem of scheduling with earliness and tardiness costs. The linear model maintains a set of relaxed optimal start times which are used to guide the constraint programming search heuristic. In addition, the constraint programming problem model employs the strong constraint propagation techniques responsible for many of the advances in constraint programming for scheduling in the past few years. Empirical results validate our approach and show, in particular, that creating and solving a subproblem containing only the activities with direct impact on the cost function and then using this solution in the main search, significantly increases the number of problems that can be solved to optimality while significantly decreasing the search time.     

The Linear Rational Pseudospectral Method with Preassigned Poles

We present a linear rational pseudospectral (collocation) method with preassigned poles for solving boundary value problems. It consists in attaching poles to the trial polynomial so as to make it a rational interpolant. Its convergence is proved by transforming the problem into an associated boundary value problem. Numerical examples demonstrate that the rational pseudospectral method is often more efficient than the polynomial method.     

Making Use of Incomplete Observations for Regression in Bivariate Normal Model

Two estimates of the regression coefficient in bivariate normal distribution are considered: the usual one based on a sample and a new one making use of additional observations of one of the variables. They are compared with respect to variance. The same is done for two regression lines. The conclusion is that the additional observations are worth using only when the sample is very small.     

Robust Output Tracking Control of an Uncertain Linear System via a Modified Optimal Linear-Quadratic Method

This study investigates the robust output tracking problem for a class of uncertain linear systems. The uncertainties are assumed to be time invariant and to satisfy the matching conditions. According to the selected nominal parameters, an optimal solution with a prescribed degree of stability is determined. Then, an auxiliary input via the use of an adapting factor, connected to the nominal optimal control, is introduced to guarantee the robustness and prescribed degree of stability for the output tracking control of the uncertain linear systems. This method is very simple and effective and can reject bounded uncertainties imposed on the states. A maglev vehicle model example is given to show its effectiveness.     

Invariant Simultaneous Solutions of Evolution Equations of Integrable Hierarchies

We construct classical point symmetry groups for joint pairs of evolution equations (systems of equations) of integrable hierarchies related to the auxiliary equation of the method of the inverse problem of second order. For the two cases: the hierarchy of Korteweg--de Vries (KdV) equations and of the systems of Kaup equations, we construct simultaneous solutions invariant with respect to the symmetry group. The problem of the construction of these solutions can be reduced, respectively, to the first and second Painlevé equations depending on a parameter. The Painlevé equations are supplemented by the linear evolution equations defining the deformation of the solution of the corresponding Painlevé equation.     

On Oscillation Criteria of Fourth Order Linear Differential Equations

The paper deals with oscillation criteria of fourth order linear differential equations with quasi-derivatives.     

Optimal Operations Management and Network Planning of a District Heating System with a Combined Heat and Power Plant

District heating plants are becoming more common in European cities. These systems make it possible to furnish users with warm water while locating the production plants in the outskirts having the double benefit of lowering the impact of pollution on the center of the city and achieving better conversion performances. In order to amortize the costs throughout the year, the system often includes a combined heat and power (CHP) plant, to exploit the energy during the summer as well, when the demand for warm water decreases. A linear programming model for the optimal resource management of such a plant is presented and some results for a real case are reported. A distribution network design problem is also addressed and solved by means of mixed integer linear programming.     

Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.