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This paper studies multi-depot rural postman problems on an undirected graph. These problems extend the well-known undirected rural postman problem to the case where there are several depots instead of just one. Linear integer programming formulations that only use binary variables are proposed for the problem that minimizes the overall routing costs and for the model that minimizes the length of the longest route. An exact branch-and-cut algorithm is presented for each considered model, where violated constraints of both types are separated in polynomial time. Despite the difficulty of the problems, the numerical results from a series of computational experiments with various types of instances illustrate a quite good behavior of the algorithms. When the overall routing costs are minimized, over 43 % of the instances were optimally solved at the root node, and 95 % were solved at termination, most of them with a small additional computational effort. When the length of the longest route is minimized, over 25 % of the instances were optimally solved at the root node, and 99 % were solved at termination.

In this paper the following facility location problem in a mixed planar-network space is considered: We assume that traveling along a given network is faster than traveling within the plane according to the Euclidean distance. A pair of points (A i ,A j ) is called covered if the time to access the network from A i plus the time for traveling along the network plus the time for reaching A j is lower than, or equal to, a given acceptance level related to the travel time without using the network. The objective is to find facilities (i.e. entry and exit points) on the network that maximize the number of covered pairs. We present a reformulation of the problem using convex covering sets and use this formulation to derive a finite dominating set and an algorithm for locating two facilities on a tree network. Moreover, we adapt a geometric branch and bound approach to the discrete nature of the problem and suggest a procedure for locating more than two facilities on a single line, which is evaluated numerically.

This paper introduces a model-based approach to the important data mining tool Multivariate adaptive regression splines (MARS), which has originally been organized in a more model-free way. Indeed, MARS denotes a modern methodology from statistical learning which is important in both classification and regression, with an increasing number of applications in many areas of science, economy and technology. It is very useful for high-dimensional problems and shows a great promise for fitting nonlinear multivariate functions. The MARS algorithm for estimating the model function consists of two algorithms, these are the forward and the backward stepwise algorithm. In our paper, we propose not to use the backward stepwise algorithm. Instead, we construct a penalized residual sum of squares for MARS as a Tikhonov regularization problem which is also known as ridge regression. We treat this problem using continuous optimization techniques which we consider to become an important complementary technology and model-based alternative to the concept of the backward stepwise algorithm. In particular, we apply the elegant framework of conic quadratic programming. This is an area of convex optimization which is very well-structured, herewith, resembling linear programming and, hence, permitting the use of powerful interior point methods. Based on these theoretical and algorithmical studies, this paper also contains an application to diabetes data. We evaluate and compare the performance of the established MARS and our new CMARS in classifying diabetic persons, where CMARS turns out to be very competitive and promising.

Manufacturing of steel involves thermal energy intensive processes with coal as the major input. Energy generated is a direct function of ash content of coal and as such it weighs very high as regards the choice of coal. In this paper, we study a multiobjective transportation problem to introduce a new type of coal in a steel manufacturing unit in India. The use of new type of coal serves three non-prioritized objectives, viz. minimization of the total freight cost, the transportation time and the ratio of ash content to the production of hot metal. It has been observed from the past data that the supply and demand points have shown fluctuations around their estimated values because of changing economic conditions. To deal with uncertainties of supply and demand parameters, we transform the past data pertaining to the amount of supply of the ith supply point and the amount of demand of the jth demand point using level (λ,ρ) interval-valued fuzzy numbers. We use a linear ranking function to defuzzify the fuzzy transportation problem. A transportation algorithm is developed to find the non-dominated solutions for the defuzzified problem. The application of the algorithm is illustrated by numerical examples constructed from the data provided by the manufacturing unit.

In this paper we deal with a slight modification of the extended rapid transit network design problem to allow circular lines. A two-stage approach is proposed for solving this problem. In the first stage, an integer model is solved for selecting the stations to be constructed and the links between them. It drastically reduces the dimension of a modification of a 0–1 model given in the literature to adapt it to our problem. In the second stage, the line design problem is solved by means of a procedure that assigns each selected link to exactly one line under certain constraints. We report some computational experiments that show that our approach also produces a drastic reduction on the computational effort required for solving the modification of the 0–1 model given in the literature.

This paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system’s lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system’s lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system’s lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated.