Abstract: Abstract
Many applications in operations research begin with a set of points in a Euclidean space that is partitioned into clusters. Common data analysis tasks then are to devise a classifier deciding to which of the clusters a new point is associated, finding outliers with respect to the clusters, or identifying the type of clustering used for the partition. One of the common kinds of clusterings are (balanced) least-squares assignments with respect to a given set of sites. For these, there is a ‘separating power diagram’ for which each cluster lies in its own cell. In the present paper, we aim to develop new, efficient algorithms for outlier detection and the computation of thresholds that measure how similar a clustering is to a least-squares assignment for fixed sites. For this purpose, we devise a new model for the computation of a ‘soft power diagram’, which allows a soft separation of the clusters with ‘point counting properties’; e.g. we are able to prescribe the maximum number of points we wish to classify as outliers. As our results hold for a more general non-convex model of free sites, we describe it and our proofs in this more general way. We show that its locally optimal solutions satisfy the aforementioned point counting properties, by studying the corresponding optimality conditions. For our target applications that use fixed sites, our algorithms are efficiently solvable to global optimality by linear programming. PubDate: 2014-10-12

Abstract: Abstract
In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concepts of (Φ, ρ)-V-type I, (pseudo, quasi) (Φ, ρ)-V-type I and (quasi, pseudo) (Φ, ρ)-V-type I functions, in which the involved functions are locally Lipschitz. Based upon these generalized (Φ, ρ)-V-type I functions, the sufficient optimality conditions for weak efficiency, efficiency and proper efficiency are derived. Mond-Weir duality results are also established under the aforesaid functions. PubDate: 2014-10-04

Abstract: In this paper, we introduced modified Mann iterative algorithms by the new hybrid projection method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of the split generalized equilibrium problem and the set of solutions of the general system of the variational inequality problem for two-inverse strongly monotone mappings in real Hilbert spaces. The strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions are provided. PubDate: 2014-10-03

Abstract: Abstract
Upgrading p-median problem is a problem of finding the best median of the given graph through modification of its parameters. The current paper develops a polynomial-time model to address this problem when the weights of vertices can be varying under a given budget. Moreover, in the case where the considering graph has a special structure, namely a path, a linear time algorithm will be proposed for solving the problem with uniform cost. PubDate: 2014-10-02

Abstract: Abstract
A new polynomial algorithm is developed for the classical multiprocessor scheduling problem in which independent jobs are nonpreemptively scheduled on identical parallel machines with the objective of minimizing the makespan, i.e. the latest job finishing time. The algorithm at first generates and merges a set of partial solutions in order to obtain a feasible solution for the multiprocessor scheduling problem. Then a set of bin packing problems are solved in order to improve the solution, by iteratively using a M
u
l
t
i
F
i
t type procedure on different job sets. The effectiveness of this approach is evaluated by solving a large number of benchmark instances. The results indicate that the proposed algorithm, called PSMF, is very competitive with well known constructive algorithms for a wide range of instances. Furthermore, PSMF is competitive with respect to some of the best heuristics for parallel machine scheduling problems only when it uses a 2-exchange procedure. PubDate: 2014-09-26

Abstract: When we are dealing with multivariate problem then we need an allocation which is optimal for all the characteristics in some sense because the individual optimum allocations usually differ widely unless the characteristics are highly correlated. So an allocation called “Compromise allocation” is to be worked out suggested by Cochran. When auxiliary information is also available, it is customary to use it to increase the precision of the estimates. Moreover, for practical implementation of an allocation, we need integer values of the sample sizes. In the present paper the problem is to determine the integer optimum compromise allocation when the population means of various characteristics are of interest and auxiliary information is available for the separate and combined ratio and regression estimates. This paper considers the optimum compromise allocation in multivariate stratified sampling with non-linear objective function and probabilistic non-linear cost constraint. The probabilistic non-linear cost constraint is converted into equivalent deterministic one by using Chance Constrained programming. The formulated multi-objective nonlinear programming problem is solved by Fuzzy Goal programming approach and Chebyshev approximation. Numerical illustration is also given to show the practical utility of the approaches. PubDate: 2014-09-01

Abstract: In this paper, three approaches given by Dinklebaeh (Manag Sci 13(7):492–498, 1967) and Jagannathan (Z Oper Res 17:618–630, 1968) for both primal and mixed type dual of a non differentiable multiobjective fractional programming problem in which the numerator of objective function contains square root of positive semi definite quadratic form are introduced. Also, the necessary and sufficient conditions of efficient solution for fractional programming are established and a parameterizations technique is used to established duality results under generalized ρ-univexity assumption. PubDate: 2014-09-01

Abstract: Considering the possible correlation between the characteristics (variables) in multivariate stratified random sampling, a modified Prékopa’s approach is suggested for the problem of optimum allocation in multivariate stratified random sampling. An example is solved by applying the proposed methodology. PubDate: 2014-09-01

Abstract: Capacitated covering models aim at covering the maximum amount of customers’ demand using a set of capacitated facilities. Based on the assumptions made in such models, there is a unique scenario to open a facility in which each facility has a pre-specified capacity and an operating budget. In this paper, we propose a generalization of the maximal covering location problem, in which facilities have different scenarios for being constructed. Essentially, based on the budget invested to construct a given facility, it can provide different service levels to the surrounded customers. Having a limited budget to open the facilities, the goal is locating a subset of facilities with the optimal opening scenario, in order to maximize the total covered demand and subject to the service level constraint. Integer linear programming formulations are proposed and tested using ILOG CPLEX. An iterated local search algorithm is also developed to solve the introduced problem. PubDate: 2014-09-01

Abstract: In this paper, we are interested in handling the limited availability of machines in the two-stage assembly flow shop scheduling problems. Emphasis is put on the semiresumable case with respect to the minimization of the makespan. We provide, when possible, heuristics with a tight worst-case ratio bound of 2. PubDate: 2014-09-01

Abstract: In this paper, we consider the application of revenue management techniques in the context of the car rental industry. In particular, the paper presents a dynamic programming formulation for the problem of assigning cars of several categories to different segments of customers, with rental requests arising dynamically and randomly with time. Customers make a rental request for a given type of car, for a given number of days at a given pickup time. The rental firm can satisfy the demand for a given product with either the product requested or with a car of at most one category superior to that initially required, in this case an “upgrade” can take place. The one-way rental scenario, which allows the possibility of the rental starting and ending at different locations, is also addressed. In the framework considered, the logistic operator has to decide whether to accept or reject a rental request. Since the proposed dynamic programming formulations are impractical due to the curse of dimensionality, linear programming approximations are used to derive revenue management decision policies for the operator. Indeed, primal and dual acceptance policies are developed (i.e. booking limits, bid prices) and their effectiveness is assessed on the basis of an extensive computational phase. PubDate: 2014-09-01

Abstract: In this paper, we study a renewal input working vacations queue with state dependent services and Bernoulli-schedule vacations. The model is analyzed with single and multiple working vacations. The server goes for exponential working vacation whenever the queue is empty and the vacation rate is state dependent. At the instant of a service completion, the vacation is interrupted and the server resumes a regular busy period with probability 1 − q (if there are customers in the queue), or continues the vacation with probability q (0 ≤ q ≤ 1). We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. Finally, using some numerical results, we present the parameter effect on the various performance measures. PubDate: 2014-09-01

Abstract: In this paper, a pair of second-order mixed symmetric nondifferentiable multiobjective dual programs over arbitrary cones where each of the objective functions contains a pair of support functions is considered. Further, weak, strong and converse duality theorems are established under the assumptions of second-order K- (F,ρ)-convexity. Moreover, we have illustrated a numerical example which is second-order K- (F,ρ)-convex but not second-order F-convex. Several special cases are also obtained. PubDate: 2014-06-18

Abstract: This paper deals with the identification and elimination of ground echoes in radar images using their textural features. The images collected in Setif (Algeria) by a non Doppler radar, are processed. Two kinds of texture-based techniques have been considered, consisting in calculating either the histograms of their sum and difference or the pattern recognition. Energy and local homogeneity are found to be the textural parameters that clearly separate the precipitation and ground echoes. To get only the rainfall echoes, the resulting template is applied to each of the raw radar images and the filtering is improved by removing the residual clutter with pattern recognition. This method allows as to completely removing the ground clutter with minimal alterations of the rain echoes with reduced calculation time. It has the advantages of effectiveness and simplicity. However, when there is overlap of precipitation echoes with the ground echoes, significant small cells may occur. In this case, these cells are restored by interpolating from neighboring pixels with a regularization function. The application of this optimization algorithm of filtered images can effectively reproduce true structure of clouds. The radar images can be processed in real-time because the computation time needed by these techniques is small. PubDate: 2014-06-10

Abstract: An attempt has been made to obtain a compromise allocation based on maximization of individual reliabilities of repairable and replaceable components with in the subsystems, using the information of failed and operational components and a non linear cost function with fixed budget. A solution algorithm of fuzzy programming technique is used to solve the Bi-Objective Selective Maintenance Allocation Problem (BSMAP). Also, the problem has been solved by two other suggested methods; “Weighted Criterion Technique” and “Desirability Function Technique”. A numerical example is also presented to illustrate the computational details. PubDate: 2014-06-01

Abstract: This paper applies He’s homotopy perturbation method to compute a large variety of integral transforms. The Esscher, Fourier, Hankel, Laplace, Mellin and Stieljes integrals transforms are particular cases of our generalized integral transform. Our method is of practical importance in order to derive new integration formulae, to approximate certain difficult integrals as well as to calculate the expectation of certain nonlinear functions of random variable. PubDate: 2014-06-01

Abstract: This paper presents the encoding of binary arithmetic operations within Integer Programming (IP) formulations, specifically the encoding of binary multiplication and addition/subtraction. This allows the direct manipulation of integer quantities represented as binary strings of arbitrary size. Many articles published in the past within the Chemical Engineering community have used this representation of integer quantities within Mixed-Integer formulations for Process Optimization and Design. Applications such as these can benefit from the formulations derived in this work. As a demonstrative application we consider the simple number factorization problem, according to which given an odd number C factors A and B are to be found such that C equals their product. If any such factors are found the number is factorable, else it is proven to be prime. An IP formulation is derived involving upper and lower bounding logical constraints to encode for the value of the binary string digits. The formulation involves
\({\cal O}(\log C)\)
binary variables,
\({\cal O}((\log C)^{2})\)
continuous variables, and
\({\cal O}((\log C)^{2})\)
constraints to describe the problem. Computational results demonstrate the validity of this approach, highlighting also the fact that such formulations are not very tight thus resulting in large numbers of iterations of the Branch and Bound algorithm used. It is also observed that the formulations become significantly tighter if logical upper bounding constraints forcing continuous variables involved to be zero are included. PubDate: 2014-06-01

Abstract: This paper presents a heuristic algorithm for the earliest arrival flow problem. Existing exact algorithms, even polynomial in the output size, contain submodular function optimization as a frequently called subroutine, and thus are not practical in real-life applications. In this paper we propose an algorithm that does not involve the submodular function optimization. Although solving an EAF near-optimal, the algorithm is remarkably simple and efficient as it only involves shortest path computations on a static network. A numerical example illustrates how the algorithm works. As an application, we demonstrate the algorithm’s solution quality and computational performance by solving a real-size network. PubDate: 2014-06-01

Abstract: A class of functions called higher-order (F, α, ρ, d)-V-type I functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for higher-order Wolfe and Mond-Weir type multiobjective dual programs in order to relate the efficient solutions of primal and dual problems. PubDate: 2014-06-01

Abstract: We present a full-Newton step primal-dual infeasible interior-point algorithm based on Darvay’s search directions. These directions are obtained by an equivalent algebraic transformation of the centering equation. The algorithm decreases the duality gap and the feasibility residuals at the same rate. During this algorithm we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Each main iteration of the algorithm consists of a feasibility step and some centering steps. The starting point in the first iteration of the algorithm depends on a positive number ξ and it is strictly feasible for a perturbed pair, and feasibility steps find strictly feasible iterate for the next perturbed pair. By using centering steps for the new perturbed pair, we obtain strictly feasible iterate close to the central path of the new perturbed pair. The algorithm finds an ϵ-optimal solution or detects infeasibility of the given problem. The iteration bound coincides with the best known iteration bound for linear optimization problems. PubDate: 2014-06-01