Authors:Gour Chandra Mahata Pages: 363 - 392 Abstract: Abstract In a supplier-retailer-customer supply chain, a credit-worthy retailer frequently receives a permissible delay on the entire purchase amount without collateral deposits from his/her supplier (i.e., an up-stream full trade credit). By contrast, a retailer usually requests his/her credit-risk customers to pay a fraction of the purchase amount at the time of placing an order, and then grants a permissible delay on the remaining balance (i.e., a down-stream partial trade credit). Also, in selecting an item for use, the selling price of that item is one of the decisive factors to the customers. It is well known that the higher selling price of item decreases the demand rate of that item where the lesser price has the reverse effect. Hence, the demand rate of an item is dependent on the selling price of that item. In addition, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model to allow for: (a) the strategy that supplier offers retailer a full trade credit policy whereas the retailer offers their customers a partial trade credit policy, (b) selling price dependent demand rate, (c) a profit maximization objective and (d) deteriorating items not only deteriorate continuously but also have their expiration dates. For the objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined. PubDate: 2015-04-19 DOI: 10.1007/s10852-014-9269-5 Issue No:Vol. 14, No. 4 (2015)

Authors:Aleksandr Kochurov; Dimitrii Golovashkin Pages: 393 - 405 Abstract: Abstract The paper proposes a method to extend the dimension of grids that GPU-aided implicit finite difference method is capable to work with. The approach is based on the pyramid method. A predictive mathematical model for computation duration is proposed. This model allows to find optimal algorithm parameters. The paper provides computation experiment results that has shown the model to be accurate enough to predict optimal algorithm parameters. PubDate: 2015-04-21 DOI: 10.1007/s10852-015-9272-5 Issue No:Vol. 14, No. 4 (2015)

Authors:Shafi Ullah; Irfan Ali; Abdul Bari Pages: 407 - 424 Abstract: Abstract This paper provide a profound study on optimum allocation of two stage multivariate stratified Warner’s randomized response (RR) model with linear and non linear cost function. The multi-objective problem is formulated as a Geometric Programming Problem (GPP). The fuzzy programming approach is adopted to solve the formulated problem. A numerical example is given to illustrate the computational details of the suggested method. PubDate: 2015-04-22 DOI: 10.1007/s10852-015-9276-1 Issue No:Vol. 14, No. 4 (2015)

Authors:Saber Shiripour; Nezam Mahdavi-Amiri; Iraj Mahdavi Pages: 425 - 451 Abstract: Abstract We are concerned with a capacitated location-multi allocation-routing problem in a road network with flexible travel times. It is assumed that all links are two-way and capacities of the server nodes and arcs for accepting of population are limited. The aim of our work is to find numbers and locations of server nodes, allocation of the existing population in existing demand nodes on the network to the servers and the allocation of existing population in each node to different routes to determine the decided server for each member so that total transportation time is minimized. Here, two basic concepts are considered: multi allocation and flexible travel times. The concept of multi allocation arises from the possibility of allocating the existing population in a demand node to more than one server node. Also, flexible travel times concentrate on impact of traveling population on the times of links simultaneously, that is, depending on how the population is distributed on the network, the travel times on links may be increased. So, to have the least increase in the time of each link, it is necessary to decide upon the distribution of population in the network. We formulate the proposed problem as a mixed-integer nonlinear programming model and then present a genetic algorithm (GA) for solving large problems Finally, we make two sets of numerical experiments and analyze the obtained results by LINGO solver and GA. Numerical results show the proposed GA to be highly efficient. PubDate: 2015-05-19 DOI: 10.1007/s10852-015-9277-0 Issue No:Vol. 14, No. 4 (2015)

Authors:Qunyan Zhou; Chun Zhang Pages: 453 - 467 Abstract: Abstract A new adaptive trust region algorithm with simple conic models is proposed. By use of the simple conic model, the new method needs less memory capacitance and computational complexity. The nonmonotone and adaptive techniques are introduced to improve the efficiency of the proposed algorithm. The convergence results of the method are proved under certain conditions. Numerical tests show that the new algorithm is efficient and robust. PubDate: 2015-03-26 DOI: 10.1007/s10852-015-9279-y Issue No:Vol. 14, No. 4 (2015)

Authors:Satyabrata Paul; Madhumangal Pal; Anita Pal Pages: 469 - 479 Abstract: Abstract L(0,1)-labelling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of non-negative integers such that adjacent vertices get number zero apart, and vertices at distance two get distinct numbers. The goal of L(0,1)-labelling problem is to produce a legal labelling that minimize the largest label used. In this article, it is shown that, for a permutation graph G with maximum vertex degree Δ, the upper bound of λ 0,1(G) is Δ−1. Finally, we prove that the result is exact for bipartite permutation graph. PubDate: 2015-05-01 DOI: 10.1007/s10852-015-9280-5 Issue No:Vol. 14, No. 4 (2015)

Authors:Yousaf Shad Muhammad; Javid Shabbir; Ijaz Husain; Mitwali Abd-el.Moemen Pages: 255 - 265 Abstract: Abstract In the present paper, a new Gamma cost function is proposed for an optimum allocation in multivariate stratified random sampling with linear regression estimator. Extended lexicographic goal programming is used for solution of multi-objective non-linear integer allocation problem. A real data set is used to illustrate the application. PubDate: 2015-08-01 DOI: 10.1007/s10852-014-9270-z Issue No:Vol. 14, No. 3 (2015)

Authors:P. Vijaya Laxmi; K. Jyothsna Pages: 267 - 285 Abstract: Abstract This paper presents the analysis of a renewal input multiple working vacations queue with balking, reneging and heterogeneous servers. Whenever the system becomes empty the second server leaves for a working vacation whereas the first server remains idle in the system. During a working vacation the second server provides service at a slower rate rather than completely stopping service. The steady-state probabilities of the model are obtained using supplementary variable and recursive techniques. Various performance measures of the model such as expected system length, expected balking rate, etc., have been discussed. Finally, some numerical results have been presented to show the effect of model parameters on the system performance measures. PubDate: 2015-08-01 DOI: 10.1007/s10852-015-9271-6 Issue No:Vol. 14, No. 3 (2015)

Authors:Kaveh Khalili-Damghani; Amir-Reza Abtahi; Amir Ghasemi Pages: 287 - 312 Abstract: Abstract Supply, manufacture, and distribution of perishable products are challenging jobs in supply chains. Location of warehouses and routing of vehicles are essential issues to distribute perishable products properly. In this paper, a new bi-objective mixed integer mathematical programming is proposed to reduce the total cost of the supply chain and to balance the workload of distribution centers while the due dates of delivery of perishable product are met, concurrently. The considered properties and constraints of proposed model made it well-posed to illustrate the real life situation. As the proposed model is NP-Hard, an evolutionary algorithm called Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) is customized to solve the problem. The structure of chromosome and genetic operators are customized for the problem. The performance of proposed NSGA-II and an efficient exact Multi-objective method, called ε-constraint, is compared using accuracy and diversity metrics on several benchmark instances. PubDate: 2015-08-01 DOI: 10.1007/s10852-015-9274-3 Issue No:Vol. 14, No. 3 (2015)

Authors:Md. Abul Kalam Azad; Ana Maria A. C. Rocha; Edite M. G. P. Fernandes Pages: 313 - 330 Abstract: Abstract The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0–1 multidimensional knapsack problems that are NP-hard. In the last decades, several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simplified binary version of the artificial fish swarm algorithm is presented, where a point/fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fish behavior that are randomly selected by using two user defined probability values. In order to make the points feasible, the presented algorithm uses a random heuristic drop-item procedure followed by an add-item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50 % of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems. PubDate: 2015-08-01 DOI: 10.1007/s10852-015-9275-2 Issue No:Vol. 14, No. 3 (2015)

Authors:Roberto de Souza Salgado; Guido Rossetto Moraes Pages: 331 - 341 Abstract: Abstract This work focuses on the solution of a set of algebraic nonlinear equations representing the steady state operation of electrical power systems. The classical modelling of the so-called power flow problem requires the statement of the power balance equations and the specification of some network variables. Usually Newton method is applied to solve these equations, which requires the solution of a linear system at each iteration. Here, the formulation of the power flow problem is modified by increasing the number of variables to be computed, such that an under-determined linear system is solved at each iteration. This strategy imparts flexibility to obtain solutions with respect to selected performance indexes. Numerical results obtained with test-systems ranging from 26 to 1916 equations and 30 to 2013 variables illustrate the main features of the proposed application. PubDate: 2015-03-08 DOI: 10.1007/s10852-015-9273-4 Issue No:Vol. 14, No. 3 (2015)

Authors:S. Grandcolas; C. Pinto Pages: 343 - 361 Abstract: Abstract In this paper we propose a new exact procedure for the two-dimensional orthogonal packing problem, based on F. Clautiaux et al. approach (Clautiaux et al. Eur. J. Oper. Res. 183(3), 1196–1211, 2007). The principle consists in searching first the positions of the items on the horizontal axis, so as that, at each position, the sum of the heights of the items does not exceed the height of the bin. Each time a valid placement of all the items is encountered, another procedure determines if it can be extended to a solution of the packing problem, searching the positions of the items on the vertical axis. Novel aspects of our approach include a simple and efficient search procedure, which only generates restricted placements, at least in a first stage, in order to reduce the search space, and the memorization of unsuccessful configurations, which are then used to detect dead-ends. We tested our implementation on a selection of orthogonal packing problems and strip packing problems, and we compared our results with those of recent successful approaches. PubDate: 2015-03-14 DOI: 10.1007/s10852-015-9278-z Issue No:Vol. 14, No. 3 (2015)

Authors:Giuseppe Paletta; Alex J. Ruiz-Torres Pages: 125 - 143 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: 2015-06-01 DOI: 10.1007/s10852-014-9262-z Issue No:Vol. 14, No. 2 (2015)

Authors:Ali Reza Sepasian; Freydoon Rahbarnia Pages: 145 - 157 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: 2015-06-01 DOI: 10.1007/s10852-014-9265-9 Issue No:Vol. 14, No. 2 (2015)

Authors:Chunlei Yan; Baocheng Feng Pages: 159 - 172 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: 2015-06-01 DOI: 10.1007/s10852-014-9264-x Issue No:Vol. 14, No. 2 (2015)

Authors:S. Borgwardt Pages: 173 - 196 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: 2015-06-01 DOI: 10.1007/s10852-014-9263-y Issue No:Vol. 14, No. 2 (2015)

Authors:Heni Bouhamed; Afif Masmoudi; Thierry Lecroq; Ahmed Rebaï Pages: 197 - 237 Abstract: Abstract The use of Bayesian Networks (BNs) as classifiers in different application fields has recently witnessed a noticeable growth. Yet, using the Naïve Bayes application, and even the augmented Naïve Bayes, to classifier-structure learning, has been vulnerable to some extent, which accounts for the resort of experts to other more sophisticated types of algorithms. Consequently, the use of such algorithms has paved the way for raising the problem of super-exponential increase in computational complexity of the Bayesian classifier learning structure, with the increasing number of descriptive variables. In this context, the main objective of our present work lies in trying to conceive further solutions to solve the problem of the intricate algorithmic complexity imposed during the learning of Bayesian classifiers structure through the use of sophisticated algorithms. Our results revealed that the newly suggested approach allows us to considerably reduce the execution time of the Bayesian classifier structure learning without any information loss. PubDate: 2015-06-01 DOI: 10.1007/s10852-014-9266-8 Issue No:Vol. 14, No. 2 (2015)

Authors:Peng Zhang Pages: 239 - 253 Abstract: Abstract In this paper, we consider a multi-period portfolio selection problem in a fuzzy investment environment, in which the return and risk of assets are characterized by possibilistic mean value and possibilistic semivariance, respectively. Based on the theories of possibility, a new multi-period possibislistic portfolio selection model is proposed, which contains risk control, transaction costs, borrowing constraints, threshold constraints and cardinality constraints. the proposed model can be transformed into a crisp nonlinear dynamic optimization problem by using fuzzy programming approach. Because of the transaction costs and cardinality constraints, the multi-period portfolio selection is a mix integer dynamic optimization problem with path dependence A forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, a comparison analysis of the different cardinality constraints is provided to illustrate the efficiency of the proposed approaches and the designed algorithm. PubDate: 2015-06-01 DOI: 10.1007/s10852-014-9268-6 Issue No:Vol. 14, No. 2 (2015)

Authors:S. K. Gupta; D. Dangar; N. Kailey; S. Kumar Pages: 103 - 123 Abstract: 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: 2015-03-01 DOI: 10.1007/s10852-014-9260-1 Issue No:Vol. 14, No. 1 (2015)