Using a few very basic observations, we proposed recently a direct and finite algorithm for the computation of the l(infinity) regression line on a discrete set {(x(i), y(i))}(i)(n) under the assumption that x(1) <...
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Using a few very basic observations, we proposed recently a direct and finite algorithm for the computation of the l(infinity) regression line on a discrete set {(x(i), y(i))}(i)(n) under the assumption that x(1) < x(2) < ... algorithm to the case with at least one, possibly multiple y-values for each distinct xi. Our algorithm finds all the regression lines in O(n(2)) operations in the worst-case scenario and improves the existing best-known computational complexity result for this problem, Numerical results on random problems are included.
We study a problem of cyclic no-wait scheduling of identical parts on m sequential machines. A number of robots are used to transport the parts from one machine to another. We consider the problem that has two perform...
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We study a problem of cyclic no-wait scheduling of identical parts on m sequential machines. A number of robots are used to transport the parts from one machine to another. We consider the problem that has two performance measures: one is the number of robots to be used, the other is the period of a cyclic schedule. We find the minimal number of robots needed to meet a given cyclic schedule, for all possible cycle lengths, the complexity of the suggested algorithm being O(m(5)), independently of the range within which the cycle length value may vary.
We study a dual-mode production planning problem with emission constraints, where a manufacturer produces a single product with two optional technologies. The manufacturer is equipped with the regular and green techno...
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We study a dual-mode production planning problem with emission constraints, where a manufacturer produces a single product with two optional technologies. The manufacturer is equipped with the regular and green technologies to comply with emission limitations, and either one or both can be adopted for production. We first investigate the problem under a mandatory emission-cap policy and then extend it to consider emission trading under an emission cap-and-trade scheme. Based on the structural properties of the problem and a multi-level decomposition approach, a polynomial dynamic programming algorithm is developed to solve the models optimally. Our analysis shows that the manufacturer should only use a mix of both technologies when the emission cap is a binding constraint. Numerical results show that the manufacturer's decisions and benefits are significantly affected by the emission cap under the mandatory emission-cap policy, especially when the cap is at a relatively low level. However, the carbon price may not remarkably affect the manufacturer's cost because its influence could be abated through the flexible technology switch under the emission cap-and-trade scheme. (C) 2015 Elsevier B.V. All rights reserved.
In the due date assignment, the bicriteria scheduling models are motivated by the trade-off between the due date assignment cost and a performance criterion of the scheduling system. The bicriteria scheduling models r...
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In the due date assignment, the bicriteria scheduling models are motivated by the trade-off between the due date assignment cost and a performance criterion of the scheduling system. The bicriteria scheduling models related to the maximum tardiness and the weighted number of tardy jobs have been studied in the literature. In this paper we consider a new model with criteria of the due date assignment cost and the total weighted tardiness. The main results are polynomial-time algorithms for the linear combination version, the constraint version, and the Pareto optimization version of bicriteria scheduling.
We develop a new approach for characterizing k-primitive matrix families. Such families generalize the notion of a primitive matrix. They have been intensively studied in the recent literature due to applications to M...
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We develop a new approach for characterizing k-primitive matrix families. Such families generalize the notion of a primitive matrix. They have been intensively studied in the recent literature due to applications to Markov chains, linear dynamical systems, and graph theory. We prove, under some mild assumptions, that a set of k nonnegative matrices is either k-primitive or there exists a nontrivial partition of the set of basis vectors, on which these matrices act as commuting permutations. This gives a convenient classification of k-primitive families and a polynomial-time algorithm to recognize them. This also extends some results of Perron-Frobenius theory to nonnegative matrix families.
The uncapacitated facility location problem is considered in case when the transportation matrix has a totally balanced characteristic matrix. Since this problem is equivalent to the minimization problem of a polynomi...
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The uncapacitated facility location problem is considered in case when the transportation matrix has a totally balanced characteristic matrix. Since this problem is equivalent to the minimization problem of a polynomial in Boolean variables, an efficient algorithm is developed in terms of the latter. The idea of the algorithm is based on the fact that the minimization problem of a totally balanced polynomial can be reduced to the minimization problem of a similar polynomial having one fewer variables. (C) 2001 Published by Elsevier Science B.V.
作者：
Plesník, JComenius Univ
Fac Math Phys & Informat Dept Numer & Optimizat Methods Bratislava 84248 Slovakia
Given a graph G with nonnegative edge costs and an integer k, we consider the problem of finding an edge subset S of minimum total cost with respect to the constraint that S covers exactly k vertices of G. An O(n(3)) ...
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Given a graph G with nonnegative edge costs and an integer k, we consider the problem of finding an edge subset S of minimum total cost with respect to the constraint that S covers exactly k vertices of G. An O(n(3)) algorithm is presented where n is the order of G. It is based on the author's previous paper dealing with a similar problem asking S to cover at least k vertices.
We consider the Reconfigurable Transfer Line Balancing Problem. This problem consists of allocating a set of operations (necessary to machine a single part) to different workstations placed into a serial line. Each wo...
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We consider the Reconfigurable Transfer Line Balancing Problem. This problem consists of allocating a set of operations (necessary to machine a single part) to different workstations placed into a serial line. Each workstation can contain multiple machines operating in parallel. The machines considered are mono-spindle head CNC machines which may imply sequence-dependent setup times between operations in order to perform tool changes. Therefore, the operations allocated to a workstation should be sequenced. Besides, accessibility, inclusion, exclusion and precedence constraints between operations are considered. In this article, we propose a polynomial exact algorithm that balances the transfer line provided the overall sequence of the operations (called 'giant sequence') is given. We use this algorithm to solve the balancing problem when the overall sequence of operations is not fixed by embedding it in a metaheuristic framework. We perform experimentation on literature instances. The results obtained show the effectiveness of the proposed approach compared to literature.
This paper deals with the stable b-matching problem in multigraphs, called the stable multiple activities problem, SMA for short. In an SMA instance a multigraph G = (V, E), capacity b(v) and a linear order <(v) on...
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This paper deals with the stable b-matching problem in multigraphs, called the stable multiple activities problem, SMA for short. In an SMA instance a multigraph G = (V, E), capacity b(v) and a linear order <(v) on the set of edges incident to v, for each vertex v is an element of V are given. A stable b-matching is sought, i.e. a set of edges M such that each vertex v is incident with at most b(v) edges and for each edge e is not an element of M a vertex v incident with e and b(v) distinct edges f(1),...,f(b(v)) incident to v exist in M, all of them <(v)-smaller than e. We show how to decrease the computational complexity of the SMA algorithm to run in O(vertical bar E vertical bar) time and derive some properties of stable b-matchings. (C) 2007 Elsevier B.V. All rights reserved.
The input to an inverse shortest path lengths problem (ISPL) consists of a graph G with arc weights, and a collection of source-sink pairs with prescribed distances that do not necessarily conform to the shortest path...
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The input to an inverse shortest path lengths problem (ISPL) consists of a graph G with arc weights, and a collection of source-sink pairs with prescribed distances that do not necessarily conform to the shortest path lengths in G. The goal is to modify the arc weights, subject to a penalty on the deviation from the given weights, so that the shortest path lengths are equal to the prescribed values. We show that although ISPL is an NP-hard problem, several ISPL classes are polynomially solvable. These cases include ISPL where the collection of the pairs share a single source and all other nodes as destinations (the single-source all-sink problem SAISPL). For the case where the collection contains a single node pair (the single-source single-sink problem SSISPL), we identify conditions on the uniformity of the penalty functions and on the original arc weights, which make SSISPL polynomially solvable. These results cannot be strengthened significantly as the general single-source ISPL is NP-hard and the all-sink case, with more than one source, is also NP-hard. We further provide a convex programming formulation for a relaxation of ISPL in which the shortest path lengths are only required to be no less than the given values (LBISPL). It is demonstrated how this compact formulation leads to efficient algorithms for ISPL. (C) 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 56(1), 20-29 2010
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