In this paper we study a special class of multiobjective discrete control problems on dynamic networks. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize...
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In this paper we study a special class of multiobjective discrete control problems on dynamic networks. We assume that the dynamics of the system is controlled by p actors (players) and each of them intend to minimize his own integral-time cost by a certain trajectory. Applying Nash and Pareto optimality principles we study multiobjective control problems on dynamic networks where the dynamics is described by a directed graph. polynomial-time algorithms for determining the optimal strategies of the players in the considered multiobjective control problems are proposed exploiting the special structure of the underlying graph. Properties of time-expanded networks are characterized. A constructive scheme which consists of several algorithms is presented. (c) 2007 Elsevier B.V. All rights reserved.
We present a linear programming based algorithm for a class of optimization problems with a multi-linear objective function and affine constraints. This class of optimization problems has only one objective function, ...
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We present a linear programming based algorithm for a class of optimization problems with a multi-linear objective function and affine constraints. This class of optimization problems has only one objective function, but it can also be viewed as a class of multi-objective optimization problems by decomposing its objective function. The proposed algorithm exploits this idea and solves this class of optimization problems from the viewpoint of multi-objective optimization. The algorithm computes an optimal solution when the number of variables in the multi-linear objective function is two, and an approximate solution when the number of variables is greater than two. A computational study demonstrates that when available computing time is limited the algorithm significantly outperforms well-known convex programming solvers IPOPT and CVXOPT, in terms of both efficiency and solution quality. The optimization problems in this class can be reformulated as second-order cone programs, and, therefore, also be solved by second-order cone programming solvers. This is highly effective for small and medium size instances, but we demonstrate that for large size instances with two variables in the multi-linear objective function the proposed algorithm outperforms a (commercial) second-order cone programming solver. (C) 2017 Elsevier Ltd. All rights reserved.
This paper considers the nonpreemptive scheduling of a given set of jobs on several identical, parallel machines. Each job must be processed on one of the machines. Prior to processing, a job must be loaded (setup) by...
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This paper considers the nonpreemptive scheduling of a given set of jobs on several identical, parallel machines. Each job must be processed on one of the machines. Prior to processing, a job must be loaded (setup) by a single server onto the relevant machine. The paper considers a number of classical scheduling objectives in this environment, under a variety of assumptions about setup and processing times. For each problem considered, the intention is to provide either a polynomial- or pseudo-polynomial-time algorithm, or a proof of binary or unary NP-completeness;The results provide a mapping of the computational complexity of these problems. (C) 2000 Elsevier Science B.V. All rights reserved.
A collection of objects, some of which are good and some of which are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that ea...
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A collection of objects, some of which are good and some of which are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then a fair division may not exist. What is the smallest number of objects that must be shared between two or more agents to attain a fair and efficient division? In this paper, fairness is understood as proportionality or envy-freeness and efficiency as fractional Pareto-optimality. We show that, for a generic instance of the problem (all instances except a zero-measure set of degenerate problems), a fair fractionally Pareto-optimal division with the smallest possible number of shared objects can be found in polynomialtime, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where agents??? valuations are aligned for many objects.
We study two problems where k autonomous mobile agents are initially located on distinct nodes of a weighted graph with nnodes and medges. Each agent has a predefined velocity and can only move along the edges of the ...
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We study two problems where k autonomous mobile agents are initially located on distinct nodes of a weighted graph with nnodes and medges. Each agent has a predefined velocity and can only move along the edges of the graph. The first problem is to deliver one package from a source node to a destination node. The second is to simultaneously deliver two packages, each from its source node to its destination node. These deliveries are achieved by the collective effort of the agents, which can carry and exchange a package among them. For one package, we propose an O(kn logn + km) timealgorithm for computing a delivery schedule that minimizes the delivery time. For two packages, we show that the problem of minimizing the maximum or the sum of the delivery times is NP-hard for arbitrary agent velocities, but polynomial-time solvable for agents with equal velocity. (C) 2020 Elsevier Inc. All rights reserved.
We. show that the chromatic number of {P-5, K-p - e}-free graphs can be computed in polynomialtime for each fixed p. Additionally, we prove polynomial-time solvability of the weighted vertex coloring problem for (P-5...
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We. show that the chromatic number of {P-5, K-p - e}-free graphs can be computed in polynomialtime for each fixed p. Additionally, we prove polynomial-time solvability of the weighted vertex coloring problem for (P-5, (P-3 + P-2) over bar}-free graphs. (C) 2016 Elsevier B.V. All rights reserved.
A multi-unit assignment valuation is a function represented by a weighted bipartite graph. In this paper, we provide a characterization of such a function in terms of maximizer sets of perturbed functions. We then pre...
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A multi-unit assignment valuation is a function represented by a weighted bipartite graph. In this paper, we provide a characterization of such a function in terms of maximizer sets of perturbed functions. We then present an algorithm that checks whether a given bivariate function is a multi-unit assignment valuation, and if the answer is "yes," computes a weighted bipartite graph representing the function.
A dynamic network consists of a graph with capacities and transit times on its edges. The quickest transshipment problem is defined by a dynamic network with several sources and sinks, each source has a specified supp...
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A dynamic network consists of a graph with capacities and transit times on its edges. The quickest transshipment problem is defined by a dynamic network with several sources and sinks, each source has a specified supply and each sink has a specified demand. The problem is to send exactly the right amount of flow our of each source and into each sink in the minimum overall time. Variations of the quickest transshipment problem have been studied extensively: the special case of the problem with a single sink is commonly used to model building evacuation. Similar dynamic network Row problems have numerous other applications: in some of these, the capacities are small integers and it is important to rind integral Rows. There are no polynomial-time algorithms known for most of these problems. In this paper we give the first polynomial-time algorithm for the quickest transshipment problem. Our algorithm provides an integral optimum flow. Previously, the quickest transshipment problem could only be solved efficiently in the special case of a single source and single sink.
We consider a transportation problem defined on a node-weighted undirected graph. Weight is positive if the amount of commodity is stored at a node, and negative if the amount is needed at the node. We want to meet al...
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We consider a transportation problem defined on a node-weighted undirected graph. Weight is positive if the amount of commodity is stored at a node, and negative if the amount is needed at the node. We want to meet all demands by transporting commodities using vehicles prepared either at nodes or edges which only travel to and from neighbors. In a trip from a node to a neighbor we can send commodities and also bring back some other commodities. Problem is to decide whether we can meet all demands by carrying out a set of trips in a few rounds. We define three different schemes to solve the problem and examine their performances. We present a polynomial-time algorithm for deciding whether there is a single round of trips using one vehicle at each node that meet all demands for one-commodity case.
We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capac...
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We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all the arcs, and the location of sources and sinks. The concave cost over each arc is assumed to be evaluated through an oracle machine, i.e., the oracle machine returns the cost over an arc in a single computational step, given the flow value and the arc index. We propose an algorithm whose running time is polynomial in the number of columns of the grid for the following cases: (1) the grid has a constant number of rows, a constant number of different capacities over all the arcs, and sources and sinks in at most two rows;(2) the grid has two rows and a constant number of different capacities over all the arcs connecting rows;(3) the grid has a constant number of rows and all sources in one row, with infinite capacity over each arc. These are presumably the most general polynomially solvable cases, since we show that the problem becomes NP-hard when any condition in these cases is removed. Our results apply to several variants and generalizations of the single item dynamic lot sizing model and answer several questions raised in serial supply chain optimization.
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