We investigate the complexity of the min-max assignment problem under a fixed number of scenarios. We prove that this problem is polynomial-time equivalent to the exact perfect matching problem in bipartite graphs. an...
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We investigate the complexity of the min-max assignment problem under a fixed number of scenarios. We prove that this problem is polynomial-time equivalent to the exact perfect matching problem in bipartite graphs. an infamous combinatorial optimization problem of unknown computational complexity. (c) 2005 Published by Elsevier B.V.
This paper presents a significant improvement to the traditional neural approach to the assignment problem (AP). The technique is based on identifying the feasible space (F) with a linear subspace of R-n2, and then an...
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This paper presents a significant improvement to the traditional neural approach to the assignment problem (AP). The technique is based on identifying the feasible space (F) with a linear subspace of R-n2, and then analyzing the orthogonal projection onto F, The formula for the orthogonal projection is shown to be surprisingly simple and easy to integrate into the traditional neural model, This projection concept was first developed in [4], but here we show that the projection can be computed in a much simpler way, and that the addition of a ''clip'' operator at the boundaries of the cube can improve the results by an order of magnitude in both accuracy and run time. It is proven that the array of numbers that define an AP can be projected onto F without loss of information and the network can be constrained to operate exclusively in F until a neuron is saturated (i.e., reaches the maximum or minimum activation). Two ''clip'' options are presented and compared, Statistical results are presented for randomly generated AP's of sizes n = 10 to n = 50. The statistics confirm the theory.
We consider the assignment problem with interval data, where it is assumed that only upper and lower bounds are known for each cost coefficient. It is required to find a minmax regret assignment. The problem is known ...
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We consider the assignment problem with interval data, where it is assumed that only upper and lower bounds are known for each cost coefficient. It is required to find a minmax regret assignment. The problem is known to be strongly NP-hard. We present and compare computationally several exact and heuristic methods, including Benders decomposition, using CPLEX, a variable depth neighborhood local search, and two hybrid population-based heuristics. We report results of extensive computational experiments. (C) 2010 Elsevier Ltd. All rights reserved.
We consider a general model for scheduling jobs on unrelated parallel-machines with maintenance interventions. The processing times are deteriorating with their position in the production sequence and the goal of the ...
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We consider a general model for scheduling jobs on unrelated parallel-machines with maintenance interventions. The processing times are deteriorating with their position in the production sequence and the goal of the maintenance is to help to restore good processing conditions. The maintenance duration is depending on the time elapsed since the last maintenance intervention. Several performance criteria and different maintenance systems have been proposed in the literature, leading basically to assignment problems as the underlying model. We shall inverse the approach and start first to set up the matrix for the assignment problems, which catches all the information for the production-maintenance system. This can be done for very general processing times and maintenance durations. The solutions to the assignment problems are determined first. They define the order in which the jobs are to be processed on the various machines and only then the vital informations about the schedule are retrieved, like completion and maintenance times. It will be shown that these matrices are easily obtained, and this approach does not necessitate any complex calculations. (C) 2015 Elsevier B.V. All rights reserved.
The Reviewer assignment problem is a critical management problem faced by academic journals, conferences, and research funding agencies. Previous relevant literature focuses on performing an optimized assignment of ma...
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The Reviewer assignment problem is a critical management problem faced by academic journals, conferences, and research funding agencies. Previous relevant literature focuses on performing an optimized assignment of manuscripts (or proposals) to reviewers. In this paper, we study a group-to-group reviewer assignment problem, where manuscripts and reviewers are divided into groups, with groups of reviewers are assigned to groups of manuscripts. We formulate this problem as a multi-objective mixed integer programming model, which is proven NP-hard. An effective two-phase stochastic-biased greedy algorithm is then proposed to solve the problem. Results of comprehensive experiments demonstrate the effectiveness of the algorithm. The approach is applied to a real application, for which the result receive positive and encouraging feedback from users. (C) 2012 Elsevier Ltd. All rights reserved.
This paper investigates a two-objective k-cardinality assignment problem. As a result, a chance-constrained goal programming model is constructed for the problem. Also, tabu search algorithm based on fuzzy simulation ...
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This paper investigates a two-objective k-cardinality assignment problem. As a result, a chance-constrained goal programming model is constructed for the problem. Also, tabu search algorithm based on fuzzy simulation is designed to solve the problem. Finally, a numerical example is presented to show the application of the algorithm. (c) 2005 Elsevier B.V. All rights reserved.
The lower bound 1 + 1/e + O(n-1+epsilon) almost-equal-to 1.368 is established for the expected minimal cost in the n X n random assignment problem where the cost matrix entries are drawn independently from the Uniform...
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The lower bound 1 + 1/e + O(n-1+epsilon) almost-equal-to 1.368 is established for the expected minimal cost in the n X n random assignment problem where the cost matrix entries are drawn independently from the Uniform(0, 1) probability distribution. The expected number of independent zeroes created in the initial assignment of the Hungarian Algorithm is asymptotically equal to (2 - e-1/e - e(-e-1/e) + o(1))n almost-equal-to 0.807n.
Our main contribution is an O(n log n) algorithm that determines with high probability a perfect matching in a random 2-out bipartite graph. We also show that this algorithm runs in O(n) expected time. This algorithm ...
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Our main contribution is an O(n log n) algorithm that determines with high probability a perfect matching in a random 2-out bipartite graph. We also show that this algorithm runs in O(n) expected time. This algorithm can be used as a subroutine in an O(n2) heuristic for the assignment problem. When the weights in the assignment problem are independently and uniformly distributed in the interval [0, 1], we prove that the expected weight of the assignment returned by this heuristic is bounded above by 3 + O(n(-a)), for some positive constant a.
We study a labor market with finitely many heterogeneous workers and fi rms to illustrate the decentralized (myopic) blocking dynamics in two-sided one-to-one matching markets with continuous side payments (assignment...
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We study a labor market with finitely many heterogeneous workers and fi rms to illustrate the decentralized (myopic) blocking dynamics in two-sided one-to-one matching markets with continuous side payments (assignment problems, Shapley and Shubik [24]). Assuming individual rationality, a labor market is unstable if there is at least one blocking pair, that is, a worker and a firm who would prefer to be matched to each other in order to obtain higher payoffs than the payoffs they obtain by being matched to their current partners. A blocking path is a sequence of outcomes (specifying matchings and payoffs) such that each outcome is obtained from the previous one by satisfying a blocking pair (i.e., by matching the two blocking agents and assigning new payoffs to them that are higher than the ones they received before). We are interested in the question if starting from any (unstable) individually rational outcome, there always exists a blocking path that will lead to a stable outcome. In contrast to discrete versions of the model (i.e., for marriage markets, one-to-one matching, or discretized assignment problems), the existence of blocking paths to stability cannot always be guaranteed. We identify a necessary and sufficient condition for an assignment problem (the existence of a stable outcome such that all matched agents receive positive payoffs) to guarantee the existence of paths to stability and show how to construct such a path whenever this is possible.
We study the on-line assignment problem, where the testing of effectiveness incurs a cost. An optimal testing policy to maximize expected net effectiveness is derived.
We study the on-line assignment problem, where the testing of effectiveness incurs a cost. An optimal testing policy to maximize expected net effectiveness is derived.
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