Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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TL;DR: This paper reviews research into solving the two-dimensional (2D) rectangular assignment problem and combines the best methods to implement a k-best 2D rectangular assignment algorithm with bounded runtime.
Abstract: This paper reviews research into solving the two-dimensional (2D) rectangular assignment problem and combines the best methods to implement a k-best 2D rectangular assignment algorithm with bounded runtime. This paper condenses numerous results as an understanding of the "best" algorithm, a strong polynomial-time algorithm with a low polynomial order (a shortest augmenting path approach), would require assimilating information from many separate papers, each making a small contribution. 2D rectangular assignment Matlab code is provided.
135 citations
TL;DR: A polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost is described and computational results demonstrate the effectiveness of the conic reformulation.
135 citations
TL;DR: It is shown that the expected value of this minimum sum is less than 3, independent of n, if X consists of independent random variables uniformly distributed from 0 to 1.
Abstract: Given an n by n matrix X, the assignment problem asks for a set of n entries, one from each column and row, with the minimum sum. It is shown that the expected value of this minimum sum is less than 3, independent of n, if X consists of independent random variables uniformly distributed from 0 to 1.
135 citations
TL;DR: In this article, the authors extended the current state-of-the-art by proposing novel set partitioning models and analyzed the effects of different discretization schemes and the impact of using a time-variant/invariant quay crane allocation policy.
Abstract: Most of the operational problems in container terminals are strongly interconnected. In this paper, we study the integrated Berth Allocation and Quay Crane Assignment Problem in seaport container terminals. We will extend the current state-of-the-art by proposing novel set partitioning models. To improve the performance of the set partitioning formulations, a number of variable reduction techniques are proposed. Furthermore, we analyze the effects of different discretization schemes and the impact of using a time-variant/invariant quay crane allocation policy. Computational experiments show that the proposed models significantly improve the benchmark solutions of the current state-of-art optimal approaches.
134 citations
01 Jun 1996
TL;DR: This paper investigates the complexity and approximation ratio of two lower bound computation algorithms from both a theoretical and practical point of view and presents a new pruning technique that takes advantage of the partitioning.
Abstract: The set covering problem and the minimum cost assignment problem (respectively known as unate and binate covering problem) arise throughout the logic synthesis flow. This paper investigates the complexity and approximation ratio of two lower bound computation algorithms from both a theoretical and practical point of view. It also presents a new pruning technique that takes advantage of the partitioning.
134 citations