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: 0-1 linear programming formulations exploiting the stated hierarchy are proposed and used to derive a formal proof that the joint OR planning and scheduling problem is NP-hard.
140 citations
TL;DR: An efficient algorithm is developed, an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way, using a node-arc formulation of the problem.
Abstract: The traffic assignment problem associated with a given transportation network is the process of distributing zone-to-zone trips on links of the network. A number of methods have been proposed to solve this problem, but none have been found to be entirely satisfactory. This paper is concerned with the nonlinear mathematical model of the problem, where the link-traveling costs are increasing functions of the link flows and no explicit capacity constraint is imposed on individual links. An efficient algorithm is developed, using a node-arc formulation of the problem. It is an adaptation of the convex-simplex method that takes advantage of the very special network structure of the traffic assignment problem formulated in this way. Numerical results obtained with a moderate size street network are presented.
140 citations
TL;DR: This work surveys recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignments problems, in particular lower bounds, special cases and asymptotic results.
140 citations
TL;DR: In this paper, the authors present a new formulation of the quadratic assignment problem by transforming the objective function into a linear objective function by introducing a number of new variables and constraints and the resulting problem is a 0-1 linear integer program with a highly specialized structure.
Abstract: In this paper we present a new formulation of the quadratic assignment problem. This is done by transforming the quadratic objective function into a linear objective function by introducing a number of new variables and constraints. The resulting problem is a 0-1 linear integer program with a highly specialized structure. This permits the use of the partitioning scheme of Benders where only the original variables need be considered. The algorithm described thus iterates between two problems. The master problem is a pure 0-1 integer program, and the subproblem is a transportation problem whose optimal solution is shown to be readily available from the master problem in closed form. Computational experience on problems available in the literature is provided.
139 citations
TL;DR: This paper uses signatures to describe a method for finding optimal assignments that terminates in at most n-1n-2/2 pivot steps and takes at most On3 work.
Abstract: The "signature" of a dual feasible basis of the assignment problem is an n-vector whose ith component is the number of nonbasic activities of type i, j. This paper uses signatures to describe a method for finding optimal assignments that terminates in at most n-1n-2/2 pivot steps and takes at most On3 work.
139 citations