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.

Solving the transportation problem

Abstract: A simplified description of a new computing procedure for the Hitchcock-Koopmans transportation problem is given, together with a step by step solution of an illustrative example. The procedure is based on Kuhn's combinatorial algorithm for the assignment problem and a simple “labeling process” for solving maximal flow problems in networks. The proposed computation appears to be considerably more efficient than the specialized form of the simplex method which is in common use.

On combining maximum entropy trip matrix estimation with user optimal assignment

Abstract: This note shows how the maximum entropy trip matrix estimation procedure incorporated in ME2 as proposed by Willumsen (Van Zuylen and Willumsen, 1980) can be combined with a user optimal assignment model such as SATURN (Van Vliet, 1982) into a single mathematical problem. The resulting problem has the form of a bilevel programming problem similar to matrix estimation methods proposed by Nguyen (1981). The mathematical framework for the user optimal assignment problem is summarized, followed by a description of the maximum entropy trip matrix estimation procedure proposed by Willumsen. The two models are then combined into a single problem and a discussion follows on solution procedures.

A modified Frank-Wolfe algorithm for solving the traffic assignment problem

Abstract: This paper presents a very simple modification of the Frank-Wolfe algorithm for the solution of the traffic assignment problem. It is shown that the modified algorithm can be implemented without much increase in computational effort over the original one. Convergence of the algorithm is proved and computational results are reported to demonstrate the validity of the modification.

An Algorithm For The Three-Index Assignment Problem

Abstract: We describe a branch-and-bound algorithm for solving the axial three-index assignment problem. The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds, and a novel branching strategy that exploits problem structure to fix several variables at each node and reduce the size of the total enumeration tree. Computational experience is reported on problems with up to 78 equations and 17,576 variables. The primal heuristics were tested on problems with up to 210 equations and 343,000 variables. (This abstract was borrowed from another version of this item.)

Dual Processor Scheduling with Dynamic Reassignment

Abstract: The problem of finding an optimal dynamic assignment of a modular program for a two-processor system is analyzed. Stone's formulation of the static assignment problem is extended to include the cost of dynamically reassigning a module from one processor to the other and the cost of module residence without execution. By relocating modules during the course of program execution, changes in the locality of the program can be taken into account. It is shown that network flow algorithms may be used to find a dynamic assignment that minimizes the sum of module execution costs, module residence costs, intermodule communication costs, and module reassignment costs. Techniques for reducing the size of the problem are described for the case where the costs of residence are negligible.