Topic
Augmented assignment
About: Augmented assignment is a research topic. Over the lifetime, 111 publications have been published within this topic receiving 3179 citations. The topic is also known as: compound assignment.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the Hungarian method is used to find the minimal cost assignment and the best assignment after excluding the minimum cost assignment, which can be used to rank all the assignments in a sequence in order of cost.
Abstract: The Hungarian method gives an efficient algorithm for finding the minimal cost assignment. However, in some cases it may be useful to determine the second minimal assignment (i.e., the best assignment after excluding the minimal cost assignment) and in general the kth minimal assignment for k = 1, 2, …. These things can easily be determined if all the assignments can be arranged as a sequence in increasing order of cost. This paper describes an efficient algorithm for such a ranking of all the assignments. The maximum computational effort required to generate an additional assignment in the sequence is that of solving at most (n − 1) different assignment problems, one each of sizes 2, 3, …, n.
583 citations
TL;DR: A branch and bound algorithm is developed that solves the generalized assignment problem by solving a series of binary knapsack problems to determine the bounds.
Abstract: This paper describes what is termed the “generalized assignment problem”. It is a generalization of the ordinary assignment problem of linear programming in which multiple assignments of tasks to agents are limited by some resource available to the agents. A branch and bound algorithm is developed that solves the generalized assignment problem by solving a series of binary knapsack problems to determine the bounds. Computational results are cited for problems with up to 4 000 0–1 variables, and comparisons are made with other algorithms.
506 citations
TL;DR: A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.
Abstract: The generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents. A new algorithm for the generalized assignment problem is presented that employs both column generation and branch-and-bound to obtain optimal integer solutions to a set partitioning formulation of the problem.
473 citations
TL;DR: In this paper, a similarity coefficient matrix is used as the input to the assignment problem and closed loops in the form of subtours are identified after solving the problem and are used as a basis for grouping.
Abstract: SUMMARY The problem of grouping of parts has been addressed in the past using clustering methods and integer programming. This paper presents an assignment model to solve the grouping problem. A similarity coefficient matrix is used as the input to the assignment problem. Closed loops in the form of subtours are identified after solving the problem and are used as the basis for grouping. The method has been applied to a number of examples. Compared with the earlier mathematical programming model, viz., the p-median model, the assignment method emerges as a distinctly superior technique both in terms of quality of solution and computational time.
279 citations
TL;DR: A new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined and ordered classes through the resolution of linear programs.
203 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 3 |
| 2016 | 2 |
| 2015 | 3 |
| 2014 | 2 |
| 2013 | 2 |
| 2012 | 6 |