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Open AccessJournal ArticleDOI

A survey of algorithms for the generalized assignment problem

Dirk Cattrysse, +1 more
- 10 Aug 1992 - 
- Vol. 60, Iss: 3, pp 260-272
TLDR
A survey of branch-and-bound algorithms for the problem of finding the minimum cost assignment of jobs to agents as discussed by the authors shows that most approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation.
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This article is published in European Journal of Operational Research.The article was published on 1992-08-10 and is currently open access. It has received 378 citations till now. The article focuses on the topics: Generalized assignment problem & Heuristics.

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Citations
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Journal ArticleDOI

A genetic algorithm for the generalised assignment problem

P. C. Chu, +1 more
- 01 Jan 1997 - 
TL;DR: Computational results show that the genetic algorithm heuristic is able to find optimal and near optimal solutions that are on average less than 0.01 % from optimality.
Journal ArticleDOI

Assignment problems : A golden anniversary survey

David W. Pentico
- 16 Jan 2007 - 
TL;DR: A limited survey of what appear to be the most useful of the variations of the assignment problem that have appeared in the literature over the past 50 years and what they are called so as to make it easier for a researcher trying to develop some variation of the assignments problem for a particular application to find the relevant literature.
Journal ArticleDOI

A Branch-and-Price Algorithm for the Generalized Assignment Problem

Martin W. P. Savelsbergh
- 01 Dec 1997 - 
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.
Journal ArticleDOI

Heuristics for the generalised assignment problem: simulated annealing and tabu search approaches

Ibrahim H. Osman
- 01 Dec 1995 - 
TL;DR: The effectiveness of the approaches is established by comparing their performance in terms of solution quality and computional requirement to other specialized branch-and-bound tree search, simulated annealing and set partitioning heuristics on a set of standard problems from the literature.
Book ChapterDOI

Mobile Edge Computing

Ben Liang
TL;DR: In this article, the authors present an augmented-reality application, where the user's mobile device continuously records its current view, computes its own location, and streams the combined information to the cloud server, while the Cloud server performs pattern recognition and information retrieval and sends back to the mobile device contextual augmentation labels, to be seamlessly displayed overlaying the actual scenery.
References
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Journal ArticleDOI

The Lagrangian Relaxation Method for Solving Integer Programming Problems

Marshall L. Fisher
- 01 Dec 2004 - 
TL;DR: This paper is a review of Lagrangian relaxation based on what has been learned in the last decade and has led to dramatically improved algorithms for a number of important problems in the areas of routing, location, scheduling, assignment and set covering.
Journal ArticleDOI

A generalized assignment heuristic for vehicle routing

Marshall L. Fisher, +1 more
- 01 Jun 1981 - 
TL;DR: This paper presents a heuristic for this problem in which an assignment of customers to vehicles is obtained by solving a generalized assignment problem with an objective function that approximates delivery cost and shows that it has outperformed the best existing heuristics on a sample of standard test problems.
Journal ArticleDOI

A dual-based procedure for uncapacitated facility location

Donald Erlenkotter
- 01 Dec 1978 - 
TL;DR: This approach has obtained and verified optimal solutions to all the Kuehn-Hamburger location problems in well under 0.1 seconds each on an IBM 360/91 computer, with no branching required.
Journal ArticleDOI

An Applications Oriented Guide to Lagrangian Relaxation

Marshall L. Fisher
- 01 Apr 1985 - 
TL;DR: This tutorial provides a practical guide to the use of Lagrangian relaxation and an on-line computerized routing and scheduling optimizer.
Journal ArticleDOI

A branch and bound algorithm for the generalized assignment problem

G. Terry Ross, +1 more
- 01 Dec 1975 - 
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.
Related Papers (5)

A branch and bound algorithm for the generalized assignment problem

G. Terry Ross, +1 more
- 01 Dec 1975 - 

A multiplier adjustment method for the generalized assignment problem

Marshall L. Fisher, +2 more
- 01 Sep 1986 - 

Knapsack Problems: Algorithms and Computer Implementations

Silvano Martello, +1 more

A genetic algorithm for the generalised assignment problem

P. C. Chu, +1 more
- 01 Jan 1997 - 

A Branch-and-Price Algorithm for the Generalized Assignment Problem

Martin W. P. Savelsbergh
- 01 Dec 1997 - 
Frequently Asked Questions (7)
Q1. What are the contributions mentioned in the paper "A survey of algorithms for the generalized assignment problem d.g. cattrysse and l.n. van wassenhove report 9010/a" ?

This paper surveys algorithms for the well-known problem of finding t he minimum cost assignment of jobs to agents so that each job is assigne d exactly once and agents are not overloaded. 

If the algorithm terminates without closing the duality gap because it is no longer possible to generate a valid inequality, a branch and bound approach can be used to carry on the solution procedure. 

The advantage of the heuristic is that itcan be used in a reduction algorithm that attempts to reduce the problem size by fixing variables to one or to zero. 

The second procedure of arnsten and Varbrand (1987) generates bounds through the solution of a surrogate relaxation of the knapsack constraints (2) and valid inequalities of the knapsack type (17). 

In the practical problems (with number of jobs >> number of agents) that were solved the heuristic led to solutions within 0.1% of the lower bound and consequently within 0.1% of the optimal solution. 

The strengthened relaxation is given by :(GR) min 1 22 (ci - wj + 8) xij (2), (4) } (16)15Their branching scheme is a combination of depth-first and breadth-first branching. 

TheLagrangean procedure of Mrnsten and Varbrand discussed in the previoussection appears to be more efficient (stronger bound at root node, less valid inequalities added) than the surrogate one.