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##
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An algebraic approach to assignment problems

1977
*
Mathematical programming
*

*Special*cases of

*the*

*general*model are

*the*linear

*assignment*

*problem*,

*the*linear bottleneck

*problem*, lexicographic multicriteria

*problems*, p-norm

*assignment*

*problems*and others. ... Further a polynomial bounded

*algorithm*

*for*solving this

*generalized*

*assignment*

*problem*is stated.

*The*algebraic approach can be extended to a broader class of combinatorial optimization

*problems*. ...

*The*

*general*linear

*assignment*

*problem*(GLAP) Let S be a nonempty

*set*together

*with*

*an*internal composition * and

*an*

*order*relation ~<. ...

##
###
A branch and bound algorithm for the generalized assignment problem

1975
*
Mathematical programming
*

Computational results are cited

doi:10.1007/bf01580430
fatcat:fcddvnfmcnannmuwfibdhkoztm
*for**problems**with*up to 4 000 0-1 variables, and comparisons are made*with*other*algorithms*. ... 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. ... Nauss regarding both*the*Lagrangean relaxation interpretation of*the**algorithm*and its computational implementation. ...##
###
Page 852 of Mathematical Reviews Vol. , Issue 83b
[page]

1983
*
Mathematical Reviews
*

Author’s summary: “

*The*article considers some*algorithms**for**assignment**problems**with**special*subclasses of initial matrices. ... .” 83b:90101 83b:90102 Johnson, Ellis L.; Padberg, Manfred W. 83b:90103 A note on*the*knapsack*problem**with**special**ordered**sets*. ...##
###
Page 4810 of Mathematical Reviews Vol. , Issue 84k
[page]

1984
*
Mathematical Reviews
*

*An*intersection

*assignment*

*for*a graph G

*assigns*to each vertex x of G a

*set*S(x) so that

*for*all xy in V, {x,y} EE S(x)NS(y)# @. ... “Finally, we consider in Chapter 6

*an*application of

*the*algebraic matroid flow theory

*for*a

*special*choice of (H,+*,<). ...

##
###
Integrating facility location and production planning decisions

2009
*
Networks
*

We show that

doi:10.1002/net.20315
fatcat:vf7xivzdwzfyhlwd5vyvw6scnm
*the**problem*, in*general*, is as hard to approximate as*the**set*cover*problem*. We therefore focus on developing approximation*algorithms**for**special*cases of*the**problem*. ... We develop a modified greedy*algorithm*together*with**the*idea of cost-scaling to provide*an**algorithm**for*this class of*problems**with**an*approximation guarantee of 1.52. ... Acknowledgments We thank*the*anonymous referees*for*their helpful suggestions that led to a better presentation of*the*paper. ...##
###
Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem

1992
*
Transportation Science
*

feasible solutions in SD

doi:10.1287/trsc.26.1.4
fatcat:nrwk6o32a5fthehm573ek7y55i
*algorithms**for*convex*problems*over Cartesian product*sets*,*with*application to*the*symmetric traffic*assignment**problem*. ...*The*new*algorithm*, which is referred to as disaggregate simplicial decomposition (DSD), is given along*with*a*specialized*solution method*for**the*disaggregate master*problem*. ... Professor Michael Florian provided us*with**the*networks of Hull and Winnipeg, and Professor Barcelo supplied*the*network of Barcelona. Olof Damberg helped us*with*some coding details. ...##
###
Page 3850 of Mathematical Reviews Vol. , Issue 96f
[page]

1996
*
Mathematical Reviews
*

*An*optimal solution

*for*

*the*continuous relaxation of

*the*

*problem*is obtained by

*generalizing*

*the*alternating basis

*algorithm*of Barr, Glover, and Klingman

*for*

*the*pure

*assignment*

*problem*. ... Summary: “This manuscript presents a

*specialized*primal simplex

*algorithm*to obtain near optimal integer solutions

*for*

*the*singly constrained

*assignment*

*problem*. ...

##
###
A note on 'Exact and approximate methods for a one-dimensional minimax bin-packing problem' [Annals of Operations Research (2013) 206:611-626]
[article]

2014
*
arXiv
*
pre-print

We also propose a pseudo-polynomial

arXiv:1402.1616v1
fatcat:m7fxhyvbnfgwtowzxq6sqge6ay
*algorithm**for**the**special*case and a constructive heuristic*for**the**general**problem*. ... In this note, we show that this*problem*is NP-hard*for**the**special*case and that it is strongly NP-hard*for**the**general**problem*. ... End*For**The*computationally expensive part of*the**algorithm*is*the**ordering*of*the**sets*and items on*the*groups, which is step 2a. ...##
###
Production Scheduling and Customer Orders Assignment in a Three-Level Supply Chain

2014
*
ISRN Industrial Engineering
*

This paper extends

doi:10.1155/2014/163637
fatcat:l4uxumc3ifbbdmn7xixukfsnqi
*the**problem*of production-distribution centers*assignment*by considering sequencing decisions in*the*supply network. ...*The*computational results show*the*superiority of*the*variable neighborhood search*algorithm*. ... Conflict of Interests*The*authors declare that there is no conflict of interests regarding*the*publication of this paper. ...##
###
A fundamental problem in linear inequalities with applications to the travelling salesman problem

1972
*
Mathematical programming
*

Recent published work indicates that this

doi:10.1007/bf01584550
fatcat:bjmpi3ramfcwlblnkp2aackese
*algorithm*has applications in integer linear programming.*An**algorithm**for*this*problem*using a*set*covering approach is described. ...*The**problem*is to develop*an*efficient*algorithm*to determine whether there exists a feasible basis which contains all*the**special*column vectors as basic column vectors and to find such a basis if one ... Acknowledgements I wish to thank*the**the*presentation. referee*for*suggesting several improvements in ...##
###
Page 6840 of Mathematical Reviews Vol. , Issue 94k
[page]

1994
*
Mathematical Reviews
*

By using

*the*observation that*an**ordered*product matrix is either doubly graded or a so-called max-distribution ma- trix of a*special*type,*the*author derives*an*O(n)*algorithm**for**the*considered*problem*...*For*such so-called*ordered*product distance matrices*an*O(n*)*algorithm*is known. ...##
###
Online Ad Assignment with Free Disposal
[chapter]

2009
*
Lecture Notes in Computer Science
*

Furthermore, our

doi:10.1007/978-3-642-10841-9_34
fatcat:crrxszhjtzf7ferlrb27lezdx4
*algorithm*can be applied to a*general**set*of*assignment**problems*including*the*ad words*problem*as a*special*case, matching*the*previously known 1 − 1/e competitive ratio. ...*With*free disposal, we provide*an**algorithm**for*this*problem*that achieves a competitive ratio of 1 − 1/e against*the*offline optimum, and show that this is*the*best possible ratio. ...*The**Generalized**Assignment**Problem*In*the**Generalized**Assignment**Problem*(GAP), a*set*A of bins/machines and a*set*I of items/jobs is given. ...##
###
Introduction to the Special Issue: Evolutionary Algorithms for Scheduling

1998
*
Evolutionary Computation
*

*For*

*the*

*generic*

*problem*of

*assigning*N tasks to M resources

*with*a particular

*ordering*of tasks at each resource,

*the*number of possible solutions is superexponential growth as a function of

*the*number ... •

*the*need

*for*additional information beyond

*an*

*ordered*

*assignment*of tasks to resources, such as absolute times, routes traveled, and manufacturing plans 1 ...

*For*

*the*

*generic*

*problem*of

*assigning*N tasks to M resources

*with*a particular

*ordering*of tasks at each resource,

*the*number of possible solutions is N + M − 1 M − 1 N ! ...

##
###
T-colorings of graphs: recent results and open problems

1991
*
Discrete Mathematics
*

Here,

doi:10.1016/0012-365x(91)90258-4
fatcat:6bmqbfltm5cbloaeembmxryhku
*the*vertices of G are transmitters,*an*edge represents interference, f(x) is a television or radio channel*assigned*to x, and T is a*set*of disallowed separations*for*channels*assigned*to interfering ... This paper surveys*the*results and mentions open*problems*concerned*with*T-colorings and their variations and*generalizations*. ... Acknowledgements*The*author gratefully acknowledges*the*support of Air Force Office of Scientific Research grants AFOSR-85-0271, AFOSR-89-0512, and AFOSR-!%I-0008 to Rutgers University. ...##
###
Page 6790 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

*An*illustrative example is included.” 90k:90108 90C10 05C20 90C20 90C27 Flood, Merrill M. (1-UCSD) Exact and heuristic

*algorithms*

*for*

*the*weighted feedback arc

*set*

*problem*: a

*special*case of

*the*skew-symmetric ... This is a

*special*case of

*the*Koopmans-Beckmann quadratic

*assignment*

*problem*. ...

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