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### An algebraic approach to assignment problems

Rainer E. Burkard, Willi Hahn, Uwe Zimmermann
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

G. Terry Ross, Richard M. Soland
1975 Mathematical programming
Computational results are cited 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

H. Edwin Romeijn, Thomas C. Sharkey, Zuo-Jun Max Shen, Jiawei Zhang
2009 Networks
We show that 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 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]

Mariona Vilà, Jordi Pereira
2014 arXiv   pre-print
We also propose a pseudo-polynomial 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 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

Katta G. Murty
1972 Mathematical programming
Recent published work indicates that this 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]

Jon Feldman, Nitish Korula, Vahab Mirrokni, S. Muthukrishnan, Martin Pál
2009 Lecture Notes in Computer Science
Furthermore, our 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

David Montana
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

Fred S. Roberts
1991 Discrete Mathematics
Here, 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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