TY - GEN

T1 - Algorithms and extended formulations for one and two facility network design

AU - Chopra, Sunil

AU - Gilboa, Itzhak

AU - Sastry, S. Trilochan

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1996.

PY - 1996

Y1 - 1996

N2 - We consider the problem of sending flow from a source to a destination, where there are flow costs on each arc and fixed costs toward the purchase of capacity. Capacity can be purchased in batches of C units on each arc. We show the problem to be NP-hard in general. If d is the quantity to be shipped from the source to the destination, we give an algorithm that solves the problem in time polynomial in the size of the graph but exponential in(formula presented). Thus for bounded values of (formula presented) the problem can be solved in polynomial time. This is useful since a simple heuristic gives a very good approximation of the optimal solution for large values of (formula presented). We also show a similar result to hold for the case when there are no flow costs but capacity can be purchased either in batches of 1 unit or C units. The results characterizing optimal solutions are used to obtain extended formulations in each of the two cases. The LP-relaxations of the extended formulations are shown to be stronger than the natural formulations considered by earlier authors, even with a family of strong valid inequalities added.

AB - We consider the problem of sending flow from a source to a destination, where there are flow costs on each arc and fixed costs toward the purchase of capacity. Capacity can be purchased in batches of C units on each arc. We show the problem to be NP-hard in general. If d is the quantity to be shipped from the source to the destination, we give an algorithm that solves the problem in time polynomial in the size of the graph but exponential in(formula presented). Thus for bounded values of (formula presented) the problem can be solved in polynomial time. This is useful since a simple heuristic gives a very good approximation of the optimal solution for large values of (formula presented). We also show a similar result to hold for the case when there are no flow costs but capacity can be purchased either in batches of 1 unit or C units. The results characterizing optimal solutions are used to obtain extended formulations in each of the two cases. The LP-relaxations of the extended formulations are shown to be stronger than the natural formulations considered by earlier authors, even with a family of strong valid inequalities added.

UR - http://www.scopus.com/inward/record.url?scp=21344463741&partnerID=8YFLogxK

U2 - 10.1007/3-540-61310-2_4

DO - 10.1007/3-540-61310-2_4

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AN - SCOPUS:21344463741

SN - 3540613102

SN - 9783540613107

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 44

EP - 57

BT - Integer Programming and Combinatorial Optimization - 5th International IPCO Conference, 1996 Proceedings

A2 - Cunningham, William H.

A2 - McCormick, S.Thomas

A2 - Queyranne, Maurice

PB - Springer Verlag

T2 - 5th International Conference Integer Programming and Combinatorial Optimization, IPCO 1996

Y2 - 3 June 1996 through 5 June 1996

ER -