Bottleneck Capacity Expansion Problems with General Budget Constraints

Rainer E. Burkard; Bettina Klinz; Jianzhong Zhang

RAIRO - Operations Research (2010)

  • Volume: 35, Issue: 1, page 1-20
  • ISSN: 0399-0559

Abstract

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This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family F of feasible subsets of E and a nonnegative real capacity ĉe for all e ∈ E. Moreover, we are given monotone increasing cost functions fe for increasing the capacity of the elements e ∈ E as well as a budget B. The task is to determine new capacities ce ≥ ĉe such that the objective function given by maxF∈Fmine∈Fce is maximized under the side constraint that the overall expansion cost does not exceed the budget B. We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expansion problem. For an important subclass of bottleneck capacity expansion problems we propose algorithms which perform a strongly polynomial number of steps. In this manner we generalize and improve a recent result of Zhang et al. [15].

How to cite

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Burkard, Rainer E., Klinz, Bettina, and Zhang, Jianzhong. " Bottleneck Capacity Expansion Problems with General Budget Constraints." RAIRO - Operations Research 35.1 (2010): 1-20. <http://eudml.org/doc/116589>.

@article{Burkard2010,
abstract = { This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family F of feasible subsets of E and a nonnegative real capacity ĉe for all e ∈ E. Moreover, we are given monotone increasing cost functions fe for increasing the capacity of the elements e ∈ E as well as a budget B. The task is to determine new capacities ce ≥ ĉe such that the objective function given by maxF∈Fmine∈Fce is maximized under the side constraint that the overall expansion cost does not exceed the budget B. We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expansion problem. For an important subclass of bottleneck capacity expansion problems we propose algorithms which perform a strongly polynomial number of steps. In this manner we generalize and improve a recent result of Zhang et al. [15]. },
author = {Burkard, Rainer E., Klinz, Bettina, Zhang, Jianzhong},
journal = {RAIRO - Operations Research},
keywords = {Capacity expansion; bottleneck problem; strongly polynomial algorithm; algebraic optimization.; strongly polynomial algorithm; algebraic optimization. },
language = {eng},
month = {3},
number = {1},
pages = {1-20},
publisher = {EDP Sciences},
title = { Bottleneck Capacity Expansion Problems with General Budget Constraints},
url = {http://eudml.org/doc/116589},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Burkard, Rainer E.
AU - Klinz, Bettina
AU - Zhang, Jianzhong
TI - Bottleneck Capacity Expansion Problems with General Budget Constraints
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 1
SP - 1
EP - 20
AB - This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family F of feasible subsets of E and a nonnegative real capacity ĉe for all e ∈ E. Moreover, we are given monotone increasing cost functions fe for increasing the capacity of the elements e ∈ E as well as a budget B. The task is to determine new capacities ce ≥ ĉe such that the objective function given by maxF∈Fmine∈Fce is maximized under the side constraint that the overall expansion cost does not exceed the budget B. We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expansion problem. For an important subclass of bottleneck capacity expansion problems we propose algorithms which perform a strongly polynomial number of steps. In this manner we generalize and improve a recent result of Zhang et al. [15].
LA - eng
KW - Capacity expansion; bottleneck problem; strongly polynomial algorithm; algebraic optimization.; strongly polynomial algorithm; algebraic optimization.
UR - http://eudml.org/doc/116589
ER -

References

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