# 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

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topBurkard, 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 -

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