## Thesis etd-11262009-005543 |

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Thesis type

Tesi di dottorato di ricerca

Author

PASCALI, FAUSTO

email address

PASCALI@DI.UNIPI.IT

URN

etd-11262009-005543

Thesis title

Chance Constrained Network Design

Academic discipline

INF/01

Course of study

MATEMATICA PER LE DECISIONI ECONOMICHE

Supervisors

**relatore**Prof. Frangioni, Antonio

**commissario**Prof. Gallo, Giorgio

**commissario**Prof. Cappanera, Paola

**tutor**Prof.ssa Scutellà, Maria Grazia

Keywords

- chance
- design
- network
- optimization
- robust
- routing

Graduation session start date

17/12/2009

Availability

Full

Summary

the thesis deals with important problem of planning of telecommunication

networks (and other networks which carry demand between different network nodes

requiring allocation of capacities along the network links). More specifically, the problem

is to find the network with the minimal cost which will satisfy uncertain demand. Two

descriptions of uncertainty are considered. In the first one the demand matrices belong to

a known set defined by different sets of linear constraints, this approach of robust

optimization. In the second one the demand matrices belong to a given set with some

specified probability, this problem formulation can be classified as stochastic

programming problem with probability (chance) constraints.

- In robust setting an interesting and important special case is found when the static

routing in certain sense gives no worse results as dynamic routing.

- In chance constrained case several approximate deterministic formulations are

developed and studied. These approximations are critical from the point of view of

computability because the original chance constrained formulation presents considerable

computational difficulties.

Extensive numerical experiments with different problem formulations are presented which allows to analyze meaningfully relative properties of different approximations

networks (and other networks which carry demand between different network nodes

requiring allocation of capacities along the network links). More specifically, the problem

is to find the network with the minimal cost which will satisfy uncertain demand. Two

descriptions of uncertainty are considered. In the first one the demand matrices belong to

a known set defined by different sets of linear constraints, this approach of robust

optimization. In the second one the demand matrices belong to a given set with some

specified probability, this problem formulation can be classified as stochastic

programming problem with probability (chance) constraints.

- In robust setting an interesting and important special case is found when the static

routing in certain sense gives no worse results as dynamic routing.

- In chance constrained case several approximate deterministic formulations are

developed and studied. These approximations are critical from the point of view of

computability because the original chance constrained formulation presents considerable

computational difficulties.

Extensive numerical experiments with different problem formulations are presented which allows to analyze meaningfully relative properties of different approximations

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