# Uncertainty: Synchronous Optical Network Ring Design¶

Direct download AIMMS Project NetworkRingDesign.zip

Go to the example on GitHub: https://github.com/aimms/examples/tree/master/Practical%20Examples/Uncertainty/NetworkRingDesign

Problem type: MIP (medium - hard)

Keywords: Synchronous Optical Network, SONET, ring assignment, stochastic programming, stochastic integer programming, uncertain data, Benders decomposition, network object.

Description: To prevent failures of a single optical telecommunication fiber, selfhealing rings (SHR) are utilized to connect client nodes by a ring of fibers. These rings automatically reroute telecommunication traffic in the case of equipment failure, providing essential survivability to high-bandwidth networks.

In this problem we consider the assignment of rings to nodes in a network. The objective is to minimize the total cost of the network subject to a ring capacity limit. Demands are given for each pair of nodes. If one of the nodes is not assigned to a ring then the corresponding demand is unmet, and penalized in the objective.

In practice, the demand may depend on several unknown factors. In such cases, a network design that considers this uncertainty may perform better than one that does not. In this project we deal with this uncertainty by using stochastic programming, which results in this case in a 2-stage stochastic integer program. One way to solve the stochastic integer program is by using the Benders decomposition algorithm of CPLEX.

This example uses the network structure of several instances used by Goldschmidt, Laugier and Olinick (2003). These instances can be found at: https://lyle.smu.edu/~olinick/papers/srap/srap.html

Note: To run the Benders decomposition algorithm with CPLEX, version 12.7 or higher is required.

References: Smith, J.C., A. J. Schaefer, J. W. Yen, A Stochastic Integer Programming Approach to Solving a Synchronous Optical Network Ring Design Problem, NETWORKS 44(1) (2004), pp. 12-26.

Goldschmidt, O., A. Laugier, E.V. Olinick, SONET/SDH ring assignment with capacity constraints, Discrete Applied Mathematics 129 (2003), pp. 99-128

Last Updated: September, 2020