# Bouygues Telecom — Network Expansion Planning

Bouygues Telecom is a French mobile phone, Internet service provider, and IPTV company (\$7.3 billion in annual revenue, 5,500 employees). For many years, Bouygues Telecom has used the expertise of LocalSolver to develop custom software solutions for revenue management, data analysis, marketing operation planning, and network design.

## Context and problem

The network of an Internet Service Provider is always evolving for robustness reasons: to reach new customers, to update old technologies, or to satisfy unique needs. In 2014, Bouygues Telecom’s strategy was to expand its core network to reach new customers with a very competitive DSL offer. Bouygues Telecom had to decide which of the 14,000 connecting nodes in France to link to its core network. Adding a new node to its core network increases the company revenue, but it comes with a cost. One must connect each new node to the core network through a network of preinstalled dark fibers. The company makes savings if several nodes share a common path to the core network. Bouygues Telecom’s objective was to connect around 1,500 new nodes to its core network to maximize its profits (revenues of new nodes minus connection costs).

#### Key figures

• 14,000 nodes
• 1,500 new nodes to connect

#### Constraints

• Ensuring connectivity
• Design constraints

#### Objective

• Maximize profits

## Results

Due to the large scale of the problem, the mathematical model was challenging to solve, involving more than 1 million variables. As in most network design problems, the connectivity constraint modeling was intricate and led to several auxiliary expressions.

• 1,400,000 variables
• 120,000 binaries
• 360,000 constraints

Once modeled, LocalSolver delivered quality solutions in a few minutes of running time on a standard laptop, including input and output processing times. In addition, the solution quality was checked by solving a combinatorial relaxation of the problem showing tighter lower bounds.

Bouygues Telecom’s network engineering team started to use our optimization solution in 2014. Since that time, the company has connected 3,000 new nodes in addition to the ones they already operated. This strategy allowed Bouygues Telecom to offer a competitive DSL offer to a much larger customer base, contributing to gain hundreds of thousands of new customers. Since then, Bouygues Telecom has leveraged several other optimization solutions built upon LocalSolver to solve network design and expansion problems to deploy new telecom technologies.

## Why LocalSolver?

Bouygues Telecom’s network experts had to evaluate several scenarios with different economical hypotheses. In this context, having solutions in short running times was critical. Additional business constraints were subsequently added to the mathematical model to forbid impractical designs. LocalSolver was able to handle these highly nonlinear design constraints straightforwardly, then reducing the time between planning iterations.

Your services were a crucial help for our project, and we have total confidence in Julien who, over the years, continues to impress me with the quality of his support, his versatility, and his professionalism! True added value and innovative technology.

Alexis Bruno, Network Software Architect, Bouygues Telecom

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