In INOCS, we consider that an optimization problem presents a complex structure (CS) when two types of decision are addressed jointly and are interrelated. Examples are decisions of different types/nature (i.e. strategic, tactical or operational), and/or presenting some hierarchical leader-follower structure. CS problems lead to extremely challenging problems since a global optimum with respect to the whole sets of decision variables and constraints must be determined. INOCS models and develops innovative solution methods for CS problems according to three types of optimization paradigms: mathematical optimization, bilevel optimization, and robust/stochastic optimization.

CS problems are pervasive. They appear in a broad range of application fields such as :

• the energy sector where decisions of distinct nature such as production and distribution are jointly determined;
• supply chain management where location and routing decisions have to be defined jointly even if they refer to different time horizons;
• revenue management where the determination of prices for services or products requires taking explicitly into account the strategic consumers’ behavior. Significant advances have been made in optimization to solve academic problems. Nowadays large-scale instances of some NP-Hard problems are routinely solved to optimality. Our vision within INOCS is to make the same advances while addressing CS optimization problems. To achieve this goal we aim to develop global solution approaches at the opposite of the current trend.