In order to handle the uncertainties in the decision-making problems, two alternative optimization models are usually considered, namely stochastic programming and robust optimization.

 

Scenario-based stochastic programming uses a finite number of scenarios representing different realizations of the uncertain parameters. In addition, each scenario has associated a probability of occurrence. Then, the stochastic programming problem determines the decision variables that minimize (maximize) the expected cost (profit) over all scenarios, taking into account the constraints of the problem for each scenario realization.

 

Aqui no Livro do Baringo ele traz de volta aquela velha definição de otimizar o valor esperado do lucro/prejuízo. Lembrar que na verdade ou você otimiza a Função Utilidade ou você otimiza alguma métrica de risco.

 

In order to generate accurate scenarios, two important issues arise. On one hand, it is needed information about the probability distribution functions of uncertain parameters. On the other hand, a large enough number of scenarios are generally needed since the feasibility of the problem is only guaranteed for the considered scenarios.

 

An alternative to stochastic programming is robust optimization that uses uncertainty sets, e.g., based on confidence bounds, instead of considering some predefined scenarios. Robust optimization optimizes the worst case of the objective function considering that uncertain parameters can take any value within the considered uncertainty sets. Moreover, the feasibility of the problem is guaranteed for all realizations of the uncertain parameters within these uncertainty sets. Robust optimization is mainly useful when the probability distribution functions of uncertain parameters are not available.

 

Two different robust optimization models can be formulated depending on the decisions made in the decision-making process, namely robust optimization without recourse, also known as static robust optimization, and robust optimization with recourse, also known as two-stage robust optimization or adaptive robust optimization.