Production planning under uncertainty: Stochastic programming versus robust optimization

Abstract

Optimizing production planning problems under uncertainty is a challenge, because it is necessary to define whether there is a methodology more appropriate to deal with the type of uncertainty of the problem, whether such methodology is computationally tractable, and which advantages and disadvantages the approaches available in the literature can bring to the analysis of the problem. In this paper, we analyze two important methodologies to deal with uncertainties in a production planning problem: two-stage stochastic programming and robust optimization. Whereas stochastic programming is one of the techniques most traditionally used in production planning problems under uncertainty, such approach can generate intractable models when a very large number of scenarios is considered. Robust optimization arises as an alternative technique to overcome the potential drawback of stochastic programming models, but it can be overly conservative depending on how the uncertainties are modeled. This paper also discusses the advantages and disadvantages of each methodology based on a practical problem of production planning in the furniture industry. The comparison between both approaches is given in terms of objective function, service level, and computational effort. The overall results suggest that both techniques are competitive when less conservative budgets of uncertainty are used in the robust optimization model. It was also verified that the robust counterpart model can be more easily solved compared with the stochastic version model, which is especially important when the deterministic model is already difficult to solve.