Price of Robustness Optimization through Demand Forecasting and Robust Planning Models Integration in Waste Management

Robust optimization can be effectively used to protect production plans against uncertainties. This is particularly important in sectors where variability is inherent the process that must be optimally planned. The drawback is that, in real situations, some information can be added in order to better control the extra-cost resulting from considering the parameter variability. This work investigates how demand forecasting can be used in conjunction with robust optimization in order to achieve an optimal planning considering demand uncertainties. In the proposed procedure forecast is used to update uncertain parameters of the robust model. Moreover the robustness budget is optimized at each planned stage in a rolling planning horizon. In this way the parameters of the robust model can be dynamically updated tacking information from the data. The study is applied to a reverse logistics case, where the planning of sorting for material recycling is affected by uncertainties in the demand, consisting of the waste material to be sorted and recycled. Results are compared with the standard robust optimization approach, using real case instances, showing potentialities of the proposed method.

Joint Estimation and Robustness Optimization

Many real-world optimization problems have input parameters estimated from data whose inherent imprecision can lead to fragile solutions that may impede desired objectives and/or render constraints infeasible. We propose a joint estimation and robustness optimization (JERO) framework to mitigate estimation uncertainty in optimization problems by seamlessly incorporating both the parameter estimation procedure and the optimization problem. Toward that end, we construct an uncertainty set that incorporates all of the data, and the size of the uncertainty set is based on how well the parameters are estimated from that data when using a particular estimation procedure: regressions, the least absolute shrinkage and selection operator, and maximum likelihood estimation (among others). The JERO model maximizes the uncertainty set’s size and so obtains solutions that—unlike those derived from models dedicated strictly to robust optimization—are immune to parameter perturbations that would violate constraints or lead to objective function values exceeding their desired levels. We describe several applications and provide explicit formulations of the JERO framework for a variety of estimation procedures. To solve the JERO models with exponential cones, we develop a second-order conic approximation that limits errors beyond an operating range; with this approach, we can use state-of-the-art second-order conic programming solvers to solve even large-scale convex optimization problems. This paper was accepted by J. George Shanthikumar, special issue on data-driven prescriptive analytics.