Robust goal programming using different robustness echelons via norm-based and ellipsoidal uncertainty sets

Abstract

The notion of robust goal programming (RGP) using cardinality-constrained robustness via interval-based uncertainty was first examined over a decade ago. Since then, the RGP methodology has not been widely researched, specifically when considering different uncertainty sets to implement. Within this context, this paper compares interval-based and norm-based uncertainty sets using cardinality-constrained robustness. Strict robustness using ellipsoidal uncertainty sets is also examined in the RGP realm. The aforementioned methods are demonstrated for a simple instance from the literature, and the results are summarized. Conclusions are made regarding the proposed RGP models when likened to a similar RGP model seen in the literature. Further, the suitability of each RGP model is offered when a decision maker's risk preference or computing availability are taken into consideration. Inferences are made regarding the effectiveness of each uncertainty set in the context of solutions that are relatively unaffected by data uncertainty – that is, robust solutions.