Light Robust Goal Programming

Robust goal programming (RGP) is an emerging field of research in decision-making problems with multiple conflicting objectives and uncertain parameters. RGP combines robust optimization (RO) with variants of goal programming techniques to achieve stable and reliable goals for previously unspecified aspiration levels of the decision-maker. The RGP model proposed in Kuchta (2004) and recently advanced in Hanks, Weir, and Lunday (2017) uses classical robust methods. The drawback of these methods is that they can produce optimal values far from the optimal value of the "nominal" problem. As a proposal for overcoming the aforementioned drawback, we propose light RGP models generalized for the budget of uncertainty and ellipsoidal uncertainty sets in the framework discussed in Schobel (2014) and compare them with the previous RGP models. Conclusions regarding the use of different uncertainty sets for the light RGP are made. Most importantly, we discuss that the total goal deviations of the decision-maker are very much dependent on the threshold set rather than the type of uncertainty set used.