Abstract
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 Schöbel (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.
Highlights
A decision-making process implies the need to face conflicts, whether it is a management strategy, government policy, firm resource allocation, or individual budget planning; a certain course of action usually involving multiple conflicting objectives or criteria has to be taken [1]
As a proposal for overcoming the aforementioned drawback, we propose light Robust goal programming (RGP) models generalized for the budget of uncertainty and ellipsoidal uncertainty sets in the framework discussed in Schöbel (2014) and compare them with the previous RGP models
Contrary to the conservative models provided in the literature (c.f., [13,16,19,21,22]), we present light robust goal programming (LRGP) models generalized to two arbitrary sets—the budget of uncertainty and the ellipsoidal uncertainty set
Summary
A decision-making process implies the need to face conflicts, whether it is a management strategy, government policy, firm resource allocation, or individual budget planning; a certain course of action usually involving multiple conflicting objectives or criteria has to be taken [1]. One of the drawbacks of this RO approach is that the solutions provided can be suboptimal if compared with the solution of the so-called nominal problem, i.e., a problem without uncertainty in which the parameter values are fixed (for instance, to some point estimation). Hanks et al [13] proposed norm-based uncertainty sets using cardinality-constrained robustness and strict robustness via ellipsoidal uncertainty and compared their approach with the interval-based approach in [19] Their robust models have the aforementioned drawback—they can be highly suboptimal if compared to the solution of the nominal problem, e.g., their quality is low or, equivalently, they are very conservative. The light robustness approach addresses the conservatism of the RGP by setting a limit to the deterioration of the objective value compared to the nominal solution.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
