scholarly journals Erratum to: Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study

2016 ◽  
Vol 14 (2) ◽  
pp. 293-296
Author(s):  
Andreas Bärmann ◽  
Andreas Heidt ◽  
Alexander Martin ◽  
Sebastian Pokutta ◽  
Christoph Thurner
Keyword(s):  
Extended Formulations ◽  
Polyhedral Approximation ◽  
Uncertainty Sets ◽  
Ellipsoidal Uncertainty

Polyhedral approximation of ellipsoidal uncertainty sets via extended formulations: a computational case study

2015 ◽  
Vol 13 (2) ◽  
pp. 151-193 ◽  
Author(s):  
Andreas Bärmann ◽  
Andreas Heidt ◽  
Alexander Martin ◽  
Sebastian Pokutta ◽  
Christoph Thurner
Keyword(s):  
Extended Formulations ◽  
Polyhedral Approximation ◽  
Uncertainty Sets ◽  
Ellipsoidal Uncertainty

scholarly journals A Robust Optimization Approach to the Multiple Allocation p-Center Facility Location Problem

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 588 ◽  
Author(s):  
Bo Du ◽  
Hong Zhou
Keyword(s):  
Robust Optimization ◽  
Facility Location ◽  
Location Problem ◽  
Facility Location Problem ◽  
Optimization Approach ◽  
Robust Solutions ◽  
Demand Node ◽  
Uncertainty Sets ◽  
Ellipsoidal Uncertainty ◽  
Multiple Allocation

In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness.

scholarly journals Light Robust Goal Programming

2019 ◽  
Vol 24 (4) ◽  
pp. 85 ◽  
Author(s):  
Mensah ◽  
Rocca
Keyword(s):  
Decision Maker ◽  
Goal Programming ◽  
Aspiration Levels ◽  
Conflicting Objectives ◽  
Optimal Value ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
Programming Techniques ◽  
Ellipsoidal Uncertainty ◽  
Optimal Values

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.

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