i have to build a robust optimization model for my masterthesis at the Technical University in Braunschweig. Therefore i choose the Minimax-Regret Function! These approach deals with different scenarios k. I need to implement this function in an existing basic model, which is a single factory location problem. The basic model calculates the minimal sum of all deviations "d" from target values (so it is a Goal Programming approach) and based on these deviations the output of the model is one compromise-optimal location solution (the basic model is based on one scenario).
So first i implement a new index k for the scenarios to dealwith more than one scenario. How to deal with a minimax-obejctive function in AIMMS is already explained very well in one of the AIMMS Modeling Guides (https://download.aimms.com/aimms/download/manuals/AIMMS3OM_LinearProgrammingTricks.pdf). But i have some issues with the Regret. The definition of the regret is R = d - d*. Therefore, d is the deviation of location i in scenario k and d* is the optimal solution in scenario k (= the minimal sum of deviations = the solution of the basic model). Should i use a for-loop (e.g. for i = k) or is there another way?
I hope my description is understandable! And maybe one of you had the same problem in the past and can give me some advises. I would be very thankful for any information or support!
Best answer by alexanderwenzelView original
And you want to minmax R(k,i) ?
Are you able to write down the formulation on paper?