Activation Minimax criterion Stochastic
Dear colleagues,
From worldcup back to work...
Any idea how to activate the Minimax criterion (Savage, minimising maximum regret) ?
I remember this was implemented in TIMES some years ago ?
Thank you,

Dear Wouter,

Yes, simplistic support for the Minimax criterion was added in 2009.

The support is simplistic in the sense that it only provides a means to solve the "middle" problem of the three steps in applying the Minimax criterion, by minimizing the maximum deviation from the perfect information solution.

As you probably know, according to Loulou & Kanudia ("Minimax regret strategies for greenhouse gas abatement: methodology and application”, Operations Research Letters, 25: 219230), applying the Minimax criterion requires the following steps:

1.      Solve the deterministic perfect information problem for all sow, obtaining the objective values M(sow) ;

2.      Solve the Minimax problem, minimizing the worst regret (difference from the perfect information solution), obtaining the optimal hedging strategy;

3.      Solve the deterministic problem for all sow again, fixing the initial periods to the optimal hedging strategy.

The first (1) step above can be done by using the sensitivity analysis facility of TIMES. The "middle" step (2) above can be carried out by defining the following parameters for the stochastic problem:

S_UC_RHS('OBJ1','FX','2',sow) = M(sow)

Defining these parameters will activate the Minimax formulation under stochastic mode. The third step above can again be done by using the sensitivity analysis facility of TIMES, fixing the first periods to the solution from the second step.

As you can see, even if the formulation needed in step (2) is supported by TIMES, using the Minimax criterion requires considerable manual effort.  (It could, of course, be automated further, should there be general interest in that).


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