Minimax Regret in Linear Programming Problems with an Interval Objective Function

An achievement rate approach to linear programming problems with an interval objective function

“…In order to cope with such defects of necessarily and possibly optimal solutions, a minimax regret solution has been proposed in [7]. A minimax regret solution coincides 'This assumption is introduced to guarantee the convergence of the algorithm discussed in what follows.…”

“…The fact that a maximin achievement rate solution is possibly optimal can be proved by using the following lemma proved in [7].…”

“…For the purpose of comparing the proposed maximin achievement rate solution with the minimax regret solution, a minimax regret solution is computed and obtained as follows by the algorithm proposed in [7]:…”

“…The solution is necessarily optimal when a necessarily optimal solution exists. As such a criterion, the minimax regret criterion has been proposed in [7]. A solution algorithm based on the relaxation procedure has also been proposed to obtain a minimax regret solution.…”

Multiple objective linear programming models with interval coefficients – an illustrated overview

“…In this sense, some algorithms only deal with uncertainty in the objective functions, others handle uncertainty both in the objective functions and in the RHS of the constraints, and others deal with uncertainty in all the coefficients of the model. Inuiguchi and Kume (1994) and Inuiguchi and Sakawa (1995) consider two different approaches to deal with an interval objective function: the satisficing approach and the optimizing approach. In the satisficing approach each interval objective function is transformed into one or several objective functions (the lower bound, the upper bound and the central value of the intervals are usually used) in order to obtain a compromise solution (e.g.…”