Inverse linear programming with interval coefficients

The paper deals with the inverse linear programming problem over intervals. More precisely, given interval domains for the objective function coefficients and constraint coefficients of a linear program, we ask for which scenario a prescribed optimal value is attained. Using continuity of the optimal value function (under some assumptions), we propose a method based on parametric linear programming techniques. We study special cases when the interval coefficients are situated in the objective function and/or in the right-hand sides of the constraints as well as the generic case when possibly all coefficients are intervals. We also compare our method with the straightforward binary search technique. Finally, we illustrate the theory by an accompanying numerical study, called “Matrix Casino”, showing some approaches to designing a matrix game with a prescribed game value.