Flexible linear programs with a restricted overall flexibility level

It is usually supposed that tolerance levels are determined by the decision maker a priori in flexible linear programming (FLP) problems. In this paper we shall suppose that the decision maker does not care about the particular values of tolerance levels, but he wishes to keep their sum below a predetermined level, which we call his overall flexibility level. We also suppose that his overall flexibility level is soft, i.e. it is admissible to exceed it (to a certain extent). This is a new statement of FLP problems, because here the tolerance levels are also treated as variables, and the only restriction on them is that their sum should not exceed very much a given level. In this setup, we shall prove that the consistency level of FLP problems depends continuously on the decision maker’s overall flexibility level.