Bounding constraints in certain linear programming problems and the principle of safety first

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Through a modification of Roy's principle of safety first, the behavioral bounding constraints often encountered in descriptive applications of linear programming are interpreted as planes of support for a quadratic constraint that reflects the decision-maker's attitude toward uncertainty. In this way a linkage is established from the bounding constraint to the elements of uncertainty, the variances and covariances of relevant random variables. To illustrate the development, an application is made to interpret the “flexibility” constraints used in the recursive programming models of Henderson-Day. In contrast to the assumptions made in most studies using such constraints, we find that to be consistent with the modified safety first principle, the “flexibility” coefficients cannot be constant, but must change from period to period through a well-defined (though complicated) dependence on past levels of decision variables.