Abstract
A conventional mathematical programming problem can be described as a maximization of a well-defined objective function subject to well-defined constraints on a set of possible alternatives. Standard software tools (for example MPSX, APEX, etc.) can be used to calculate the optimal solution of the model, if the objective function and the constraints are linear functions and the possible alternatives are vectors of real or integer values. This is a very important advantage, but the possibility of application of mathematical programming is limited by the strict structure of the model. The underlying restricting assumptions are as follows: The considerations focus on a single objective function. The set of constraints differentiates exactly between feasible solutions and infeasible ones even if these violate a constraint only to a very small degree. Constraints are aggregated by intersection. This corresponds to the logical “and”. The set of feasible solutions is independent of the objective function. The objective function depends hierarchically on the constraints.
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