Multicriterion Design of High-Productivity Systems

Further developments on de novo approach to linear programming and its multiobjective versions is being reported. First, optimal design of systems, rather than optimizing with respect to a given system, is introduced. Duality theory and shadow prices are explored and their unreliable use in traditional LP noted. A multicriterion optimal design for high-productivity system is demonstrated in terms of making an ideal solution feasible. The problem of choosing an optimal systems, rather than choosing an alternative from a given system, is introduced into MCDM; the expanded concept of optimality is shortly discussed. Two algorithms for efficient solving of large-scale LP problems characterized by mixed hard and soft constraints (including both extremes) are presented: External Reconstruction Approach (ERA) and Invariant Cone Method (ICM). Numerical examples are given throughout the paper.