Recent Developments in Linear and Non-linear Multiobjective Programming for Multilevel Systems |
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23 constraints a₁ analytical decision-aid assumed attractive property body for analytical common constraints common resources compromise weights computational conflicting objectives convex combination coordination Dantzig and Wolfe decision problem decision units decomposition denote determine diagonal diagonal matrix distribution of resources dual variables related economic emission of pollution example facet policies finite number geometric programming model give rise global optimality guarantees a convergence indirect methods input-output interactive MOD procedure Johansen linear Linear Programming loss for objective main diagonal max W21 max W22 maximum attainable level minimum multi-component multi-objective geometric program multilevel planning method multiobjective programming Nijkamp and Rietveld numerical application Obviously optimal parametric program pay-off matrix policy model policy structure policy units ponent primal Raiffa relevant represented RICERCA OPERATIVA shadow prices solve spillover effects subdivisions systems components Table Ten Kate Theil tive typical element vector ween weights attached welfare x₁ Zeleny