A MULTI-OBJECTIVE ASSESSMENT OF INPUT–OUTPUT MATRIX UPDATING METHODS

This paper shows that important insights can be lost when assessing the relative performance of balancing methods solely based on individual optima. This is demonstrated through a multi-objective assessment. A trade-off curve between RAS and sign-preserving absolute differences (SPAD) is obtained based on the 60×60 Norwegian 2001 input–output table. The trade-off curve takes on a form that is close to a step function. This demonstrates that the solution surface around the RAS and SPAD optimums are very flat. Solutions can be identified that improve on the other objective or measure with little or marginal cost to the original objective function. Motivation for the assessment is provided, the technique applied is presented and the implications of the findings are discussed in an input–output and industrial ecology context.

[1]  D. H. Marks,et al.  A review and evaluation of multiobjective programing techniques , 1975 .

[2]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[3]  J. Oosterhaven.  GRAS versus minimizing absolute and squared differences: a comment , 2005 .

[4]  Yasushi Kondo,et al.  The Waste Input‐Output Approach to Materials Flow Analysis , 2007 .

[5]  Robert E. Bixby,et al.  Implementing the Simplex Method: The Initial Basis , 1992, INFORMS J. Comput..

[6]  Faye Duchin,et al.  Input-Output Economics and Material Flows , 2009 .

[7]  Michael Bacharach,et al.  Biproportional matrices & input-output change , 1970 .

[8]  Richard Stone,et al.  A Programme for Growth, 1. A Computable Model of Economic Growth , 1963 .

[9]  Sangwon Suh,et al.  A mixed-unit input-output model for environmental life-cycle assessment and material flow analysis. , 2007, Environmental science & technology.

[10]  Manfred Lenzen,et al.  Some Comments on the GRAS Method , 2007 .

[11]  Alan T. Murray,et al.  Alternative Input-Output Matrix Updating Formulations , 2004 .

[12]  Christian Solli,et al.  Applying Leontief's Price Model to Estimate Missing Elements in Hybrid Life Cycle Inventories , 2008 .

[13]  Michael Green.  Biproportional Matrices and Input‐Output Change , 1971 .

[14]  Jan Oosterhaven,et al.  The Solution of Updating or Regionalizing a Matrix with both Positive and Negative Entries , 2003 .

[15]  Gjalt Huppes,et al.  System boundary selection in life-cycle inventories using hybrid approaches. , 2004, Environmental science & technology.

[16]  Hajime Tanji,et al.  Updating an Input–Output Matrix with Sign-preservation: Some Improved Objective Functions and their Solutions , 2008 .