, Volume 12, Issue 6, pp 373-380
Date: 26 Jun 2006

Efficient algorithms for Life Cycle Assessment, Input-Output Analysis, and Monte-Carlo Analysis

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Goal, Scope, and Background

As Life Cycle Assessment (LCA) and Input-Output Analysis (IOA) systems increase in size, computation times and memory usage can increase rapidly. The use of efficient methods of solution allows the use of a wide range of analysis techniques. Some techniques, such as Monte-Carlo Analysis, may be limited if computational times are too slow.

Discussion of Methods

In this article, I describe algorithms that substantially reduce computation times and memory usage for solving LCA and IOA systems and performing Monte-Carlo analysis. The algorithms are based on well-established iterative methods of solving linear systems and exploit the power series expansion of the Leontief inverse. The algorithms are further enhanced by using sparse matrix algebra.

Results and Discussion

The algorithms presented in this article reduce computational time and memory usage by orders of magnitude, while still retaining a high degree of accuracy. For a 3225×3225 LCA system, the algorithm reduced computation time from 70s to 0.06s while retaining an accuracy of 10−3%. Storage was reduced from 166 megabytes to 1.8 megabytes. The algorithm was used to perform a Monte-Carlo analysis on the same system with 1,000 samples in 90s. I also discuss various issues of power series convergence for general LCA and IOA systems and show that convergence will generally hold due to the mathematical structure of LCA and IOA systems.


By exploiting the mathematical structure of LCA and IOA iterative techniques substantially reduced the computational times required for solving LCA and IOA systems and for performing Monte-Carlo simulations. This allows more wide-spread implementation analysis techniques, such as Monte-Carlo analysis, in LCA and IOA.

Recommendations and Perspectives

It is suggested that algorithms, such as the ones described in this article, should be implemented in LCA packages. Various checks can be used to verify that computational errors are kept to a minimum.