Consequential LCA and LCC using linear programming: an illustrative example of biorefineries

Maik Budzinski,Daniela Thrän,Mattia Sisca

doi:10.1007/s11367-019-01650-6

Abstract

PurposeThis paper aims to demonstrate how LCA can be improved by the use of linear programming (LP) (i) to determine the optimal choice between new technologies, (ii) to identify the optimal region for supplying the feedstock, and (iii) to deal with multifunctional processes without specifying a certain main product. Furthermore, the contribution of LP in the context of consequential LCA and LCC is illustrated.MethodsWe create a mixed integer linear program (MILP) for the environmental and economic assessment of new technologies. The model is applied in order to analyze two residual beech wood-based biorefinery concepts in Germany. In terms of the optimal consequences for the system under study, the principle of the program is to find a scaling vector that minimizes the life cycle impact indicator results of the system. We further transform the original linear program to extend the assessment by life cycle costing (LCC). Thereby, two multi-objective programming methods are used, weighted goal programming and epsilon constraint method.Results and discussionThe consequential case studies demonstrate the possibility to determine optimal locations of newly developed technologies. A high number of potential system modifications can be studied simultaneously without matrix inversion. The criteria for optimal choices are represented by the objective functions and the additional constraints such as the available feedstock in a region. By combining LCA and LCC targets within a multi-objective programming approach, it is possible to address environmental and economic trade-offs in consequential decision-making.ConclusionsThis article shows that linear programming can be used to extend standard LCA in the field of technological choices. Additional consequential research questions can be addressed such as the determination of the optimal number of new production plants and the optimal regions for supplying the resources. The modifications of the program by additional profit requirements (LCC) into a goal program and Pareto optimization problem have been identified as promising steps toward a comprehensive multi-objective LCSA.

Highlights

Life cycle assessment (LCA), and in particular consequential LCA, is regarded as an appropriate tool for the assessment of environmental impacts of new bio-based technologies (e.g., Pawelzik et al 2013)
The aim of this paper is, to demonstrate how LCA can be extended by the use of linear programming (i) to determine the optimal choice between new technologies, (ii) to identify the optimal region for supplying the feedstock, and (iii) to deal with multifunctional processes without specifying a certain main product
To solve the mixed integer linear program, the intlinprog solver in Matlab was used

Summary

Introduction

Life cycle assessment (LCA), and in particular consequential LCA, is regarded as an appropriate tool for the assessment of environmental impacts of new bio-based technologies (e.g., Pawelzik et al 2013). The choice for either determining consequences or attributional impacts affects the way of modeling in terms of the multifunctional problem. This problem arises when a process provides more than one product that is not used within the system under study (Heijungs and Frischknecht 1998; Heijungs and Guinée 2007). Consequential LCA approaches prefer to use substitution method to deal with the problem, whereas attributional LCA is a synonym for using the partitioning method (Ekvall and Weidema 2004; Thomassen et al 2008; Schmidt 2010). In any way, dealing with multifunctional processes by using partitioning and/or substitution method depends on a model choice (Majeau-Bettez et al 2015). To solve systems with more products than processes (rectangular technology matrix), linear programming is a suitable way (Heijungs and Suh 2002)

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