Consequential LCA and LCC using linear programming

Purpose: This 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. Methods: We 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 discussion: The 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. Conclusions: This 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.