Multi-objective optimisation and impact assessment

2.3.1 Multi-objective optimisation

For sustainable processes, a low environmental impact and a high economic performance has to be achieved. These objectives are combined in a multi-objective optimisation (MOO) problem. Two most used MOO methods are the weighted-sum method, and the 𝜖-constraint method. The weighted-sum method combines multiple objectives into one objective function, by assigning weights to each objective (Marler & Arora, 2010). The 𝜖-constraint method minimises one of the objective functions, while the other objective function(s) are incorporated in the constraint section of the model and limited to a maximum value (𝜖𝑗).

The strong influence of the assigned weights on the obtained solutions is the main disadvantage of the weighted-sum method. This drawback does not exists for the 𝜖-constraint method as a set of solutions are generated (Mavrotas, 2009). The optimal solutions that represent the trade- off between objectives are visualised in Pareto plots. The optimisation problem is formulated as: 𝑚𝑖𝑛 𝑓_𝑗(𝑥) (1) 𝑠. 𝑡. 𝑓_𝑖(𝑥) ≤ 𝜖𝑗 𝑐(𝑥) ≤ 0 𝑐𝑒𝑞(𝑥) = 0 𝐴𝑥 ≤ 𝑏 𝐴_𝑒𝑞𝑥 = 𝑏_𝑒𝑞 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 ≤ 𝑥 ≤ 𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 𝑥 ∈ ℝ

where 𝑓𝑗(𝑥) and 𝑓𝑖(𝑥) are the objective functions. In this study the objective functions are: 1)

the environmental impact and 2) the economic impact. The objective functions are affected by the decision variables 𝑥 (i.e. the operational variables). The operational variables are process or product related, and an example in this case is to what concentration the milk is concentrated

by reverse osmosis prior to evaporation. Another example is the temperature at which the dryer operates. To minimise the objective value(s), a set of constraints should be satisfied. 𝑐 represents the non-linear inequality and equality constraints on the decision variables 𝑥. 𝐴 and 𝑏 concern the linear equality and inequality constraints. Examples of constraints are the production target, and process limitations. The decision variables 𝑥 are restricted by its lower and upper bounds. These are mainly set to ensure the product properties and quality, for example to make sure that the product is not exposed too high temperatures. A list of all decision variables and constraints is given in Appendix 2. Besides optimisation of the operational conditions, all possible routes from the superstructure were evaluated. The models were developed in MATLAB 2017b.

2.3.2 LCA impact assessment

After defining the goal and scope the inventory analysis of the system will result in a large amount of data on amounts of resources used and pollutant emissions related to the functional unit (e.g. 1 tonne of milk powder). The inventory results are characterised by sub groups, so called impact categories. LCA has multiple impact categories and using them all together with the cost objective and product constraints, would lead to a complex problem. For this reason, the different impact categories are combined into a single impact. Combing them into a single impact is achieved by normalizing and assigning weights to the results. To go from the inventory results into a single impact can be summarised into the following steps: classification, characterisation, normalisation, and weighting (Bauman & Tillman, 2012). These steps are summarised in Figure 4, and discussed in further detail in the next sections.

Figure 4. Step wise aggregation of information in LCA. From inventory results to a single impact by weighting the characterisation results with factor 𝑾_𝒋 per impact category 𝒋 (adapted from Bauman and

Tillman (2012)).

Classification and characterisation

The LCA impact categories relevant for the system were selected (characterised) (see Table 1), and values were assigned to each energy and material in- and outputs defined in the

119 superstructure from the GaBi database. The impact categories were based on the inventory analysis given by Taxiarchou et al. (2015). The impact for all categories for each production route was derived from the size of in- and output streams and their contributions to the impact categories:

𝐼𝑖,𝑗= ∑ 𝑅𝑖,𝑥,𝑗∙ 𝐼𝑥,𝑗 𝑥

(2) in which 𝐼 is the impact of category 𝑗 for processing route 𝑖 in the superstructure, and 𝑥 is the resources type. 𝑅 is the amount of resources used during production. For each route the total environmental impact of each impact category was estimated.

Table 1. Selected impact categories with their units and the applied European normalisation factors (𝑵𝒋)

from Sleeswijk et al. (2008), * marked values are taken from (Benini et al., 2014). Weighting factors (𝐖𝐣)

are based on Huppes et al. (2012).

Impact category Unit Normalisation

factor

Weighting factor

Global Warming Potential (GWP) kg CO2-eq. 4.49E+12 28 Ozone Layer Depletion Potential (ODP) kg R11-eq. 6.79E+06 5 Particulate Matter Formation (PMF) kg PM10-eq. 8.12E+09 8 Acidification Potential (AP) kg SO2-eq. 2.84E+10 5 Resource depletion, mineral and fossil (ARD) kg Sb eq. 7.23E+11 8

Ecotoxicity CTUe 6.80E+12 * 13

Human Toxicity (carcinogenic) CTUh 2.63E+05 * 7

Human Toxicity (non-carcinogenic) CTUh 4.42E+05 * 5 Photochemical Oxidant Formation (POF) kg NMOVC eq. 2.80E+10 6 Eutrophication Potential (freshwater) kg P eq. 3.47E+08 3 Eutrophication Potential (marine) kg N eq. 5.89E+09 3 Terrestrial Eutrophication mole N eq. 9.04E+10 * 3

Water depletion (WD) m3 _{eq. 4.06E+10 * 6}

Normalisation

The magnitude and units of the different impact categories differ. Moreover, the importance of the impact categories varies. To compare impact categories of alternative production systems a normalisation step was applied on the impact categories. By normalising the data, the impact of each impact category is translated into a relative impact on national, regional or even global level (Bauman & Tillman, 2012). Sleeswijk et al. (2008) derived normalisation factors for an European and a global system (Sleeswijk et al., 2008). The normalisation factors refer to the reference situation of the extractions and emissions in the year 2000. Not all factors were covered by Sleeswijk et al., the missing factors were taken from Benini et al. (2014) (see Table 1).

Weighting

To compare the LCA results to the production costs of the process, the results for the impact categories were combined into a single score as expressed in Equation (3). Hereby, weighting factors were assigned to each individual impact category. The combined LCA score is defined as: 𝐼𝑠𝑖𝑛𝑔𝑙𝑒,𝑖= ∑ ( 𝐼_𝑖,𝑗 𝑁𝑗 ∙ 𝑊𝑗) 𝑗 (3) in which 𝐼𝑠𝑖𝑛𝑔𝑙𝑒 is the combined result of the environmental impact for each process route 𝑖 in

the superstructure, and 𝑊𝑗 is the weighting factor of impact of category 𝑗.

The weighting factor expresses the importance of an impact category relative to the others. The choice of weighting and normalisation factors has a large influence on the final score (Shen, Worrell, & Patel, 2010)). Several approaches have been developed in the past years to assign objective weighting factors, examples are the Ecoindicator99, Nogepa, BEES and EPA (Finnveden, Eldh, & Johansson, 2006; Goedkoop & Spriensma, 2001; G. Huppes et al., 2007; Lippiatt, 2007). Huppes et al. (2012) did a large analytic survey on weighting environmental impacts, combining the different available approaches. The resulting weighting factors are listed in Table 1. In contrast to the work of Huppes et al. land use and ionising radiation were not considered as relevant impact factors in our study. Whereas for eutrophication three categories were used in this study; freshwater, marine, and terrestrial eutrophication. Therefore, the weighting factor Huppes et al. assigned to eutrophication are divided equally over the three eutrophication categories used.

2.3.3 Economic impact assessment

The economic indicator used in our study is the Total Annual Costs (TAC). The TAC consists of both investment for equipment and utility costs (energy, water, etc.). For the ranking of production scenarios, the costs for labour, cleaning, laboratory and overhead are assumed to be similar for the scenarios and therefore not included. Detailed description of the economic indicator is listed in Appendix 4.

3 Results and discussion