Development of a Generic Decision Tree for the Integration of Multi-Criteria Decision-Making (MCDM) and Multi-Objective Optimization (MOO) Methods under Uncertainty to Facilitate Sustainability Assessment: A Methodical Review

When the study has multiple discrete alternatives and there are multiple conflicting criteria associated with those alternatives, MCDM methods should be employed first to identify the best alternative and then MOO methods can be applied to optimize the supply chain of that best alternative to obtain the best alternative with an optimized system. For applying MCDM under the compensatory type of methods, researchers often need to answer two more questions about their preferences on criteria weights and uncertainty. If they decide to incorporate DMs’ and stakeholders’ preferences for the criteria and sometimes for alternatives (i.e., in AHP), they need to decide about uncertainty as well. Without including DMs’ preferences, they can either use the objective weighting method (i.e., entropy) or skip weighting (equal weight). But for including DMs’ preferences, ideally, they need to deal with uncertainty. Subjective weights based on expert opinion and/or DMs’ preferences and/or group decisions, and a combination of objective and subjective weights are the options for the weighting method in MCDM with uncertainty. After deciding on the weighting method and uncertainty consideration, the next step in MCDM is to apply a suitable ranking method to rank the alternatives based on weighted criteria to find the best alternative (interim outcome). From the reviewed articles, it is clear that there is a wide range of MCDM methods and numerous examples of applying them in different fields of research. Moreover, minor differences among these methods do not have any significant effect on the results [36,52,111,112]. TOPSIS or PROMETHEE II may be the most suitable to use as a ranking method based on the review findings (Table S3).

After identifying the best alternative, researchers need to answer another question regarding uncertainty considerations for MOO problems. For MCDM problems, only the alternatives and their respective values for each criterion are required, whereas MOO problems require more information. MCDM problems can be integrated with MOO if all the required input–output functions are available for the identified best process. If the practitioners want to deal with uncertainty in model parameters, they need to conduct robust optimization, which can be via either metaheuristic or mathematical programming. Without considering uncertainty, they can simply conduct any metaheuristic or mathematical programming model. Choosing between metaheuristic and mathematical programming methods can be guided by the decision tree developed by Turner et al. [126]. Deciding between mathematical and metaheuristic methods really depends on the preferences of the researchers with respect to computational intensity, complete vs. approximate searches, and flexibility in model development [126]. From the review findings, it can be said that metaheuristic MOO methods are the most used, especially NSGA-II and PSO methods (Table S3).

In this section, a case study is illustrated to demonstrate how the proposed decision tree can guide the methodological choices in a given application context, by combining MOO and MCDM methods. Plant-based proteins are attracting increased attention for being environmentally more sustainable [127,128] and healthier than animal-based proteins [129,130]. In recent years, there has been significant growth in innovative food processing technologies to obtain plant-based proteins with improved quality and functionality, which may make the market for meat substitutes grow to USD 140 billion by 2029 [131,132]. Pulses are one of the main sources of plant-based proteins, in part due to their nutritional and sustainability attributes [133,134,135].

Canada is one of the largest pulse producers and exporters in the world and produces dry peas, chickpeas, lentils, and beans. Pulse production in Canada is increasing annually, and there is a similarly significant growth in pulse processing. Pulses are processed to obtain pulse flour, pulse protein, pulse fibre, pulse starch, and various other products and ingredients. Though there may be differences in the granular levels from facility to facility, dry fractionation and wet fractionation are the commonly used pathways for pulse protein extraction, and both are energy-intensive pathways [136]. Dry fractionation involves producing pulse protein concentrates from raw pulses through the dehulling, milling, and air classification stages [137]. On the other hand, wet fractionation is more energy-intensive as it requires isoelectric precipitation, centrifugation, and spray drying to procure protein-rich pulse protein isolates [138]. Methods for making these processing pathways more efficient in terms of energy use, economics, and environmental performance continue to evolve. For example, several studies tried to identify more technically feasible and efficient fractionation pathways to produce plant-based proteins [139]. However, simultaneously considering all important factors from a sustainability perspective (i.e., technical, economic, and environmental) is uncommon, which hinders identifying sustainable and optimized extraction pathways. As these objectives may conflict, an MOO model/problem can be formulated to identify the optimized pathways (i.e., dry fractionation and wet fractionation). For example, if we want to optimize the dry fractionation pathway based on environmental (i.e., minimizing environmental impacts in different impact categories in the life cycle assessment model); economic (i.e., minimizing production costs/maximizing profit/revenue); and technical (i.e., maximizing yield and energy use efficiency) criteria, MOO will produce a Pareto-optimal set of solutions showing different trade-offs among the objective functions. The main advantage of performing MOO is to consider multiple conflicting objectives, but before applying MOO methods, we need to make sure that all of the input–output functions are available. After obtaining the solution set, an MCDM method is required to identify the best-optimized pathway from that solution set. In this case, all of the solutions from the Pareto-optimal set will become the alternatives and the objectives (i.e., economic, technical, and environmental) will be the criteria.

Following the developed decision tree (Figure 2), as the case study is about studying a specific product system (pulse protein extraction pathways), there are two options for integrating MOO with MCDM methods. The DMs’ and stakeholders’ (pulse farmers, pulse processing facilities, Pulse Canada, etc.) preferences can be integrated before or after solving the MOO problem. Conventionally, a posteriori integration is more common, assuming the system input–output functions are available. A more comprehensive analysis would test both a posteriori and the integrated a priori and a posteriori results via sensitivity analysis and compare potential changes in the final optimization outcome. In the a posteriori pathway, the existing fractionation processes will be optimized based on given objective functions regarding environmental, technical, and economic variables. Environmental objective functions could include minimizing GHG emissions, land use footprints, water use footprints, mineral/fossil fuel usage, etc. Technical functions can be formulated with the aim of maximizing total yield from the process, minimizing energy use, maximizing protein content, etc. Economic objective functions could include minimizing production costs/operation costs, maximizing net present value/profit, etc. After formulating these objective functions and considering the constraints (if any), a suitable MOO method should be utilized. Based on the findings of the literature review, an evolutionary-based metaheuristic method like NSGA-II may be useful for finding the non-dominated Pareto-optimal solution set. The uncertainty associated with input data/model parameters also needs to be taken into account. Monte Carlo Simulation and/or triangular fuzzy numbers can be used to deal with the uncertainty in the MOO model.

There will be several optimized pathway options which can indicate the trade-offs among different objective functions. As these solutions are non-dominated, it is not easy to select the best option without the help of MCDM methods. First, a suitable weighting method must be used, ideally including a combination of objective and subjective weights. After assembling all of the stakeholders’ preferences, either AHP or BWM can be used to find the subjective weights for all criteria. Then, entropy-derived objective weights can be combined with the subjective weights. As it includes subjective weights, fuzzy AHP or fuzzy BWM should be used for dealing with uncertainty. In the next step, a suitable ranking method—either TOPSIS or PROMETHEE II—can be applied to rank the alternatives from the Pareto set. Finally, sensitivity analyses should be included to check the robustness of the methodological choices. Sensitivity analysis with different model parameters, different weighting methods, and different ranking methods should be outlined to see the changes in the final outcome. The methodological path suggested for the case study is highlighted in the decision tree (Figure 2). Based on the review findings, a posteriori integration between MOO and MCDM methods is prevalent. So, in the highlighted pathway, a posteriori is selected and, for the MOO and MCDM methods, the path leading to uncertainty consideration was selected as well. Especially, for the weighting method, the combination of subjective and objective weights was preferred as it ensures a comprehensive analysis.