Criteria weight intervals.
Abstract
Public decision-making problems are more and more complex in a context where decisions have to be made based concurrently on economic, social, and environmental considerations. In this context, decisions need to be evaluated in the short, medium, and long term because their planning horizons are usually of several years or even decades. A literature review on MCDA methods used in the sustainable development (SD) context shows that most MCDA methods used are static and existing research does not propose any aggregation framework for temporal assessment of actions. In the last 5 years, development of temporal MCDA has witnessed the interest of some researchers. However, the latest developments remain limited, and only a few research studies offer aggregation frameworks for multi-period settings. This paper presents two recent temporal MCDA methods that were applied in SD context. The first is MUPOM method which demonstrates how outranking methods, based on concordance-discordance principles, can be generalized to processing temporal impacts of decisions. The second, named PROMETHEE-MP, consists of a multi-period generalization of PROMETHEE under random uncertainty.
Keywords
- multi-criteria decision aid (MCDA)
- multi-period evaluations
- outranking methods
- sustainable development
- PROMETHEE
- MUPOM
1. Introduction
Decision-making processes today evolve in a context where sustainability is an important issue. Decisions have to be made while concurrently evaluating their economic, social, and environmental consequences. The most quoted definition of sustainable development (SD) is that of the report of Brundtland Commission [1] entitled “Our Common Future,” where sustainable development is defined as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs. This definition contains two key concepts: (i) the concept of needs, in particular the essential needs of the world’s poor, to which overriding priority should be given; and (ii) the idea of limitations imposed by the state of technology and social organization on the environment’s ability to meet present and future needs.” This definition indicates the three main pillars of sustainable development, i.e., economic growth, environmental protection, and social equality. Secondly, it puts emphases on the long-term vision associated with sustainable development. In fact, decision processes should take into account not only the immediate but also the future consequences of decisions in order not to compromise future generations. In such context, decisions are generally ill-defined, the impacts of decisions are uncertain and often difficult to measure, and the acceptability of decisions is more difficult to attain. And so, the need for using structured methods and novel approaches to support sustainable decisions has emerged.
A state-of-the-art survey on sustainable decision prioritization [2] shows multi-criteria decision aid (MCDA) methods are the most popular approach to support sustainable decisions. These methods enable the simultaneous consideration of conflicting criteria as it occurs in a real-world problem under sustainability imperatives. However, although sustainable development tries to reach a balance between the evaluations of actions in the short and the long term, most articles surveyed in [2] did not investigate the long-term perspective related to sustainable development. Only very recently have some researchers proposed novel temporal MCDA methods for application in SD context. But, the state of the art remains limited, and only a few research studies offer temporal aggregation frameworks.
This paper presents two novel temporal MCDA methods that were applied in SD context. The first is MUPOM method (MUlti-criteria multi-Period Outranking Method) which demonstrates how outranking methods can be used in processing the temporal impacts of decisions. The second method is named PROMETHEE-MP and consists of a temporal generalization of PROMETHEE in a context of random uncertainty. This paper is organized as follows: Section 2 presents the previous work. Section 3 proposes a formulation for decision-making problem in SD context. Sections 4 and 5 expose the MUPOM and PROMETHEE-MP methods. Section 6 provides an illustration of these two methods on the same case study. Finally, Section 7 concludes the paper.
2. Previous work
Despite the importance of temporal (multi-periods) evaluation of actions for sustainable decisions, only a few articles have dealt with this aspect. Some authors consider the long-term effects as a criterion [3, 4], while others use scenario planning and predictive techniques or fuzzy modeling to deal with future unknowns [5]. In [6], the long-term effects are discounted, and in [4] they are roughly and qualitatively assessed. Very recently, some temporal extensions of MCDA methods have been developed [3, 6, 7, 8, 9, 10, 11]. In a forest management context, the long-term impacts were addressed as a specific criterion [3], and the local community was asked to evaluate it. In [6], the authors proposed a sustainable environmental management system (SEMS) where actions are ranked using ELECTRE III. The authors indicate that special care was taken in the assessment of criteria and that expected short- and long-term consequences were considered but without any explanation on how this was achieved. In [9], a multi-period multi-criteria method based on adapting TOPSIS to temporal context is proposed. But, compensation between the decision criteria on which TOPSIS rely (as scoring methods) is not appropriate for sustainability. In [10], authors generalize PROMETHEE to temporal setting. The weighted mean is applied for aggregation of the net flow scores over the periods, and then the method is compensatory. Another PROMETHEE-based model was published in [11] to assess the long-term impact of energy supply technologies. In this research work, different criteria weights were considered depending on the life cycle steps (from introduction to saturation of the market).
The literature review presented here shows a limited state of the art and an as yet largely undeveloped research area on multi-period aggregation. As discussed earlier, compensation is the main issue behind the few existing temporal proposals. We believe outranking methods are more suitable for sustainable decision problems because of their level of compensation (partial or non-compensatory), their use of thresholds, and their use of different types of data/criteria (qualitative and quantitative) without the need for normalization. To the best of our knowledge, research on developing temporal
3. Problem formulation
In order to formulate the problem, let us consider a set A of N candidate actions (
The following assumptions of the model are made. (i) All evaluations are evaluated in the future with no missing evaluations. (ii) Criteria weights may change over time. (iii) Criteria, preference functions, and thresholds can vary over time. (iv) Criteria
Figure 1 displays the decision matrices for multi-period multi-criteria decision problems.
4. MUPOM: multi-criteria multi-period outranking method
MUPOM (MUlti-criteria multi-Period Outranking Method) is a three-phase temporal outranking MCDA method. In Phase 1, multi-criteria aggregation is performed in order to obtain outranking and preference relations for each period and for each pair of actions. Then in Phase 2 and for each pair of actions, a measure of distance between preference relations is used for temporal aggregation of the preference relations obtained in Phase 1. A graph showing relations between all pairs of actions illustrates the results of this aggregation. Next, in Phase 3 an exploitation procedure is used to compute the performance of each action
Figure 2 graphs the steps of the MUPOM method.
4.1 Phase 1: multi-criteria aggregation
Multi-criteria aggregation relies on pairwise comparisons and concordance-discordance principles. For each pair of actions, we compute the concordance index (resp. discordance index), which evaluates the extent to which the criterion agrees (does not agree) with the assertion “action
4.2 Phase 2: temporal aggregation
This phase consists of aggregating the preference relations obtained for each pair of actions and at each period (results of Phase 1). This aggregation is done using a measure of distance between preorders [19]. Thus, the aggregated preference relation which minimizes the distance with the preorders at each period is obtained. The temporal aggregation phase consists of three steps [7]:
A graph representing relations between all pairs of actions displays the results.
4.3 Phase 3: exploitation
This phase consists of computing the performance of each action
MUPOM method has important contributions. First, it proposes a generalization of outranking methods based on ELECTRE principles (concordance, discordance, and credibility indexes) to multi-period and temporal settings. Consequently, the method supports partial preferences and partial rankings and confirms that the outranking methods can be generalized to temporal context. In practical terms, MUPOM provides valuable contributions for researchers and practitioners concerned with decision-making processes under sustainability. Beyond the financial dimension, it enables integration of social and environmental impacts in the short, medium, and long term. By taking into account immediate and future consequences of actions, it guarantees decisions are not made that compromise future generations.
5. PROMETHEE-MP: a generalization of PROMETHEE for multi-period evaluations under uncertainty
PROMETHEE-MP is a recently developed temporal outranking method that allows aggregation of multi-periods and uncertain evaluations. It consists of three phases. Phase 1 aggregates the criteria, at each period of the horizon, based on PROMETHEE outgoing and incoming flows and Monte Carlo simulations. Binary relations are computed for each pair of actions. Phase 2 consists of aggregating the binary relations obtained over the periods using the measure of distance between preorders [19] as is done with MUPOM. Finally, in Phase 3 the performance of each action
5.1 Phase 1: multi-criteria aggregation and Monte Carlo simulations
In Phase 1, the criteria at each period of the horizon are aggregated. The method looks at a representation of uncertainty with probability distributions for uncertain parameters (evaluations and weights) and uses Monte Carlo simulation to generate numerical values for each uncertainty scenario. In this illustration and without loss of generality, uniform distributions using intervals are simulated for each parameter and for each period
5.2 Phase 2: temporal aggregation
Here the temporal aggregation procedure of MUPOM (Section 4.2) is used to aggregate the preference relations obtained over the periods in Step 1.6. As with the MUPOM method, the measure of distance between preorders developed in [19] is used.
5.3 Phase 3: exploitation
The temporal exploitation procedure of MUPOM (Section 4.3) is used in this phase. It computes the performance of each action
6. Case study
In this section, MUPOM and PROMETHEE-MP are applied in the context of sustainable forest management. Sustainable forest management is a well-suited application context since it considers conflicting and heterogeneous criteria that should be assessed on about 150 years ahead. Actually, the selection of sustainable forest management options should arrive at a balance between biodiversity, soil and water conservation, forest productivity, socioeconomic benefits, and the population’s values and needs. Second, the impact of each decision has to be assessed long term over the period of forest regeneration (about 150 years).
Five options are for consideration: (
The AHP method was used to model the preferences in terms of criteria weights. A questionnaire was presented to an expert asking for pairwise comparisons between pairs of criteria and for the indifference, preference, and veto thresholds for each criterion, as well as the most appropriate criteria functions to be used with PROMETHEE. Also requested was the relative importance of periods. Tables 1–3 present the weights and an overview of the data used for option
Criteria | Crisp weights for MUPOM | Weights intervals for PROMETHEE-MP | |
---|---|---|---|
C1 | 5-year exploitable volume | 0.1443 | [0.137, 0.151] |
C2 | Index of caribou habitat | 0.3064 | [0.291, 0.322] |
C3 | Good habitat for moose | 0.1606 | [0.153, 0.169] |
C4 | Old forest areas | 0.3063 | [0.291, 0.322] |
C5 | Carbon footprint | 0.0825 | [0.078, 0.087] |
Period | C1 (millions of m3) | C2 (in [0, 1]) | C3 (thousands of hectares) | C4 (thousands of hectares) | C5 (tons of CO2) |
---|---|---|---|---|---|
P1 | 39 | 0.591 | 295 | 361 | 143,716,919 |
P2 | 36 | 0.588 | 297 | 362 | 145,123,580 |
… | … | … | … | … | … |
… | … | … | … | … | … |
P30 | 19 | 0.569 | 453 | 262 | 225,395,456 |
Period | C1 (millions of m3) | C2 (in [0, 1]) | C3 (thousands of hectares) | C4 (thousands of hectares) | C5 (tons of CO2) |
---|---|---|---|---|---|
P1 | [37.05, 40.95] | [0.561, 0.620] | [280.25, 309.75] | [342.95, 379.05] | [136,531,073; 150,902,765] |
P2 | [34.20, 37.80] | [0.558, 0.617] | [282.15, 311.85] | [343.90, 380.10] | [137,867,401; 152,379,759] |
… | … | … | … | … | … |
… | … | … | … | … | … |
P30 | [18.05, 19.05] | [0.540, 0.597] | [430.35, 475.65] | [248.9, 275.1] | [214,125,683; 236,665,229] |
To start, Phase 1 of MUPOM and PROMETHEE-MP is applied. Results are obtained in terms of binary relations (P, Q, I, R,
Period | Preference relation resulting from MUPOM | Preference relation resulting from PROMETHEE-MP | Period | Preference relation resulting from MUPOM | Preference relation resulting from PROMETHEE-MP |
---|---|---|---|---|---|
1 | P-1 | P-1 | 16 | R | P-1 |
2 | P-1 | P-1 | 17 | Q-1 | P-1 |
3 | Q | P-1 | 18 | Q-1 | P-1 |
4 | Q | P-1 | 19 | Q-1 | P-1 |
5 | P | Q-1 | 20 | Q-1 | Q-1 |
6 | P | I | 21 | Q-1 | Q-1 |
7 | P | I | 22 | Q-1 | Q-1 |
8 | R | I | 23 | Q-1 | I |
9 | R | Q-1 | 24 | Q-1 | I |
10 | Q | Q-1 | 25 | Q-1 | I |
11 | R | P | 26 | Q-1 | P-1 |
12 | R | R | 27 | Q-1 | P-1 |
13 | Q | Q | 28 | Q-1 | P-1 |
14 | Q | R | 29 | Q-1 | I |
15 | R | Q-1 | 30 | Q-1 | P-1 |
Pair | Aggregated relation with MUPOM | Aggregated relation with PROMETHEE-MP | Pair | Aggregated relation with MUPOM | Aggregated relation with PROMETHEE-MP |
---|---|---|---|---|---|
( | Q-1 | P-1 | ( | R | P |
( | Q | P | ( | R | P-1 |
( | P | P | ( | R | P-1 |
( | P-1 | P-1 | ( | R | P |
( | R | Q-1 | ( | Q-1 | P-1 |
( | R | Q | ( | Q | P |
( | R | P-1 | ( | R | P-1 |
( | R | P | ( | R | P |
( | Q | P | ( | R | P-1 |
( | Q-1 | P-1 | ( | R | P |
A graph representing relations between all pairs of actions illustrates the results. Phase 3 consists of exploiting the graph (Figures 5 and 6) and determining which action performs better. Results of MUPOM show {
Results show that in a deterministic context and without considering uncertainty, the two options
In future research, it will be important to validate the findings of the two models by comparing the obtained results with those given by a panel of expert in forest management. A Delphi procedure could be applied in order to get the opinion of experts on the results. A level of 70% of agreement between experts will be considered. This validation process will confirm the quality of the results given by the method.
Besides, for stronger interpretation of results, future work will focus on applying the proposed methods on different horizons. For instance, in our case study, we can apply MUPOM and PROMETHEE-MP on the short-term horizon (aggregation of evaluations of the first 20 years), the medium term (aggregation of evaluations of year 20 to year 50), and finally the long term (aggregation of evaluations of year 50 to year 150). By doing so, we can compare the different results depending on the horizon and limit the effect of the aggregation. Results will show if the best compromised option on the whole horizon will differ or not from to the best compromised options in the short, medium, and long term.
7. Conclusion
This paper presents the main results of a recent research program on developing temporal outranking MCDA methods. It presents two generalizations of outranking methods to temporal context to show how outranking methods can be of use in processing the temporal impacts of decisions. The state of the art in this research area still remains limited, and such a proposal is valuable to support sustainable decision-making processes. This paper exposes two recent temporal outranking methods and displays the results of their application in SD context. The MUPOM method demonstrates how outranking methods and, more specifically, the ELECTRE concordance-discordance principles can be of use in processing temporal impacts of decisions. PROMETHEE-MP consists of a multi-period generalization of PROMETHEE under random uncertainty using Monte Carlo simulations. Their application on the same case study shows their applicability.
Funding
This research was funded by “Fonds de recherche du Québec – Societé et Culture.”
References
- 1.
Brundtland GH. Report of the World Commission on Environment and Development: Our Common Future. Oxford: Oxford University Press; 1987 - 2.
Kandakoglu A, Frini A, Benamor S. Multi-criteria decision making for sustainable development: A systematic review. Journal of Multi-Criteria Decision Analysis. 2019; 26 :202-251 - 3.
Balana BB, Mathijs E, Muys B. Assessing the sustainability of forest management: An application of multi-criteria decision analysis to community forests in northern Ethiopia. Journal of Environmental Management. 2010; 91 :1294-1304. DOI: 10.1016/j.jenvman.2010.02.005 - 4.
Betrie GD, Sadiq R, Morin KA, Tesfamariam S. Selection of remedial alternatives for mine sites: A multicriteria decision analysis approach. Journal of Environmental Management. 2013; 119 :36-46. DOI: 10.1016/j.jenvman.2013.01.024 - 5.
Scholten L, Schuwirth N, Reichert P, Lienert J. Tackling uncertainty in multi-criteria decision analysis – An application to water supply infrastructure planning. European Journal of Operational Research. 2015; 242 :243-260. DOI: 10.1016/j.ejor.2014.09.044 - 6.
Khalili NR, Duecker S. Application of multi-criteria decision analysis in design of sustainable environmental management system framework. Journal of Cleaner Production. 2013; 47 :188-198. DOI: 10.1016/j.jclepro.2012.10.044 - 7.
Frini A, Benamor S. MUPOM: A multi-criteria multi-period outranking method for decision-making in sustainable development context. Environmental Impact Assessment Review. 2019; 76 :10-25. DOI: 10.1016/j.eiar.2018.11.002 - 8.
Urli B, Frini A, Benamor S. PROMETHEE-MP: A generalization of PROMETHEE for multi-period evaluations under uncertainty. International Journal of Multi-Criteria Decision Making. 2019; 8 (1):13-37. DOI: 10.1504/IJMCDM.2019.10019420 - 9.
Frini A, Benamor S. Making decisions in a sustainable development context: A state-of-the-art survey and proposal of a multi-period single synthesizing criterion approach. Computational Economics. 2017; 52 (2):341-385. DOI: 10.1007/s10614-017-9677-5 - 10.
Benamar I, De Smet Y. An extension of PROMETHEE II to temporal evaluations. International Journal of Multi-criteria Decision Making. 2018; 3-4 :7. DOI: 10.1504/IJMCDM.2018.094371 - 11.
Oberschmidt J, Geldermann J, Ludwig J, Schmehl M. Modified PROMETHEE approach for assessing energy technologies. International Journal of Energy Sector Management. 2010; 4 :183-212. DOI: 10.1108/17506221080000394 - 12.
Corrente S, Figueira JR, Greco S. The SMAA-PROMETHEE method. European Journal of Operational Research. 2014; 239 (2):514-522. DOI: 10.1016/j.ejor.2014.05.026 - 13.
Khalili-Damghani K, sadi-Nezhad S. A hybrid fuzzy multiple criteria group decision making approach for sustainable project selection. Applied Soft Computing. 2013a; 13 :339-352. DOI: 10.1016/j.asoc.2012.07.030 - 14.
Khalili-Damghani K, sadi-Nezhad S. A decision support system for fuzzy multi-objective multi-period sustainable project selection. Computers and Industrial Engineering. 2013b; 64 :1045-1060. DOI: 10.1016/j.cie.2013.01.016 - 15.
Baudry G, Macharis C, Vallée T. Range-based multi-actor multi-criteria analysis: A combined method of multi-actor multi-criteria analysis and Monte Carlo simulation to support participatory decision making under uncertainty. European Journal of Operational Research. 2018; 264 (1):257-269. DOI: 10.1016/j.ejor.2017.06.036 - 16.
Van Der Kleij C, Hulscher S, Louters T. Comparing uncertain alternatives for a possible airport island location in the North Sea. Ocean and Coastal Management. 2003; 46 :1031-1047. DOI: 10.1016/j.ocecoaman.2003.09.001 - 17.
Mirakyan A, De Guio R. Modelling and uncertainties in integrated energy planning. Renewable and Sustainable Energy Reviews. 2015; 46 :62-69. DOI: 10.1016/j.rser.2015.02.028 - 18.
Ascough JC, Maier HR, Ravalico JK, Strudley MW. Future research challenges for incorporation of uncertainty in environmental and ecological decision-making. Ecological Modelling. 2008; 219 :383-399. DOI: 10.1016/j.ecolmodel.2008.07.015 - 19.
Benamor S, Martel J-M. A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluation. European Journal of Operational Research. 2014; 237 :1165-1169. DOI: 10.1016/j.ejor.2014.03.036