Temporal MCDA Methods for Decision-Making in Sustainable Development Context

*Anissa Frini, Sarah Benamor and Bruno Urli*

### **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.

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 **outranking** methods is not well advanced. In this context, we started a research program to develop temporal outranking MCDA methods. In 2019, our research team proposed a generalization of outranking methods to temporal context and show how they can be applied for processing temporal impacts of decisions [7, 8]. Frini and Benamor [7] propose the first outranking method for multi-period (temporal) evaluations of actions called MUPOM. Based on pairwise comparisons, outranking relations and a measure of distance between preference relations, MUPOM accommodates the requirements of sustainable development discussed earlier and supports decisions that comply with the long-term vision related to SD context. Besides, existing research works dealing with MCDA methods under uncertainty are developed for static MCDA methods [12–18]. In order to develop extend MCDA under uncertainty to temporal context, we proposed in [8] a temporal generalization of PROMETHEE in a context of uncertainty. In the rest of the present paper, two generalizations of the outranking methods MUPOM and PROMETHEE-MP are presented and the results of their application on the same case study compared. The next sections expose the main

*Temporal MCDA Methods for Decision-Making in Sustainable Development Context*

In order to formulate the problem, let us consider a set A of N candidate actions (*a*1, … *a*NÞ, a set *T* of K assessment periods ð*P*1, ..., *PK*), a set *C* of M criteria ð Þ *C*1,*C*<sup>2</sup> … ,*CM* , a set *Π* of M criteria weights ð*π*1, ... *πM*), *a set* ð*α*1, … , *αK*) of the K

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.

**Figure 1** displays the decision matrices for multi-period multi-criteria decision

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

ð Þ *a*<sup>i</sup> the evaluation of an action*a*<sup>i</sup>

results of this research program.

*DOI: http://dx.doi.org/10.5772/intechopen.90698*

relative importance of periods (*P*1, ..., *PK*), and *gj*

(iv) Criteria ð Þ *C*1,*C*<sup>2</sup> … ,*CM* are assumed to be independent.

**4. MUPOM: multi-criteria multi-period outranking method**

**3. Problem formulation**

on criterion *j*.

problems.

**Figure 1.**

**21**

*Decision matrices for the considered decision problems.*

A state-of-the-art survey on sustainable decision prioritization [2] shows multicriteria 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, 7–11]. 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. *Temporal MCDA Methods for Decision-Making in Sustainable Development Context DOI: http://dx.doi.org/10.5772/intechopen.90698*

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 **outranking** methods is not well advanced. In this context, we started a research program to develop temporal outranking MCDA methods. In 2019, our research team proposed a generalization of outranking methods to temporal context and show how they can be applied for processing temporal impacts of decisions [7, 8]. Frini and Benamor [7] propose the first outranking method for multi-period (temporal) evaluations of actions called MUPOM. Based on pairwise comparisons, outranking relations and a measure of distance between preference relations, MUPOM accommodates the requirements of sustainable development discussed earlier and supports decisions that comply with the long-term vision related to SD context. Besides, existing research works dealing with MCDA methods under uncertainty are developed for static MCDA methods [12–18]. In order to develop extend MCDA under uncertainty to temporal context, we proposed in [8] a temporal generalization of PROMETHEE in a context of uncertainty. In the rest of the present paper, two generalizations of the outranking methods MUPOM and PROMETHEE-MP are presented and the results of their application on the same case study compared. The next sections expose the main results of this research program.
