Rural Road Maintenance in Madagascar the GENIS Project

Abstract

The paper reports a real world decision aiding process concerning rural road maintenance in Madagascar. The issue arises within AGETIPA, the National Agency in charge of conducting Public Works in Madagascar, and can be summarised as a problem of resource allocation to a number of competitive projects. The problem has been modeled using multiple criteria and a classification procedure under two objectives: make the most rational use of the limited available resources and promote participation and commitment of the local actors in the maintenance process. The project is part of an on-going partnership between the LAMSADE and AGETIPA aiming to enhance Decision Support Capacity within AGETIPA.

Appendices

Appendix

The basic concepts adopted in the procedure used (based on ELECTRE TRI) are the following.

• A set A of alternatives a _i , $i = 1\cdots m$.

• A set G of criteria g _j , $j = 1\cdots n$. A relative importance w _j (usually normalised in the interval [0, 1]) is attributed to each criterion g _j .

• Each criterion g _j is equipped with an ordinal scale $\mathcal{E}_{j}$ with degrees e _j ^l, $l = 1\cdots k$.

• A set $\mathcal{P}$ of profiles p _h , $h = 1\cdots t$, p _h being a collection of degrees, $p_{h} =\langle e_{1}^{h}\cdots e_{n}^{h}\rangle$, such that if e _j ^h belongs to profile p _h , e _j ^h+1 cannot belong to profile p _h−1.

• A set $\mathcal{C}$ of categories c _λ , $\lambda = 1\cdots t + 1$, such that the profile p _h is the upper bound of category c _h and the lower bound of category c _h+1.

• An outranking relation $S \subset (A \times \mathcal{P}) \cup (\mathcal{P}\times A$), where s(x, y) should be read as “x is at least as good as y”.

• A set of preference relations $\langle P_{j},I_{j}\rangle$ for each criterion g _j such that:

  • $\forall x \in A\;\;P_{j}(x,e_{j}^{h})\;\;\Leftrightarrow \;\;g_{j}(x) \succ e_{j}^{h}$

  • $\forall x \in A\;\;P_{j}(e_{j}^{h},x)\;\;\Leftrightarrow \;\;g_{j}(x) \prec e_{j}^{h}$

  • $\forall x \in A\;\;I_{j}(x,e_{j}^{h})\;\;\Leftrightarrow \;\;g_{j}(x) \approx e_{j}^{h}$

  $\prec,\approx$ induced by the ordinal scale associated to criterion g _j .

The procedure works in two basic steps.

• 1. Establish the outranking relation on the basis of the following rule:

  $$\displaystyle{s(x,y)\;\;\Leftrightarrow \;\;C(x,y)\;\mathbf{and\ not}\ D(x,y)}$$

  where

  $$\displaystyle{\forall x \in A,\;y \in \mathcal{P}:\; C(x,y)\;\;\Leftrightarrow \;\;\sum _{j\in G^{\pm }}w_{j} \geq c\;\;\mathbf{and}\;\;(\sum _{j\in G^{+}}w_{j} \geq \sum _{j\in G^{-}}w_{j})}$$
  $$\displaystyle\begin{array}{rcl} & & \forall y \in A,\;x \in \mathcal{P}:\; C(x,y)\;\;\Leftrightarrow {}\\ && (\sum _{j\in G^{\pm }}w_{j} \geq c\;\;\mathbf{and}\sum _{j\in G^{+}}w_{j} \geq \sum _{j\in G^{-}}w_{j})\;\;\mathbf{or}\;\;(\sum _{j\in G^{+}}w_{j} >\sum _{j\in G^{-}}w_{j}) {}\\ \end{array}$$
  $$\displaystyle\begin{array}{rcl} & & \forall (x,y) \in (A \times \mathcal{P}) \cup (\mathcal{P}\times A):\; \mathbf{not}D(x,y)\;\;\Leftrightarrow {}\\ &&\sum _{j\in G^{-}}w_{j} \leq d\;\;\mathbf{and}\;\;\forall g_{j}\;\mathbf{not}v_{j}(x,y) {}\\ \end{array}$$

  where

  • $G^{+}\; =\;\{ g_{j} \in G:\; P_{j}(x,y)\}$

  • $G^{-}\; =\;\{ g_{j} \in G:\; P_{j}(y,x)\}$

  • $G^{=}\; =\;\{ g_{j} \in G:\; I_{j}(x,y)\}$

  • $G^{\pm }\; =\; G^{+} \cup G^{=}$

  • c: the concordance threshold c ∈ [0. 5, 1]

  • d: the discordance threshold d ∈ [0, 1]

  • v _j (x, y): veto, expressed on criterion g _j , of y on x

• 2. When the relation S is established, assign any element a _i on the basis of the following rules.

  • 2.1  pessimistic assignment

    • a _i is iteratively compared with $p_{t}\cdots p_{1}$,

    • as soon as s(a _i , p _h ) is established, assign a _i to category c _h .

  • 2.2  optimistic assignment

    • a _i is iteratively compared with $p_{1}\cdots p_{t}$,

    • as soon as is established $s(p_{h},a_{i})\wedge \neg s(a_{i},p_{h})$ then assign a _i to category c _h−1.

  The pessimistic procedure finds the highest profile for which the element is not worse. The optimistic procedure finds the lowest profile against which the element is surely worse. If the optimistic and pessimistic assignments coincide, then no uncertainty exists for the assignment. Otherwise, an uncertainty exists and should be considered by the user.

Editors’ Comments on “Rural Road Maintenance in Madagascar”

Tsoukiàs and Ralijaona address a common problem in many public and private organizations: to decide which projects are approved among a set of proposals. It encompasses the problem definition and formulation stages (see Chap. 2), the definition of an aggregation procedure and its application on a pilot case. This chapter illustrates the sorting problematic based on a variant of the ELECTRE TRI method (see Chap. 4, Sect. 4.4.4) in a case of public decision-making. It is also, in this book, one of the two applications taking place in the African continent (together with Chap. 12).

The objective of the intervention was to provide decision-aiding concerning resource allocation to projects, promoting public participation and commitment of local actors. A pilot study was carried out not only to demonstrate the usefulness of MCDA, but also to transfer knowledge to the client organization. The pilot study was intended to validate the MCDA approach and to be reproducible in the future by the client independently.

The client organization was AGETIPA, an agency established by the Government of Madagascar and several companies for the area of Public Work. The intervention was sponsored by a project proposed by the Transportation Minister in collaboration with the World Bank, which can be seen as secondary clients. The analysts (the authors) were a member of the client organization and an external consultant who, as a Decision Aiding expert, would be the main source for the knowledge to be transferred. Local actors and the population in general from the Pilot Study area were also involved in the decision process. Other stakeholders included financial and fund raising institutions.

Several stages can be identified in this intervention: formulation, model building, setting parameter values, application of the model and refinement of the model. The objects under evaluation are projects submitted by local communities concerning road maintenance actions. During the problem definition stage, it was decided that the four alternatives under analysis at the time would be the set of alternatives for the pilot study. It was also defined that the evaluation criteria should take into account local commitment (two attributes), social-economic impact (four attributes, two of which further decomposed into sub-attributes), and cost. This resulted in an hierarchical criteria structure having ten attributes as leaf nodes. The idea of using criteria hierarchies is often used in MCDA (e.g. Keeney 1992; Saaty 1980), for it allows decision makers to focus on a few criteria at a time and thereby facilitates eliciting information about their relative importance.

Although the client’s problem is eventually to choose which projects are approved on a given year, a sorting problem statement was adopted. Indeed, the actors involved saw the problem as being one of justifying which projects are not selected and under which conditions such projects might be reconsidered. Thus, a sorting model would be able to distinguish projects that meet all the requirements, projects that definitely cannot be accepted, and an intermediary category of projects that are negotiable (which might be accepted if some conditions are met). One can also note that a sorting problematic allows evaluating projects on continuous “as they appear” basis. This is possible unless there are synergistic benefits or losses among projects if implemented simultaneously. In this case, an approach based on portfolio optimization (e.g., Salo et al. 2011) might be called for.

Concerning aggregation, ELECTRE TRI’s pessimistic variant was the chosen sorting method, using a simplified outranking relation (simple majority, without imprecision thresholds), but allowing for an hierarchical criteria structure. This method was chosen on the grounds that its results are easily explainable, although initially there was some resistance to accept it by one of the sponsors. The variant followed can be seen as a new method combining ideas of existing approaches and tailored to the client’s needs. There was no uncertainty modelling: data values were not considered to be subject to uncertainty, which might warrant using imprecision thresholds or sensitivity analyses.

Setting the criteria weights followed two strategies. For less important hierarchy levels all subcriteria were considered to be equally important and a simple majority rule was used. For the top level of the hierarchy weights were chosen according to the client’s preferences. The elicitation process was carried out by examining which coalitions of criteria would be strong enough to justify that an alternative outranks a category profile, and using linear programming to infer the weight values. This is an innovative elicitation approach when compared to inference based on result examples (Mousseau and Dias, 2004; Mousseau and Słowiński, 1998) or approximation methods (Figueira and Roy, 2002).

The tangible results of this decision process were the definition of a criteria hierarchy and the characterization of an ELECTRE TRI sorting model, tested in the pilot study, that can be used to sort road maintenance projects. More important, an intangible result was the capacity gained by the client to use and adapt the model in the future. The authors describe that the model has been refined due to user requests and there exist plans to apply it to different decision problems in Madagascar.

This chapter’s main relevance concerns addressing public decision making with MCDA. This is a particularly difficult problem when the client, as it should do, wishes to model the values of the public involving stakeholders and the population in general, aiming for transparency and legitimacy (see also on these issues Keeney 2004; Gregory et al. 2005). This led not only to emphasize the problem structuring phase as the most crucial one, leading to the idea of sorting with one category representing a “negotiation area”, but also led to the use of a method variant that would be more suited to this particular application.