In a previous research [22], gas stations were classified into different risk categories (Low, Medium, and High), based on well-defined criteria. From the list of the gas stations posing high risk to the environment, the BOCOM gas station, of the Douala 5^th district and its environs was selected for evaluation. The district which hosts the gas station is characterized by anarchic urbanization including constructions of several levels of a variety of standings. Bocom Bepanda station is built on land with a total area of 1350 m², stores hydrocarbon products like any other standard gas station in the country, and is surrounded by some 488 households, several schools, hospitals, markets, and other social infrastructures.

Data collection took place in April 2021. We first defined an exposure perimeter to the fire risk to which populations living near service stations (100 m) are exposed. The following assessments were made:

· The cost of relocating the gas station to a less risk-prone area.

· The cost of relocating the neighbouring population and social infrastructures (schools, hospitals, …).

· The socio-economic and environmental impacts of relocation were also evaluated.

· Finally, the cost of putting in place an emergency response plan, like the impacts of “doing nothing” was also evaluated.

The market value of buildings subject to expropriation was calculated on the basis of Order No. 0082/Y. 15.1/MNUH/D of 20 November 1987. The financial costs incurred in establishing a gas station were an average obtained from a sample of 80 gas stations selected from gas stations whose locations are not in compliance with existing regulations [22]. These amounts were obtained from their financial records, while the value of putting in place an emergency action plan was obtained from the current market value of the equipment required.

Data were collected through focus group interviews with experts/decision-makers in the city of Douala. The expert group was asked to rate the criteria using an impact scale with values of 1 to 5 (Table 1) to assess relative preferences for two items.

In all, a group of five experts (E1, E2, E3, E4, E5), drawn from the city council,

the University of Douala, the ministry of the environment and nature protection, the ministry of urban planning, and then the ministry of territorial administration was requested to rank and evaluate four alternatives (A1, A2, A3, A4) based on the four criteria (C1, C2, C3, C4). Here is an example of a questionnaire for experts regarding the overall objective”.

· With respect to the overall goal “Selection of the best sustainable development strategy”.

· Q1. How important is the cost criteria (C1) when it is compared to social impact (C2)?

· Q2. How important is cost criteria (C1) when it is compared to economic impact (C3)?

· Q3. How important is the cost criterion (C1) when compared to Environmental impact (C4)?

· Q4. How important is C2 when it is compared to C3?

· Q5. How important is C2 when it is compared to C4?

· Q6. How important C3 when it is compared to C4?

Four criteria were chosen including the cost of relocations (C1), social impact (C2), Economic impact (C3), and Environmental impact (C4). Four alternatives are denoted by A1 (“Do nothing”), A2 (Relocation of inhabitants, A3 (Relocation of gas stations, and A4 (Putting in place an emergency response plan (A4). The framework applied to green supplier selection is presented in Figure 1.

The PROMETHEE methodology (Figure 2) was employed.

The computational procedures of PROMETHEE need several steps, and this

paper has summarized seven steps based on the works of [23].

Step 1. Determine the criteria ( j = 1 , ⋯ , k ) and the set of possible alternatives in a decision problem. These are used to create an m ×n evaluation (decision) matrix (1)

[ X i j ] m n = [ x 11 ⋯ x 1 n ⋮ ⋱ ⋮ x m 1 ⋯ x m n ] (1)

Step 2. Determine the weight w_j of the criteria. It shows the relative importance of each of the criteria. The weights show the relative importance of each of the criteria and note according to (2):

∑ j = 1 k w j = 1 (2)

Step 3. Normalize the decision matrix to range 0 - 1 according to (3)

R i j = { [ x i j − min ( x i j ) ] [ max ( x i j ) − min ( x i j ) ] ,     beneficial criteria [ max ( x i j ) − x i j ] [ max ( x i j ) − min ( x i j ) ] ,     non-beneficial criteria (3)

where:

x i j = is evaluation values provided by decision-makers, with i = 1 , ⋯ , n , and j = 1 , ⋯ , m , and numbers of criteria.

Step 4. Determination of deviation by pairwise comparison (4)

d j ( a , b ) = g j ( a ) − g j ( b ) (4)

where, d j ( a , b ) denotes the difference between the evaluations of a and b on each criterion.

Step 5. Define the preference function (5)

P j ( a , b ) = F j [ d j ( a , b ) ] , ∀ a , b ∈ A (5)

where:

P j ( a , b ) = g j ( a ) − g j ( b )

and for which:

0 ≤ P j ( a , b ) ≤ 1 (6)

The smaller number of the functions denotes the indifference of the decision-maker. On the contrary, the closer to 1 indicates greater the preference. In case of a criterion to be maximised, this function is giving the preference of over for observed deviations between their evaluations on criterion, g j ( . ) . For criteria to be minimised, the preference function should be reversed or alternatively given by (7):

P j ( a , b ) = F j [ − d j ( a , b ) ] , ∀ a , b ∈ A (7)

The pair { g j ( . ) ; P j ( a , b ) } , is the generalised criterion associated to criterion g j ( . ) . Such a generalised criterion has to be defined for each criterion. In order to facilitate the identification six types of particular preference functions have been proposed (Table 2).

Linear preference function with linear preference and indifference area (type 3) and level preference function (type 4) are chosen for the selection of eco-efficient development strategy problem. Both functions are chosen based on the nature of criteria. The PROMETHEE with linear and level function method is assumed to be tailored to the nature of the criteria. For instance, linear preference function was chosen as one of the functions because it is best suited for quantitative criteria such as criterion C1 (cost). However, level preference function is best suited for qualitative criteria such as criterion C2 (social impact, economic impact, environmental impact). In addition, the level function works well in small numbers of different levels, such as the five-point impact scale used in this study.

Preference function of PROMETHEE is a function used to define deviations between alternatives for each criterion. In this paper, the definitions of preference functions are presented to fulfill the requirement of PROMETHEE algorithm that

will be implemented to a case study. With reference to Step 5, three preference functions are employed as defined below:

Définition 1: Type I: Usual criteria function is defined as

p ( x ) = { 0 ,     for   x ≤ 0 1 ,     for   x > 0 (8)

where, where x represents the deviation between two alternatives.

In type 1, indifference only occurs when f ( a ) = f ( b ) . It is used when the decision-makers cannot allocate importance for the differences between criteria values and only seem to know the formula “the more the better”.

Définition 2 Type III: Criterion with linear preference function is defined as

p ( x ) = { 0 ,     x < 0 x m ,     0 ≤ x ≥ m 1 ,     x > m (9)

The intensity of preference increases linearly and becomes strict on point m. Parameter m is arbitrary and needs to be defined.

Definition 3: Type IV: Level criterion function is defined as

p ( x ) = { 0 ,     for   x < q 1 2 ,     for   q ≤ x ≤ q + p 1 ,     for   x > q + p (10)

Indifference over the interval, − q ≤ x ≤ q .

When a preference function has been associated with each criterion by the decision-maker, all comparisons between all pairs of actions can be made for all criteria.

Step 6 Determine the multi-criteria preference index (Equation (11)).

π ( a , b ) = ∑ j = 1 k P ( a , b ) w j (11)

where,

· w j > 0 are the weights associated with each criterion, and

· the symbol p(a, b) shows that the degree of a is preferred to b over all the criteria(Equation (12))

π ( a , b ) ≈ { 0 ,     impliesaweakpreferenceof a over b 1 ,     impliesastrongpreferenceof a over b (12)

Step 7 Obtain the preference order

Here, the ranking can be made either partially or completely. Partial ranking can be obtained using PROMETHEE I, and in case complete ranking is needed, then the computation must proceed to one more step in PROMETHEE II.

a) Ranking the actions by partial ranking (PROMETHEE I)

Each alternative, a, is facing n − 1 other alternatives in A. Hence, we define the following two outranking flows:

( ϕ + ): the positive outranking flow:

ϕ + ( a ) = 1 n − 1 ∑ b ∈ A π ( a , b ) (13)

The positive outranking flow expresses how an alternative, a, is outranking all the others. It is its power, its outranking character. The higher ϕ + ( a ) the better the alternative ϕ − ( a ) the negative outranking flow:

ϕ − ( a ) = 1 n − 1 ∑ b ∈ A π ( b , a ) (14)

The negative outranking flow expresses how an alternative, a, is outranked by all the others. It is its weakness, its outranked character. The lower the, ϕ − ( a ) , better the alternative.

The PROMETHEE I Partial Ranking

The preference relation and partial ranking are derived as follows:

a P + b : { P ,     ifandonlyif   ϕ + ( a ) ≻ ϕ + ( b ) ; ∀ a , b ∈ A I ,     ifandonlyif   ϕ + ( a ) = ϕ + ( b ) ; ∀ a , b ∈ A

a P − b : { P ,     ifandonlyif   ϕ − ( a ) ≺ ϕ − ( b ) ; ∀ a , b ∈ A I ,     ifandonlyif   ϕ − ( a ) ≻ ϕ − ( b ) ; ∀ a , b ∈ A

However, not all alternatives are comparable. Thus, we need to calculate the net outranking flow in the following step.

b) Ranking the actions by a complete ranking (PROMETHEE II).

The complete rankings of alternatives can avoid incomparability

ϕ ( a ) = ϕ + ( a ) − ϕ − ( a ) (15)

where ϕ ( a ) denotes the net outranking flow for each alternative. The preference relations are as follows:

· a outranks of b ( a p ( II ) b if and only if ϕ ( a ) ≻ ϕ ( b ) , ∀ a , b ∈ A ;

· a indifférent of b ( a I ( II ) b if and only if ϕ ( a ) = ϕ ( b ) , ∀ a , b ∈ A .

It is worth noting that all the alternatives are able to be compared based on the values of ϕ ( a ) .

The highest values of ϕ ( a ) denote the most preferred alternative. In these series of computational procedures, most of the steps are fixed except Step 5. In this step, it is an arbitrary where the choice of preference functions depends very much on the characteristics of criteria and also the preference of decision-makers. Attention is paid to the choice of types of preference functions as it may affect the final net outranking values.

The ranking of the alternatives is arranged in descending order of net flow value.

1FCFA = 578USD.

The best alternative is the one having the highest net flow value, ϕ ( a ) . By using both PROMETHEE I (partial) and II (complete ranking) method, alternative A4 (Emergency response plan) is selected as the best alternative (Figure 3).

While the PROMETHEE II complete ranking is easier to explain it is also less informative as the differences between Phi+ and Phi− scores are not visible anymore. Incomparability in the PROMETHEE I ranking is interesting because it emphasizes actions that are difficult to compare and thus helps the decision-maker to focus on these difficult cases.

Both Phi+ and Phi− can be used to rank the actions. However they don’t always provide exactly the same ranking. Indeed because of the conflicting aspect of a multicriteria problem it is not always easy to compare two actions: one can be much better on one subset of criteria and the other can be much better on another subset of criteria. In such cases and according to the preference parameters defined by the decision-maker different ways of evaluation (such as Phi+ and Phi−) can lead to different rankings. Hence, the PROMETHEE Diamond (Figure 4) was used as an alternative two-dimensional joint representation of both PROMETHEE I and II rankings to confirm the results above.

The square corresponds to the (Phi+, Phi−) plane where each action is represented by a point. The plane is angled 45˚ so that the vertical dimension gives the Phi net flow. Phi+ scores increase from the left to the top corner and Phi− scores increase from the left to the bottom corner.

For each action, a cone is drawn from the action position in the plane.

As the strategy A4 cone overlaps all the other ones this action is preferred to all the other ones in the PROMETHEE I partial ranking. On the contrary, the lowest level cones corresponding to alternative A2 indicate incomparability. An

advantage of the PROMETHEE Diamond is that it is easy to visualize the proximity between Phi+ and Phi− scores globally. A PROMETHEE network (Figure 5) further demonstrate

We inferred from the above figures that alternative A4 is ranked as the first preference followed by A1. The ranking order of preference of the alternatives is obtained as A4 ≻ A1 ≻ A3 ≻ A2, where “≻” shows “more preferred than”. It can be concluded that the putting in place of an emergency response plan is the most preferred eco-efficient development strategy. A disaggregated view of the PROMETHEE II complete ranking, PROMETHEE rainbow (Figure 6) shows that the actions are displayed from left to right according.

For each action, the stacked slices show the components of the action net flow. For instance:

· Emergency response plan exhibits no negative slices as all criteria contribute positively to its net flow score. This action presents no weaknesses with respect to the other actions. The larger blue slice indicates that cost is the most important feature of this action. Its Phi score is positive.

· Relocation of gas stations has the very small slices. It has both weaknesses and disadvantages even if these are relatively small. It is quite average. Its Phi score is close to zero.

· Relocation of inhabitants is more of a mixed bag with serious environmental impacts.

Equation (8) is used to calculate these two flows. Leaving flow and entering flow

of alternatives and the results are as follows (Table 5):

a) Leaving flow and entering flow of alternatives: Positive outranking flow (leaving flow) shows the degree of the supplier dominated other suppliers. In contrast, negative outranking flow (entering flow) shows the degree of the alternative dominated by other alternatives. b) Determine the net outranking flow (PROMETHEE II) for each alternative. Net flow values are calculated to avoid incomparability. Equation (9) is used to complete the calculation of net outranking flow. It is presented in Table 6.

To understand the relationship between alternatives and criteria, the analysis of GAIA (Graphical Analysis for Interactive Assistance) is made. With a representation value of 100%, the relationship between suppliers and criteria is depicted in Figure 7.

The above screenshot shows the U-V plane. It contains three types of information:

· Actions are represented by points.

· Criteria are represented by axes.

· The weighing of the criteria and the PROMETHEE II ranking are represented by the decision axis.

In Visual PROMETHEE three dimensions are computed:

· U is the first principal component, and contains the maximum possible quantity of information.

· V is the second principal component, providing the maximum additional information orthogonal to U.

In practice, the 2D GAIA analysis is reliable when the quality level is above or close to 70%. We can identify four different types of profiles:

· The “do nothing” alternative is on its own.

· Emergency response plan is on its own, and