The study employed a mixed-methods approach to data collection. Primary data were gathered through structured questionnaires administered to experts in waste management and urban planning. These questionnaires captured pairwise comparisons of evaluation criteria, enabling us to assess their relative importance. Geospatial data supplemented this through satellite imagery and Google Earth mapping, which provided visual documentation of the proposed landfill sites’ physical characteristics. Following the collection, the dataset underwent systematic processing. Questionnaire responses were analysed using AHP OS software to generate consistency ratios and pairwise comparison matrices. For the subsequent TOPSIS and SWARA analyses, we processed the data using Python programming to determine optimal site rankings. The complete dataset is presented across three reference tables: Table 1 details expert demographics, Table 2 outlines the evaluation criteria framework, and Table 3 describes the alternative site characteristics under consideration.

The Analytical Hierarchy Process (AHP), developed by Thomas L. Saaty in the 1970s, serves as a fundamental component of our multi-criteria decision-making framework. This structured technique enables the systematic evaluation of criteria through pairwise comparisons, assigning relative weights that reflect their importance in landfill site selection. We applied Saaty’s established weighting scale, where criteria are rated from 1/9 (least important) to 9 (most important), with 1 indicating equal importance between compared elements. Table 4 presents the complete weighting scheme used in our analysis. The AHP methodology breaks down complex decisions into hierarchical structures, allowing us to quantify expert judgements and establish consistent priority rankings across all evaluation criteria.

The following equations are used in the AHP methodology.

1) Computing pairwise comparison.

$a_{ij}=\frac{1}{a_{ij}}$(1)

2) Calculating the consistency ratio after computing the mean of the elements in each row of the normalised matrix.

$\text{CI}=\frac{{\lambda }_{\max }-n}{n-1}$(2)

$\text{CR}=\frac{\text{CI}}{\text{RI}}$(3)

where ${\lambda }_{\max }$ = sum of the products between each element of the priority vector and column

n—Number of criteria

CI—Consistency index

RI—Random inconsistency index

If the consistency ratio $\text{CR}>0.10$ then there is a need to reconsider pair-wise values, until $\text{CR}<0.10$ has been reached.

3) Ranking of the results for each alternative.

${\text{Score}}_i={\displaystyle {\sum }_{j=1}^n{W}_j\cdot S_{ij}}$(4)

where,

$S_{ij}$ -is the score of alternative i with respect to j.

$W_i$ - is the weight of alternative i with respect to criteria.

The pairwise comparisons derived from expert judgments were processed using AHP OS, a dedicated online analytical tool. This software platform performed three critical functions: 1) computation of the pairwise comparison matrices, 2) automatic normalization of results, and 3) calculation of consistency ratios to validate judgment reliability. Additionally, the software generated the complete decision hierarchy structure, ensuring proper representation of the evaluation framework.

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a well-established multi-criteria decision analysis method that evaluates alternatives based on their geometric distances from ideal solutions . As developed by Hwang and Yoon, this approach operates on the fundamental principle that the optimal choice should simultaneously minimize distance from the Positive-Ideal Solution (PIS) and maximize distance from the Negative-Ideal Solution (NIS) [11] [13] . The PIS represents the hypothetical alternative achieving optimal values across all criteria, while the NIS represents the worst-case scenario . TOPSIS calculates a normalized similarity index for each alternative through systematic comparison with these reference points, as demonstrated in recent landfill site selection studies [16] [18] . The method’s effectiveness in handling complex decisions with conflicting criteria has been well documented, particularly when integrated with weighting methods like AHP [17] [20] . Following established practice, our implementation calculates relative closeness scores (Equation (5)-(9)) to rank alternatives, with higher values indicating better overall performance [12] [14] . This approach provides a robust framework for objective decision-making, particularly valuable in environmental management applications where multiple competing factors must be balanced [1] [24] .

Steps

1) To calculate the normalised decision matrix for the normalised value R_ij which is calculated as

$R_{ij}=\frac{x_{ij}}{\sqrt{{\left({\displaystyle \sum x_{ij}}\right)}^2}}j=1,2,3,\cdots \text{and}i=1,2,3,\cdots$(5)

2) Calculate the weighted value $V_{ij}$ which is calculated as

$V_{ij}=W_{ij}+R_{ij}$(6)

where,

W_i = is the weight of the i^th Attribute or criterion and ${\displaystyle \sum W_i}$

3) After determining the weighted normalised matrix, we need to calculate (identify) the positive and negative ideal solutions. For the Positive Ideal Solution (PIS) which is the maximum value (A⁺) and Negative Ideal Solutions (A⁻).

$A^{+}=\left\{V_1^{+}\cdots V_i^{+}\right\}=\left[\left(\max V_{ij}|i\in I^1\right),\left(\min V_{ij}|i\in I^1\right)\right]$(7)

$A^{-}=\left\{V_1^{-}\cdots V_i^{-}\right\}=\left[\left(\max V_{ij}|i\in I^1\right),\left(\min V_{ij}|i\in I^1\right)\right]$(8)

4) After finding positive and negative ideal solutions then calculate relative Closeness

$C_i=\frac{S_i^{-}}{S_i^{+}+S_i^{-}}$(9)

Rank preference order then choose an alternative with the maximum C_i or rank alternatives

According to C_i in descending order.

The Stepwise Weight Assessment Ratio Analysis (SWARA) method provides a structured approach for determining criteria weights, offering distinct advantages for landfill site selection. This method requires fewer pairwise comparisons than AHP while maintaining robust results, as demonstrated in waste management applications [24] . Its streamlined process makes it particularly efficient for municipal planning contexts like our Chegutu case study. The method’s effectiveness stems from its ability to directly prioritise criteria based on expert input while avoiding redundant assessment steps [25] . When integrated with other techniques like GIS, SWARA has proven valuable for environmental decision-making, particularly in landfill site selection studies [26] . For our research objectives, SWARA’s balance of simplicity and accuracy makes it well-suited to evaluate the key environmental, social, and technical factors affecting landfill suitability.

Calculate the weight values of each criterion so that their sum is equal to 1.

$W_j=\frac{Q_j}{{\displaystyle {\sum }_{j=1}^n{Q}_j}}$ (10)

where,

$W_j$ – represents the relative weight of each criterion and is also called normalising weights by summing up all $Q_j$

Comparing and contrasting results from AHP, TOPSIS, and SWARA. If the results are the same, then proceed to the final decision and draw a conclusion. If they are different, then standardize the results by calculating the average rank from the three methods.

Average rank for each alternative i

${\text{Rank}}_i^{\text{average}}=\frac{{\text{Rank}}_i^{\text{AHP}}+{\text{Rank}}_i^{\text{TOPSIS}}+{\text{Rank}}_i^{\text{SWARA}}}{3}$ (11)

The Analytical Hierarchy Process (AHP) was used to determine the relative weights for each criterion. The AHP decomposes the decision problem into levels (hierarchy) of criteria, sub-criteria, and alternatives. Pairwise comparison was done using experts’ data to establish the relative importance of each criterion. The AHP OS (Online Software) was used to calculate the consistency ratio, which ensured the reliability of the judgments. ( Figure 3 )

Pairwise comparisons

The pairwise comparison was used to determine the relative importance of the main criteria. Through expert judgement, each criterion was compared using Saaty’s scale. The results captured the consolidated pairwise matrix from the 7 different experts, as shown in Figure 4 and Figure 5 .

The matrix showed that Environmental factors were better than all other criteria. As indicated in the matrix, Environmental factors have a higher comparison value of 9.00 against technical factors and 5.00 against Economic factors. Social factors also have a high preference over other criteria except for Environmental factors. Economic factors received the lowest importance among all pairwise comparisons.

The criteria were ranked as shown in Figure 3 , where environmental factors (61.1%) ranked first, followed by social factors (18.0%), Economic factors (14.3%), and technical factors (6.6%).

The environmental, economic, social, and technical criteria show good consistency with CR values below 1% (0.1), indicating that the judgment was reliable. On the other hand, the economic factors and technical node show a CR of 0%, which is still below the acceptable limit. This shows that under economic and technical, there is average consistency in the pairwise comparisons ( Figure 6 ).

In Figure 3 and Figure 5 , it is shown that environmental factors have the highest priority and consistency ratio as compared to the other main criteria. The pairwise comparison matrix in Figure 6 exhibits the factors under environmental factors, showing their weights for each. Proximity to water sources has the highest weight in the matrix, and in Figure 7 , it has the highest priority as well.

Proximity to water sources is the only one without overlap. Its weight interval does not overlap with any other; it clearly stands out as the most important. The following groups of criteria overlap within uncertainties. ( Figure 8 )

1) distance from settlement, slope, geology and hydrology, soil type, costs, land use, community acceptance;

2) costs, land use, community acceptance, land availability, accessibility, waste management;

3) land availability, accessibility, waste management, cultural & historical, distance from roads;

4) cultural & historical, distance from road, climate & weather.

The CR for sub-criteria was calculated in Figure 7 to assess the reliability of the pairwise comparisons from the AHP. Land use, climate & weather showed perfect consistency with 0%. Community acceptance and distance from settlement have a high consistency of 0.1% each since criteria that have to do with distance were measured without people’s opinions, such as community acceptance. Other sub-criteria like costs, land availability, accessibility, and distance from road remained at an acceptable level of consistency as shown in Figure 9 .

Sensitivity Analysis

Site 2 stands out as the top-performing site, demonstrating statistically significant superiority over both Site 1 and Site 3 (no overlap in uncertainties). Site 3 & Site 1 exhibit overlapping performance ranges within uncertainty bounds. Robustness analysis showed that the percent-top critical criterion is proximity to water sources; a change from 39.8% by absolute and 29.9% will change the ranking between alternatives Site 1 and Site 2. Additionally, a small change in proximity to water sources from 39.8% by an absolute 7.3% will change the ranking between alternatives Site 1 and Site 3. Furthermore, the performance measure for alternative Site 3 under the criterion proximity to water sources, with a change from 22.2% to 2.6%, will change the ranking between Site 3 and Site 1 ( Figure 8 and Figure 10 ).

The Technique of Order Preference by Similarity to Ideal Solution (TOPSIS) is an MCDM method used to rank alternative landfill sites according to their relative closeness to an ideal solution. The method evaluates each site against a set of criteria by identifying a Positive Ideal Solution (PIS) and a Negative Ideal Solution (NIS), which represent the best and the worst. The alternatives are then ranked according to their closeness coefficient, which shows how close each site is to the ideal solution.

Nominalisation of criteria

The pairwise comparison matrix was extracted from the AHP OS, where experts’ judgments were computed. The normalized matrix is given in Table 5 . Table 7 shows the aggregated decision matrix from the original decision matrix. The judgment from seven experts shows the weight for each criterion ( Table 6 ).

Positive Ideal and Negative Ideal Solution

The Positive Solution (PIS) represents the best possible value for each criterion, and the Negative Ideal Solution (NIS) represents the worst possible value of each criterion. The PIS and NIS values are the ones that are used to rank the alternatives based on their closeness to the ideal solution.

For Positive Ideal Solution (PIS)

All the values ranged from 0.0106 (C11) to 0.4407 (C2) show the most desirable performance across different criteria. The highest PIS was observed in C2 with the value 0.4407, indicating that C2 has the most positive ideal value among all.

For Negative Ideal Solution (NIS)

Values ranged from 0.0068 in C3 to 0.5239 in C12, representing the least desirable performance. C12 has the highest NIS value of 0.5239, and it is the worst in that criterion. All in all, C2, C5, C8, and C9 have high PIS values, so they do well in these criteria; hence, they improve the alternative’s closeness to ideal. Criteria like C6 and C12 have high NIS values, given that they have poor performance in these criteria, and they can affect the alternative’s score. The availability of similar PIS and NIS values for C13 (0.1212) shows that the criterion has little or no effect in distinguishing the alternatives ( Figure 11 ).

Alternative ranking of Positive and Negative Ideal Solutions

After calculating the Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS), the Closeness Coefficient (CC) for each alternative was determined. The closeness coefficient indicates how close each alternative is to the ideal solution.

Site 1 has the highest closeness coefficient (0.5912) as shown in Figure 12 , meaning it is the most preferred site according to the evaluated criteria. Site 2 follows closely with a coefficient of 0.5691, making it the second-best option. Lastly, Site 3 has the lowest closeness coefficient (0.3902), indicating that it is the least preferred alternative among the three. Looking into the chart, Site 1 and Site 2 are both good sites but Site 1 is more preferable. However, Site 3 is far behind and it is not even competitive.

The Stepwise Assessment Ratio Analysis method was employed to calculate the relative importance through pairwise comparisons of each criterion based on the expert’s judgement in AHP OS. The following section presents the results of the SWARA, including computed weights for each criterion.

Weight and Weighted Score of Each Criterion.

In this analysis, the Step-wise Weight Assessment Ratio Analysis (SWARA) method was used to derive the global weights of various sub-criteria. SWARA is a subjective weighting method used to evaluate and prioritize multiple criteria based on expert judgment. These weights were computed using Python, and the results are shown in Table 8 .

Weighted score matrix of each criterion.

In this analysis, the Step-wise Weight Assessment Ratio Analysis (SWARA) method was used to derive the global weights of various sub-criteria ( Table 9 ). SWARA is a subjective weighting method used to evaluate and prioritize multiple criteria based on expert judgment.

Based on the weighted score evaluation Table 7 . Site 1 has the most suitable results as factors like community acceptance (C8), distance from settlement (C9), and slope (C1) carry significant weights. Site 1 has moderate results where factors like slope (C1) and proximity to water bodies (C2) are performing well. Site 3 has the lowest average weighted score with minimal contributions from highly weighted criteria, specifically distance from settlement (C11) and land availability (C7), as shown in Figure 13 .

Figure 14 shows that Site 1 has the highest score with a total weighted score of 0.4088 (40.88%), indicating that it is the most optimal among the alternatives. Secondly, Site 2 follows with a total weighted score of 0.3228 (32.28%), ranking second and not significantly different from Site 1. Site 3 has the lowest total weighted score of 0.2695 (26.95%) and is the least favourable option. The table also shows a notable gap between Site 1 and all the other sites, which indicates its relative superiority.

The final result of the MCDM was found by integrating AHP, TOPSIS, and SWARA. Each method contributed equally to the evaluation process. AHP was used to obtain initial weights through pairwise comparison of experts’ judgments. SWARA was then applied to refine these weights through the relative importance of each criterion. After the weighting, TOPSIS was then deployed to rank each alternative (site). It calculates distances from an ideal solution (best solution) and a negative-ideal solution (worst solution).

The integration of AHP, SWARA, and TOPSIS is shown in Figure 15 and Table 10 by calculating the average score of each site across the three individual methods. Each method independently evaluated and ranked the landfill sites based on the same set of criteria, but from slightly different perspectives. The arithmetic mean was selected for integration due to its simplicity and widespread use in hybrid MCDM frameworks, ensuring equal contribution from each method while maintaining interpretability [28] .

The final integrated scores were as follows: Site 2 with the highest score, 38.29% (0.4533); Site 1, 35.67% (0.4223); and Site 3, 26.03% (0.3082), as shown in Table 8 and Figure 16 . These scores clearly indicate that Site 2 is the most suitable location for landfill construction, followed by Site 1, while Site 3 ranks lowest due to its relative disadvantage across multiple criteria. The satellite image ( Figure 17 ) shows the locations of each site in its colour code.

Site 2 is the most suitable; it is situated farther away from dense urban and institutional zones, as shown in Figure 17 ; hence, it has reduced the risk to public health. Site 2 is ranked second, as it is close to infrastructure and land use. Moreover, site 3 is the least suitable, since it is located closest to the main residential areas, and it is also near schools and dense population, which makes it more likely to get a low score. The divergence in rankings (AHP favored Site 2, while TOPSIS/SWARA favored Site 1) arose from AHP’s heavy weighting of environmental criteria (61.1%), where Site 2 excelled in proximity to water sources (39.8% weight). Despite Site 1’s strong performance in TOPSIS/SWARA (community acceptance, accessibility), the integrated score favored Site 2 due to its dominance in the highest-weighted AHP criteria.