A New Model of Pro-Quality Decision Making in Terms of Products’ Improvement Considering Customer Requirements

Abstract

The idea of sustainable development enforces the pro-environmental design and production of products. It also refers to products producing green energy. The current situation in the world, mainly in Europe, further intensifies these works. The new products occurring in this dynamic market are rarely known by customers. In such a case, they have the problem of proper selection based on their own needs. Hence, the purpose is to develop a method to support the customers during their choice of product. In this methodical study, the qualitative and environmental criteria and also price of purchase were simultaneously included. This method was developed using integrated selected techniques, e.g., brainstorming (BM), the SMARTER method, rule 7 ± 2, questionnaire with Likert scale, AHP method, PROMETHEE II method, and matrix data analysis. The results from the test of method allowed the development this method for possible selection of a product according to individual customer expectations but also supported by the knowledge and experience of experts. The method is dedicated to customers but also enterprises aspiring to simultaneously develop their own products. The originality of this work is the integration of the main criteria for the selection of the product by the customer, i.e., quality, impact on natural environment, and price. The novelty of the study is the ranking of selecting products by considering qualitative and environmental criteria, limiting the customer’s necessary knowledge about the analyzed products to determine the weights of criteria, and visualization of the qualitative–environmental relationship. The model test was carried out for popular solar collectors.

1. Introduction

The limitation of negative climate change is realized by sustainability production but also by implementing and popularizing actions that reduces environmental losses [1,2]. One of these is renewable energy sources (RES) [3]. However, implementation is often a kind of barrier when customers lack the possibility of the unequivocal choice of these products due to customer expectations [4,5]. This is also due to market dynamic changes [6]. The latest reports, e.g., [7], show that the most popular are photovoltaic panels or solar collectors, which are recognized as popular, available, and safe sources of energy [8]. The demand for products is constantly growing. Among others, the cumulative global power of PV in 2012 was equal to 942 GW, whereas, total annual growth was 175 GW [7,9]. The climate and energy framework shows that by 2030, it will be necessary to improve energy efficiency by no less than 32.5%. Up to 32% is planned to be obtained from RES [10], where photovoltaic is one of the most preferred technologies to meet energy needs. However, adjusting these products to customer expectations is still difficult, for example, due to weather changes, wind speed, or environmental changes [10,11,12].

The literature review in the area of improving the quality of solar collectors and photovoltaic panels considers customer expectations. Among others, the authors of works such as [13,14] analyzed these products by combined methods, that is, AHP method (analytic hierarchy process) and QFD method (quality function deployment). This consists of the choice of the right photovoltaic, where the AHP method was used to calculate the importance of the product criteria. Then, the customers’ criteria were processed as technical criteria in the QFD method. In the work [15], the possibility of using photovoltaic energy to charge a fleet of electric vehicles was analyzed. The researchers based their study on a non-linear optimization model. The verification of customer expectations in view of RES (e.g., photovoltaic) was also undertaken by authors of the studies [6,16,17]. In the mentioned work [16], the satisfaction from using PV was tested. A survey was also used as well as decision-making methods or regression models, e.g., entropy weight method (EWM), factor analysis, and ordinal regression model. The study authors also used decision-support methods [17], in which the effectiveness of RES was verified. These methods were used for that, i.e., DEMATEL method [18], Kano model [19,20], fuzzy TOPSIS method (the technique for order of preference by similarity to ideal solution) [21], and fuzzy VIKOR method [22]. The analysis showed that for customers, the effectiveness of RES but also the price of its purchase are important. Therefore, when selecting these products for customers, it is important to simultaneously include these criteria. The method of choice of the right RES was also developed by the authors of the study [6], which was based on customer expectations and also the production and consumption of popular energy sources, that is, energy from the sun, wind, and others. The method was developed by combining a survey with a fuzzy Saaty scale, fuzzy AHP method, TOPSIS method, and qualitative-price analysis (ACJ). Another example is the study [23], in which the authors verified the possibility of using photovoltaic energy to power electric cars. The photovoltaic assembly was analyzed on the roof of these cars. Another example is the work [1], in which the possibilities of installing and utilizing PV in small- and medium-sized enterprises from Mexico were tested.

The network of connections of the thematic areas that indicate the main issues related to adapting RES to customer expectations is presented in Figure 1.

After the literature review, it was shown that analyses of using RES (mainly PV) were performed considering that the expectations were realized, for example, [24,25,26]. They were based, for example, on efficiency, price, or application possibilities [27,28,29,30]. Studies were created in which the selection of a product or predicting the direction of improvement would mainly take into account individual customer requirements and expert opinion [6,31], real parameters of product criteria [32,33,34], criterion of impact on natural environmental [33,35,36,37], or price of purchase [4,6,38,39,40]. Furthermore, MCDM (multiple-criteria decision methods) were also used, i.e., DEMATEL method, EWM method, AHP method, fuzzy AHP method, fuzzy VIKOR, and TOPSIS method. In these works, the indicated aspects appeared, but no work was found that simultaneously considered all of them in a combined manner and supported by an appropriate method, such as the example using criteria for selected works, shown in

Table 1. Summary of the key criteria and techniques used to analyze the RES quality level. Own study.

Individual Customer Expectations	Price of Purchase	Efficiency (Based on the Actual Parameters of Criteria)	Criterion of Environmental Influence	Importance (Weight) of Criteria
[13]	[18]	[16]	Not included in this approach and not combined with other selected criteria	[13]
[14]	[23]	[17]		[14]
[16]		[17]
[17]		[23]
[23]
Survey	ACJ method, Kano model, DEMATEL, factor analysis	DEMATEL, EWM, factor analysis, Kano model, fuzzy VIKOR	-	AHP, fuzzy AHP, QFD, TOPSIS

In a new proposed model, we will integrate these key criteria, i.e., individual customer expectations, price of purchase, efficiency (based on the actual parameters of criteria), criterion of environmental influence, and importance (weight) of criteria.

.

Nevertheless, these works did not constitute a single, coherent study; i.e., the key criteria for analyzing the quality level of the product were not used in a simultaneous and combined way. Furthermore, the environmental influence in the other key criteria was not included. This was considered a gap that was assumed to be filled. In a new proposed model, we will integrate these key criteria, i.e., individual customer expectations, price of purchase, efficiency (based on the actual parameters of criteria), criterion of environmental influence, and importance (weight) of criteria.

Hence, the purpose of the study was to develop a model supporting choice and the prediction of the quality of a product considering customers’ expectations towards the quality of products but also simultaneously considering the real price of purchase and sustainable development criteria (i.e., impact on the natural environment). This is achieved through real product parameters, the current price of purchase, and individual customer preference and expert opinion and also includes the impact of the product on the natural environment. For this reason, a research hypothesis was formed as follows form:

Hypothesis 1. 

It is possible to choose a product satisfying to the customer and simultaneously predict the direction of product development according to individual customer expectations and expert opinion but also according to key parameters of choice and sustainable development, i.e., current and the actual parameters of criteria, price of purchase, and impact on the natural environment.

The originality of the article is in the proposed model described as follows:

• Dedicated to the choice of the best product for THE customer;
• Supporting the prediction of future improvement actions;
• Integrating the main (key) aspects of choice of product for the customer while simultaneously including a need for environmental protection, i.e., customer and expert expectations towards qualitative criteria, price of purchase, and impact on the natural environment;
• The coherent combination of the actual values of the product criteria parameters with the values determining customer satisfaction with the quality (immeasurable) criteria;
• Dedicated both to the customer (individual choice of product according to preference) and also to production enterprises aspiring to the continuous and thoughtful improvement of their products;
• Including a new integration of techniques, i.e., SMART(-ER) method, brainstorming (BM), rule 7 + 2, a questionnaire with the Likert scale, AHP method, PROMETHEE II method, and matrix data analysis.

The developed model was tested on the example of solar collectors from one of the key EU producers.

2. Model

2.1. General Concept of Model

The concept of research relies on the developed model to choose the best product considering customer expectations and then predict the direction of improvement for current products to adjust them to the future requirements of customers. According to the literature review and earlier research, the model was developed so as to include in a combined way the following:

• Individual customer requirements and expert opinion [6,31];
• Actual parameters of the product criteria [32,33,34];
• Criterion of the impact on the natural environment [33,35,36,37];
• Price of purchase [4,6,38,39,40].

The model is preferred for use in the case of choice of product for a customer and also to determine design and improvement actions for production enterprises. In addition, the environmental impact is included in this method. In turn, the prediction of improvement of the product will be realized according to customers’ opinions about the importance of the product criteria.

The model can be used to select each RES due to customer expectations. The idea is to support an expert (e.g., an entity offering a product) in predicting which of the products available on the market will be the most satisfying for the customer. It is possible to select each RES due to the fact that the analysis is based on current data on RES, which relate to the following: current customer expectations towards RES, current RES criteria (attributes) and their environmental impact, or the current purchase price. Furthermore, the analysis is supported by expert knowledge (the entity that uses the proposed model). This means that analyses can be carried out mainly on the basis of the customer’s expectations regarding the current parameters of the criteria of any RES, which do not affect the limitations in the selection of the product. The general concept of the model is shown in Figure 2.

In the model, and integrated in a sequential way, the selected instruments support the decision making and assessment of product quality. These techniques are as follows: brainstorming (BM) [41], SMARTER method [42], rule 7 ± 2 [31,33,43], a questionnaire with the Likert scale [44], AHP method [45,46,47], and PROMETHEE II method [48,49]. The analysis was also supported by the actual purchase price of the product in a matrix data analysis dedicated to this model [6,37].

Initially, the product for verification is selected, and the choice is made by an expert after consultation with the customer. Herein, it is possible to use brainstorming (BM). Then, for the selected subject of study, the purpose is determined. In the proposed approach, the purpose should refer to the choice of the product the most preferred by customers and then predict the direction of product improvement to meet customer expectations. The purpose can be determined by using the SMARTER method. The choice of this method, conditioned by applying this method to precision, determines the purpose of the research’s dependence on the verified subject of study, as shown in, e.g., [42].

Then, all products should be characterized according to the criteria, where the number of products and criteria should be the result of the rule of decision methods and be an equal maximum of 7 ± 2 [43]. This principle indicates that the customer is able to compare a maximum of five to nine criteria at the same time. Hence, this rule was assumed to be effective regarding the customers’ processing of the criteria and their assessment of the criteria’s importance. This characteristic should include the current parameters of the product criteria.

The customer expectations are obtained for these criteria, which should refer to the importance of the criteria for the customers and their satisfaction with the current quality of the product. In this case, the Likert scale is used, in which choice results from a product’s popularity in the evaluation by customers [44].

Then, according to customer assessments, the weights of the criteria are estimated, and then, the product’s quality level is calculated. The AHP method is used to calculate the weight of the criteria. This method allows one to determine the weight (importance) of criteria according to comparison in pairs. It is an easy and effective method of comparison criteria, in which the number is consistent with that previously mentioned 7 ± 2 [43].

Moreover, the PROMETHEE II method is used to develop a ranking of choice. Its choice is conditioned by the possibility of calculation by real data and also eventually including data obtained in a qualitative (description) way. Additionally, in this method, the analysis is performed considering the importance of criteria [45,46,49]. As a result, a product-selection ranking is created, which concerns the quality of products according to the fulfilment of customer expectations. The qualitative price analysis is realized by using matrix data analysis [37], which shows which product is the most favorable for quality, impact on the environment, and price of purchase.

The last stage of the model is dedicated to the entity (expert) that, according to weights of the criteria, can plan future improvement actions. The choice of improvement actions results from the preferences of customers and, for example, the company’s capabilities (resources and others).

2.2. Assumptions and Limitations of Model

The assumptions of the model were created on previous research and the literature review. These assumptions are as follows:

• The product for research is not limited, but it is preferred for a moderately complex product [32];
• The number of products of the same type should be equal to maximum 7 ± 2 [43];
• The verification criteria should be basic (main) criteria, which have an important impact on quality of the product but also should refer to sustainable development, i.e., price of purchase and impact on the natural environment [6,32,33,34];
• The number of product criteria should be equal to maximum 7 ± 2 [43];
• The weights of the criteria are expressed in range from 0 to 1 [31,33];
• The quality levels of the products are expressed in range from 0 to 1 [5,31,32];
• The price of purchase of the product is expressed in the selected currency and is the current price of purchase by the customer for a single piece of product [6];
• The model is dedicated to choosing the product according to the individual preferences of the customer but also to improving current products considering customer expectations [5,32].

Hence, the main predicting limitations of the model are, for example, as follows:

• The effectiveness of the model is mainly in meeting the expectations of individual customers;
• The effectiveness of the model is only for the analysis of existing products (predicting customer satisfaction with current products);
• There is a need for many calculations, which is relatively time-consuming.

The algorithm of the model and its stages were developed according to assumptions. It is shown in the next part of the study.

2.3. Algorithm of Model and Its Description

As part of the development of the model, the procedure algorithm was developed. The algorithm was developed in seven main stages. These are shown in Figure 3.

The characteristics of the model are shown in the next part of the study in seven main stages.

Stage 1.

Selecting products and determining the purpose of research

The selection of products for verification is made by an entity (expert, broker, or bidder). The choice is also dependent on the individual preference of the customer. Therefore, it is recommended for the entity to initially consult with the customer. Then, the entity selects products of the same kind (type), e.g., with current availability or on sale.

The most preferred product will be selected from these products. Then, within these products, the direction of their improvement will be predicted. According to the authors of [43], the number of products of the same type should be equal to 7 ± 2.

Then, the purpose of the research is determined according to the subject of the study. The purpose should be determined by an expert. In the proposed approach, the purpose should refer to selecting the product most preferred by customers and then predicting the direction of improvement of the product to meet customer expectations. To develop the purpose of the investigation, the SMARTER method is used [42].

Stage 2.

Characteristic of products according to criteria

It is necessary to characterize all products according to their criteria (attributes). Therefore, initially, for all products, it is necessary to select criteria that characterize them. These criteria should be mainly product criteria, i.e., impacting to a significant (importance) degree the quality of the product. These criteria should be qualitative (utility) and technical, e.g., measurable or unmeasurable. In the proposed approach, it is necessary to include the additional impact of the product on the natural environment.

Therefore, it is important that this criterion is considered among the others. After a review of the literature, e.g., according to authors of studies [33,35,36,37], it is crucial to include the criterion of impact on the natural environment (which refers to the negative impact on the natural environment, e.g., due to the materials used for its production, packaging, or the method of degradation/lifetime). This is due to the global need to care for the natural environment, which is weakened by climate change and further exacerbated by waste and a competitive production environment.

According to the literature review [43], the number of product criteria should be equal to a maximum to 7 ± 2. The choice of criteria can be made according to the catalogue (specification) of the products. It is necessary to realize brainstorming (BM), as shown in studies, e.g., [41]. After determining product criteria, it is necessary to describe (characterize) them, e.g., according to product criteria. It consists of assigning, e.g., measure values (parameters) or parameter ranges to the criteria. Characterization can be carried out in the summary table of products and their criteria.

Stage 3.

Obtaining customer expectations

At this stage, it is necessary to acquire customer expectations in order to achieve the following: (a) choose a product satisfying the customer and (b) predict the direction of current product improvement for adjustment to future customer requirements. Therefore, it is necessary to obtain customer requirements, e.g., using a questionnaire or interview with the customer.

In order to choose products for customers and predict the direction of improving current products, it is necessary to obtain from them assessments determining the weights of product criteria, i.e., assessments of the importance of criteria for customers during use of the product. The popular scale of assessments is the Likert scale (1–5); hence, we choose this scale, where 1 means a practically irrelevant criterion, and 5 means a very important criterion [44]. In order to obtain customers’ expectations, a questionnaire assessing all criteria using a Likert scale must be prepared. These assessments are processed in the next stages of the model.

Stage 4.

Estimating product criteria weights

According to the assessments of customers referring to the weights (importance) of criteria, it is necessary to estimate the weights of criteria. The weights of criteria are used to calculate the quality of products in the next stage of the model but also to predict the direction for improving the current product. It was assumed that for this purpose, the AHP method will be used, the idea of which is to compare the evaluation of criteria in pairs. Therefore, initially, the weights of the evaluation of the criteria should be written in a pairwise comparison matrix (Saaty’s matrix) (1) [45]:

$$\mathrm{S}={\mathrm{S}}_{\mathrm{i}\mathrm{j}}$$

(1)

where i, j = 1, 2, …, k; the proportion of the weight of i-th and j-th criterion from a square matrix of order $\mathrm{n}\times \mathrm{n}$, where n—number of criteria, is determined as a domination matrix (2) [37,46]:

$$P\begin{array}{c}\begin{array}{cc}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}\cong \frac{{\mathrm{w}}_{\mathrm{i}}}{{\mathrm{w}}_{\mathrm{j}}}& \begin{array}{cc}\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}:& \mathrm{i},\mathrm{j}=1,2,...,\mathrm{k}\end{array}\end{array}\\ \begin{array}{ccc}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}=\frac{1}{{\mathrm{S}}_{\mathrm{i}\mathrm{j}}}& \mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}:& \mathrm{i},\mathrm{j}=1,2,...,\mathrm{k}\end{array}\end{array}$$

(2)

The diagonal of matrix S always contains values equal to 1. This means that the criteria compared with each other are equivalent. Therefore, above the diagonal are the values of pairwise comparisons, while below the diagonal are the inverse values.

Then, the calculation is performed based on Saaty’s matrix. The calculation of criteria weights is realized by using the geometric mean of S matrix rows, which are then normalized (3) [37,45,46]:

$$\begin{array}{cc}{\mathrm{w}}_{\mathrm{i}}=\frac{{\left[{\prod }_{\mathrm{j}=1}^{\mathrm{k}}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}\right]}^{\frac{1}{\mathrm{k}}}}{{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\left[{\prod }_{\mathrm{j}=1}^{\mathrm{k}}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}\right]}^{\frac{1}{\mathrm{k}}}}& \begin{array}{cc}\mathrm{f}\mathrm{o}\mathrm{r}:& \mathrm{i}...,1,...\mathrm{k}\end{array}\end{array}$$

(3)

The sum of values for the criterion should be equal to 1. Then, the correctness of the calculations is achieved, and it is assumed that values (${\mathrm{w}}_{\mathrm{i}}$) are product criteria weights, i.e., the importance of criteria for the customer. Ultimately, it is necessary to check that the results obtained do not violate the principle of constancy of preferences. It is verified by calculating of inconsistency factor $\left({\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)$, compliance factor CI, and inconsistency relationship CR, as shown in Formula (4) [37,45]:

$$\begin{gathered} {\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{1}{{\mathrm{w}}_{\mathrm{i}}}\sum _{\mathrm{j}=1}^{\mathrm{k}}{\mathrm{w}}_{\mathrm{i}\mathrm{j}}{\mathrm{w}}_{\mathrm{j}} \\ \mathrm{C}\mathrm{I}=\frac{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{n}}{\mathrm{r}\left(\mathrm{n}-1\right)} \\ \mathrm{C}\mathrm{R}=\frac{\mathrm{C}\mathrm{I}}{\mathrm{r}} \end{gathered}$$

(4)

where ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$—inconsistency factor; n—number of criteria; w—weight of criterion; i, j = 1, 2, …, n; r—the average value of the random index for n according to Saaty (

Table 2. Random index according to Saaty in the AHP method. Own study based on [37,45,46].

n	3	4	5	6	7	8	9	10	11	12	13	14	15
r	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49	1.51	1.48	1.56	1.57	1.59

).

The compatibility of results is obtained when λ max = n, CI = 0, and CR = 0. The compatibility of results is acceptable for ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ close to n and for CI < 0.1 and CR < 0.1 [46]. The lack of full or acceptable agreement of the obtained results proves that the grades were awarded inconsistently [37]. In this case, the process of estimating weight should be repeated from the beginning. After obtaining the consistency of the results, the next stage of the model should be implemented.

Stage 5.

Developing ranking of selecting products according to customer expectations

At this stage, it is necessary to create a ranking of products selection, according to which there will be the possibility to select a product that satisfies the customer, i.e., meet his expectations in terms of quality, price of purchase, and impact on the natural environment. When creating the ranking, it is necessary to rely on the criteria (from stage 2) for which the values of current parameters, purchase price, and environmental impact are determined. Unmeasurable (qualitative) criteria are assessed by an expert on a Likert scale, where 1 means the quality of the criterion practically does not meet customer satisfaction, and 5 means the quality of the criterion fully meets customer satisfaction [44]. At the same time, this method should take into account the weight of the criteria, which was specified by the customer (from step 4). In order to create a ranking for selecting the products, the PROMETHEE II method is used (a method of the family of PROMETHEE methods) [50].

In the PROMETHEE methods for each pair of variants, calculations are made to determine the aggregate index of preference and the positive and negative outflow flow. Positive outflow is a degree determining the outflow of one variant over the others. In turn, the negative outflow determines to what extent this variant outperforms the others. Decision ranking is created based on determined values of outflows [48,49,50,51].

The PROMETHEE II method is one of the variants of PROMETHEE methods as part of the creation of alternative variants [48,49]. In this approach, the purpose is to determine the synthetic ranking of alternatives (in the case of different products). It is realized using the techniques of comparison in pairs and outranking relationships [49]. Firstly, the normalization of parameters and the evaluation of criteria is realized according to Formula (5):

$${\mathrm{r}}_{\mathrm{i}\mathrm{j}}^{\mathrm{c}}=\left\{\begin{array}{c}\begin{array}{cc}\frac{{\mathrm{x}}_{\mathrm{i}\mathrm{j}}-\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)},& \mathrm{i}\mathrm{f}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\to \mathrm{m}\mathrm{a}\mathrm{x}\end{array}\\ \begin{array}{cc}\frac{\mathrm{m}\mathrm{a}\mathrm{x}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)-{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}{\mathrm{m}\mathrm{a}\mathrm{x}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)},& \mathrm{i}\mathrm{f}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\to \mathrm{m}\mathrm{i}\mathrm{n}\end{array}\end{array}\right.$$

(5)

where ${\mathrm{x}}_{\mathrm{i}\mathrm{j}}$– assessments (or parameters) of i-th and j-th product relative c-th criterion; i, j = 1, …, n.

Then, a comparison of products relative criteria is performed, as in formula [49] (6):

$${\mathrm{r}}_{\mathrm{i}\mathrm{j}}^{\mathrm{c}}=\left\{\begin{array}{c}\begin{array}{cc}{\mathrm{g}}_{\mathrm{i}}^{\mathrm{c}}-{\mathrm{g}}_{\mathrm{j}}^{\mathrm{c}},& \mathrm{i}\mathrm{f}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\to \mathrm{m}\mathrm{a}\mathrm{x}\end{array}\\ \begin{array}{cc}{\mathrm{g}}_{\mathrm{j}}^{\mathrm{c}}-{\mathrm{g}}_{\mathrm{i}}^{\mathrm{c}},& \mathrm{i}\mathrm{f}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{c}\to \mathrm{m}\mathrm{i}\mathrm{n}\end{array}\end{array}\right.$$

(6)

where ${\mathrm{x}}_{\mathrm{i}\mathrm{j}}$– assessments (or parameters) i-th and j-th product relative c-th criterion; i, j = 1, …, n.

Then, the individual index of preference is determined. This index is determined by each pair of products relative to each criterion. In this aim, the preference function is adjusted to each criterion, for example, in the form of Formula (7): [49,50,51]:

$${\mathrm{H}}^{\mathrm{c}}\left({\mathrm{a}}_{\mathrm{i}},{\mathrm{a}}_{\mathrm{j}}\right)=\left\{\begin{array}{c}\begin{array}{cc}0,& {\mathrm{r}}_{\mathrm{i}\mathrm{j}}^{\mathrm{c}}\le 0\end{array}\\ \begin{array}{cc}1,& {\mathrm{r}}_{\mathrm{i}\mathrm{j}}^{\mathrm{c}}>0\end{array}\end{array}\right.$$

(7)

where a—product with respect to the c-th criterion; r—indicators of comparison in pair; i, j = 1,…, n; c = 1,…, m.

The next stage is determining multi-criteria indexes of preference. These indexes are determined for each pair of products [48,51] (8):

$$\mathsf{\pi }\left({\mathrm{a}}_{\mathrm{i}},{\mathrm{a}}_{\mathrm{j}}\right)=\sum _{\mathrm{k}=1}^{\mathrm{m}}{\mathrm{w}}_{\mathrm{i}}{\mathrm{H}}^{\mathrm{c}}\left({\mathrm{a}}_{\mathrm{i}},{\mathrm{a}}_{\mathrm{j}}\right)$$

(8)

where ${\mathrm{w}}_{\mathrm{i}}$—weight of criterion; ${\mathrm{w}}_{\mathrm{i}}>0;$ $\sum _{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{w}}_{\mathrm{i}}=1;\mathrm{c}=1,...,\mathrm{m}$.

Then, positive flow ${\mathsf{\phi }}^{+}\left({\mathrm{a}}_{\mathrm{i}}\right)$, negative flow ${\mathsf{\phi }}^{-}\left({\mathrm{a}}_{\mathrm{i}}\right)$, and net flow $\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$ are determined. The flows are determined for each product according to Formulas (9)–(11) [50,51]:

$${\mathsf{\phi }}^{+}\left({\mathrm{a}}_{\mathrm{i}}\right)=\sum _{\mathrm{j}=1}^{\mathrm{n}}\mathsf{\pi }\left({\mathrm{a}}_{\mathrm{i}},{\mathrm{a}}_{\mathrm{j}}\right)$$

(9)

$${\mathsf{\phi }}^{-}\left({\mathrm{a}}_{\mathrm{i}}\right)=\sum _{\mathrm{j}=1}^{\mathrm{n}}\mathsf{\pi }\left({\mathrm{a}}_{\mathrm{j}},{\mathrm{a}}_{\mathrm{i}}\right)$$

(10)

$$\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)={\mathsf{\phi }}^{+}\left({\mathrm{a}}_{\mathrm{i}}\right)-{\mathsf{\phi }}^{-}\left({\mathrm{a}}_{\mathrm{i}}\right)$$

(11)

where a—product with respect to the i-th and j-th criteria; i, j = 1,…, n.

The ranking of products is created on net flows. In the classification, we assumed that the higher the net value ($\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$, the more favorable the product is for customer. Furthermore, the positive value of net flow for the i-th product determines this product as superior to the others in terms of the analyzed criteria (and vice versa). Therefore, the higher the net flow, the better it is [48,49,50,51]. In the proposed approach, a ranking of the selection of the current product for the customer is created. On its basis, the product expected by the customer can be selected according to the product quality, environmental impact, and purchase price of the product.

Stage 6.

Qualitative price analysis

In the proposed approach, it was assumed that the customer selected the product in view of the quality of product and its impact on the natural environment and also the price of purchase. This is determined by combining the value $\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$ from product ranking (including quality and impact on the natural environment) with the real price of purchasing the product. Hence, it is necessary to obtain the unit price of purchasing the product, e.g., a single piece of product in the appropriate currency (e.g., euro). Combining ranking values of the product with the price of purchase is possible by using a quality management tool belonging to the group of new tools, i.e., table (matrix) data analysis. This tool is used to compare (graphic) dependencies between two variables. The procedure for creating the table data analysis in the proposed approach is the following:

(1)

Calculate $\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$ values from ranking products (considering the quality of the product and its impact on the natural environment);

(2)

Estimate the current price of purchase for analyzed products;

(3)

Draw coordinate axes for parameters ($\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$ values and price of purchase);

(4

Scale or mark the axis;

(5)

Enter the parameter values ($\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$ and price of purchase);

(6)

Analyze the distribution of the values obtained.

As a result, it is necessary to choose a product that will meet customer quality expectations (product criteria and its impact on the natural environment) but will also satisfy the customer in view of the price of purchase.

Stage 7.

Predicting direction of product improvement

At this stage, it is possible to predict the direction of product improvement considering customer expectations. It was assumed that prediction is realized based on the weight of product criteria, i.e., the importance of the criteria for the customer. These weights are calculated during the assessment of each customer in the fourth stage of the model using the AHP method. The idea of this stage is to determine which criteria should be used to start improving the quality of products to achieve customer satisfaction. This means identifying a group of product criteria that are worth improving in the first place, where changes in these criteria will determine a significant increase in customer satisfaction.

In the proposed approach, it is necessary to acquire and process the weights of the criteria specified by the customers when using the developed model in a given time range. As mentioned in the third stage of the model, weight evaluations should be obtained through the Likert scale (1–5), where 1 is a practically irrelevant criterion, and 5 is a very important criterion. To determine the ranking of improvement criteria, the value of the arithmetic mean of the obtained weights must be calculated, according to Formula (12) [31]:

$${\stackrel{-}{\mathrm{x}}}_{\mathrm{i}}=\frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{w}}_{\mathrm{i}}}{\mathrm{n}}$$

(12)

where w—weight of product criterion; n—number of customers; i = 1, 2, …, m.

This refers to the calculation of the arithmetic mean from weight assessments for each criterion. It is necessary to calculate the average weight for each criterion selected for verification. As a result, the ranking of product criteria according to their weights is obtained. The first position in the ranking is the most important criterion, and the last position in the ranking is the least important criterion. Based on the obtained ranking, the production enterprises can select strategies for improving products, e.g., improving selected criteria according to this ranking.

3. Test of Model

RES comprise popular and still-developing energy sources. Customers often choose photovoltaic panels but also solar panels [52]. Therefore, RES were the subject of the investigation. The model was tested on RES products, which currently are the most popular and are often selected by customers around the world. These products included solar collectors from one of the UE producers. Testing of the model verified according to the algorithm of the model was completed in seven main stages.

Stage 1.

Selecting products and determining the purpose of research

The entity (expert) selected solar collectors for verification. This choice resulted from the initial consultation with the customer, who showed his preferences in a general way, i.e., an efficient solar collector for domestic use, with black color, and the possibility of being installed on the house roof. The customer mentioned that the solar collector’s quality, price of purchase, and impact on the natural environment are important to him. According to the assumptions, the entity selected seven solar collectors. From these selected products, the product most preferred for the customer was selected; for the purposes of the analysis, the range is conventionally marked P1–P7.

According to the selected research subject, the purpose of the research was determined. The SMARTER method was used. The purpose was to select the solar collector most preferred by the customer and then predict the direction for improvement of the solar collectors to meet the customers’ expectations.

Stage 2.

Characteristic of products according to criteria

All solar collectors were characterized according to their categories (attributes). Therefore, initially, the key criteria for solar collectors were determined. The choice of criteria was made after brainstorming (BM). Firstly, eleven main criteria for the product catalogue (specification) were selected, which were the qualitative (utility) and technical criteria of the product. Of these, two criteria were dropped, and the parameters were different to a small extent from each other: absorption (%), that is, the percent of energy absorbed from the amount of solar radiation from the inside of the collector, and also emission (%), which is the percent of energy from the amount of solar radiation, which is reflected from the absorber surface. Hence, the model finally decided on nine main criteria, and their number met the assumed assumptions of the model (i.e., maximum of nine criteria). Their criteria judged the impact of the quality of solar collectors but also the current price of purchase and impact on natural environment [4,5,53]:

• Impact on the natural environment—impact of the solar collector on the natural environment, e.g., in the context of the way of packing the product (amount and kind of used materials, e.g., stretch foil, foam, tapes, and other plastics), recycling of collectors or possibilities of collector recovery, or vitality (degradation), which determines the time of trouble-free operation [54];
• Total surface (${\mathrm{m}}^2$)—total outer surface occupied by the installed collector, but the surface does not have an impact on its efficiency, and the larger the surface, the more difficult an installation on the roof;
• Surface of absorber/aperture (${\mathrm{m}}^2$)—the task of the absorber is to absorb energy from the sun, which is why it generates heat and transfers it to the heating medium; the absorber generates the efficiency of the collector, but the aperture is the average of the optical device hole through which light enters, so it is the biggest surface through which light enters; in flat-plate collectors, the aperture is the internal area of the collector frame, while in vacuum collectors, it is the sum of all sections of glass tubes;
• Optical efficiency (%)—the result of sunlight absorbed by the aperture of the collector surface, which later is processed AS heat;
• Thickness of the glass pane or the wall of the glass tube (mm)—for flat-plate collectors, it is the thickness of the collector glass, while for tube-vacuum collectors, it is the wall of the glass pipe;
• Maximum volume of heated water (l)—the maximum volume of water that is able to heat the solar collector;
• System of absorber tubes or vacuum tubes that receive the generated heat from the absorber and can be in the form of parallel tubes, the so-called harp arrangement;
• Diameter of connections or vacuum tubes (mm)—diameter of connections in a flat solar collector or diameter of pipes in a vacuum solar collector;
• Housing color—external color of the solar collector.

All criteria are characterized according to the product catalogue. The characterization was performed according to the summary presented in

Table 3. Characterization of solar collectors selected for verification.

Type of Collector	Solar Collector 1 (Flat)	Solar Collector 2 (Flat)	Solar Collector 3 (Tube-Vacuum)	Solar Collector 4 (Flat)	Solar Collector 5 (Flat)	Solar Collector 6 (Flat)	Solar Collector 7 (Tube-Vacuum)
Impact on the natural environment	3	4	2	2	4	3	3
Total surface (m2)	2.0	2.8	3.61	2.0	2.8	2.5	2.98
Absorber surface/or aperture (m2)	1.8	2.6	2.67	1.8	2.8	2.3	2.21
Optical efficiency (%)	80	80	93.7	80	80	80	0.94
Thickness of glass or glass tube (mm)	4	4	2	4	4	4	2
Maximum volume of heated water (l)	100	150	150	100	150	120	100
Absorber tube layout or number of vacuum tubes (pieces)	Single harp	Double harp	22	Single harp	Single harp	Double harp	11
Diameter of connections or vacuum tubes (mm)	4 × 22	2 × 22	58	4 × 18	4 × 18	2 × 22	58
Housing color	Black	Silver	Silver/Black	Gray	Gray	Silver	Silver/Black

.

Now, the study realizes the next stage of the model.

Stage 3.

Obtaining customer expectations

Customer expectations are obtained in order to (a) choose a product satisfying the customer and (b) predict the direction of current product improvement for its adjustment to future customer requirements. The questionnaire is used to obtain customer expectations, which are used to assess the importance of solar collectors on the Likert scale. The assessments are shown in

Table 4. Assessments of the importance the solar collectors on the Likert scale.

QUESTIONNAIRE Assess the Importance of Solar Collectors on the Likert Scale Using “X” in Each Criterion
Criteria of Solar Collectors	1	2	3	4	5
Impact on the natural environment			X
Total surface (square meter)		X
Absorber surface/or aperture (square meter)				X
Optical efficiency (%) (percent)				X
Thickness of glass or glass tube (millimeter)					X
Maximum volume of heated water (liter)					X
Absorber tube layout or number of vacuum tubes (pieces)			X
Diameter of connections or vacuum tubes (millimeter)			X
Housing color		X

where 1, practically irrelevant; 2, moderately important; 3, important; 4, important; 5, very important.

.

Based on assessments of the weights of solar collectors, it is possible to realize the next stage of the model.

Stage 4.

Estimating product criteria weights

Based on customer assessments obtained for the weight (importance) of the criteria, the weights of these criteria are estimated. For that, the AHP method is used. First, according to Formulas (1) and (2), the weights of criteria weights are marked in the comparison matrix of comparison of pairs (${\mathrm{S}}_{\mathrm{i}\mathrm{j}}$), as in

Table 5. Matrix of comparison of pair of weights of solar collector criteria considering customer expectations.

Criteria	C1	C2	C3	C4	C5	C6	C7	C8	C9
C1	1.00	1.50	0.75	0.75	0.60	0.60	1.00	1.00	1.50
C2	0.67	1.00	0.50	0.50	0.40	0.40	0.67	0.67	1.00
C3	1.33	2.00	1.00	1.00	0.80	0.80	1.33	1.33	2.00
C4	1.33	2.00	1.00	1.00	0.80	0.80	1.33	1.33	2.00
C5	1.67	2.50	1.25	1.25	1.00	1.00	1.67	1.67	2.50
C6	1.67	2.50	1.25	1.25	1.00	1.00	1.67	1.67	2.50
C7	1.00	1.50	0.75	0.75	0.60	0.60	1.00	1.00	1.50
C8	1.00	1.50	0.75	0.75	0.60	0.60	1.00	1.00	1.50
C9	0.67	1.00	0.50	0.50	0.40	0.40	0.67	0.67	1.00
Sum	10.33	15.50	7.75	7.75	6.20	6.20	10.33	10.33	15.50

where C1, impact on the natural environment; C2, total surface (m²); C3, absorber surface/or aperture (m²); C4, optical efficiency (%); C5, thickness of glass or glass tube (mm); C6, maximum volume of heated water (l); C7, absorber tube layout or number of vacuum tubes (pieces); C8, diameter of connections or vacuum tubes (mm); C9, housing color.

.

Now, according to Formula (3) and based on the Saaty matrix, the calculations are realized. The weights of the criteria are geometric means of S matrix rows, which are then normalized (

Table 6. Criteria weights for solar collectors considering customer expectations.

Criteria	C1	C2	C3	C4	C5	C6	C7	C8	C9	${\mathbf{w}}_{\mathbf{i}}$
C1	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10
C2	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06
C3	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13
C4	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13
C5	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16
C6	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16
C7	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10
C8	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10
C9	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06

where C1, impact on the natural environment; C2, total surface (m²); C3, absorber surface/or aperture (m²); C4, optical efficiency (%); C5, thickness of glass or glass tube (mm); C6, maximum volume of heated water (l); C7, absorber tube layout or number of vacuum tubes (pieces); C8, diameter of connections or vacuum tubes (mm); C9, housing color.

).

It is demonstrated that the sum of values for each criterion is equal to 1, and hence, we can assume the correctness of the performed calculations. The values ${\mathrm{w}}_{\mathrm{i}}$() are obtained as weights of the solar collector criteria. Then, the obtained results are confirmed to not violate the principle of the constancy of preferences. Formula (4) is used to calculate the inconsistency factor $\left({\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}\right)$, compliance factor (CI), and the inconsistency relationship (CR). this is shown in

Table 7. Verification of the principle of the constancy of preferences in the AHP method.

Criteria	C1	C2	C3	C4	C5	C6	C7	C8	C9	${\displaystyle \sum _{\mathbf{j}=1}^{\mathbf{k}}}{\mathbf{w}}_{\mathbf{i}\mathbf{j}}$	${\displaystyle \sum _{\mathbf{j}=1}^{\mathbf{k}}}{\mathbf{w}}_{\mathbf{i}\mathbf{j}}{\mathbf{w}}_{\mathbf{j}}$
${\mathbf{w}}_{\mathbf{i}}$	0.10	0.06	0.13	0.13	0.16	0.16	0.10	0.10	0.06
C1	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.87	9
C2	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.58	9
C3	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	1.16	9
C4	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	0.13	1.16	9
C5	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	1.45	9
C6	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	0.16	1.45	9
C7	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.87	9
C8	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.10	0.87	9
C9	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.06	0.58	9
${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}=9$			CI = 0			CR = 0			where: r = 1.45

where C1, impact on the natural environment; C2, total surface (m²); C3, absorber surface/or aperture (m²); C4, optical efficiency (%); C5, thickness of glass or glass tube (mm); C6, maximum volume of heated water (l); C7, absorber tube layout or number of vacuum tubes (pieces); C8, diameter of connections or vacuum tubes (mm); C9, housing color.

.

The average value of the random index is used for the calculations, which is assumed for nine criteria according to Saaty and is equal to r = 1.45 (as in Table 1). After the calculations, the full consistency of the results are obtained because ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ = 9, CI = 0, and CR = 0. Therefore, it is possible to implement the next stage of the model.

Stage 5.

Developing ranking of selecting products according to customer expectations

The ranking of the selection of products according to the expectations of the customer is developed by using the PROMETHEE II method. Calculations are performed based on real values of parameters of solar collector criteria and assessments of experts assigned to these criteria (shown in Table 2) and based on weights of these criteria (${\mathrm{w}}_{\mathrm{i}}$) as determined by the customer and then processed by the AHP method.

Using the PROMETHEE II method, first, we determine the criteria that are so-called “max”, i.e., benefit (B),where the higher the value, the better, and those that are so-called “min”, i.e., non-benefit (NB), where the higher the value, the worse. Criteria, i.e., diameter of connections or vacuum tubes, absorber tube layout or the number of vacuum tubes, impact on the natural environment, and color, are described in a qualitative way. Hence, the expert (entity) assesses these criteria according to their own preferences and the Likert scale; that is, 1 means the quality of the criterion practically does not meet customer satisfaction (or impact on the natural environment is negligible), and 5 means the quality of the criterion fully meets customer satisfaction (or impact on the natural environment is significant). Furthermore, the maximum and minimum values of the parameters for each criterion are determined, which are used to calculate the normalized values of the assessments and the parameters of the criteria. Formula (5) is used for this. The results of these actions are shown in

Table 8. Parameters of solar collector criteria for assessing their quality in the PROMETHEE II method.

$\mathbf{Weight}\left({\mathbf{w}}_{\mathbf{i}}\right)$		0.10	0.06	0.13	0.13	0.16	0.16	0.10	0.10	0.06
Beneficial or Non-Beneficial		NB	NB	B	B	B	B	B	B	B
Criterion		C1	C2	C3	C4	C5	C6	C7	C8	C9
Parameters and assessments of criteria	P1	3	2	1.8	80	4	100	3	5	5
	P2	4	2.8	2.6	80	4	150	4	3	3
	P3	2	3.61	2.67	93.7	2	150	22	5	5
	P4	2	2	1.8	80	4	100	3	4	3
	P5	4	2.8	2.8	80	4	150	3	4	3
	P6	3	2.5	2.3	80	4	120	4	3	2
	P7	3	2.98	2.21	0.94	2	100	11	5	5
MIN		2	2	1.8	0.94	2	100	3	3	2
MAX		4	3.61	2.8	93.7	4	150	22	5	5
Normalized values of parameters and assessments of criteria	P1	−1.00	0.00	0.00	0.85	1.00	0.00	0.00	1.00	1.00
	P2	−2.00	−0.80	0.80	0.85	1.00	1.00	0.05	0.00	0.33
	P3	0.00	−1.61	0.87	1.00	0.00	1.00	1.00	1.00	1.00
	P4	0.00	0.00	0.00	0.85	1.00	0.00	0.00	0.50	0.33
	P5	−2.00	−0.80	1.00	0.85	1.00	1.00	0.00	0.50	0.33
	P6	−1.00	−0.50	0.50	0.85	1.00	0.40	0.05	0.00	0.00
	P7	−1.00	−0.98	0.41	0.00	0.00	0.00	0.42	1.00	1.00

where P1–P7, solar collectors; C1, impact on the natural environment; C2, total surface (m²); C3, absorber surface/or aperture (m²); C4, optical efficiency (%); C5, thickness of glass or glass tube (mm); C6, maximum volume of heated water (l); C7, absorber tube layout or number of vacuum tubes (pieces); C8, diameter of connections or vacuum tubes (mm); C9, housing color; B, beneficial criterion; NB, non-beneficial criterion.

.

Then, all solar collectors in view of all criteria are compared. Formula (6) is used for that. this fragment of results from the comparison of collectors is shown in

Table 9. Fragment of the results obtained after comparing solar collectors to each other in the PROMETHEE II method.

$\mathbf{Weight}\left({\mathbf{w}}_{\mathbf{i}}\right)$	0.10	0.06	0.13	0.13	0.16	0.16	0.10	0.10	0.06
Beneficial or Non-Beneficial	NB	NB	B	B	B	B	B	B	B
Criterion	C1	C2	C3	C4	C5	C6	C7	C8	C9
P1–P2	1.00	0.80	−0.80	0.00	0.00	−1.00	−0.05	1.00	0.67
P1–P3	−1.00	1.61	−0.87	−0.15	1.00	−1.00	−1.00	0.00	0.00
P1–P4	−1.00	0.00	0.00	0.00	0.00	0.00	0.00	0.50	0.67
P1–P5	1.00	0.80	−1.00	0.00	0.00	−1.00	0.00	0.50	0.67
P1–P6	0.00	0.50	−0.50	0.00	0.00	−0.40	−0.05	1.00	1.00
P1–P7	0.00	0.98	−0.41	0.85	1.00	0.00	−0.42	0.00	0.00
P2–P1	−1.00	−0.80	0.80	0.00	0.00	1.00	0.05	−1.00	−0.67
P2–P3	−2.00	−0.39	−2.87	−3.00	−2.00	−3.00	−3.00	−3.00	−3.00
P2–P4	0.00	0.00	0.00	−0.85	−1.00	0.00	0.00	−0.50	−0.33
P2–P5	2.00	0.80	−1.00	−0.85	−1.00	−1.00	0.00	−0.50	−0.33
P2–P6	−1.00	−1.50	−2.50	−2.85	−3.00	−2.40	−2.05	−2.00	−2.00
P2–P7	0.00	−0.02	−1.41	−1.00	−1.00	−1.00	−1.42	−2.00	−2.00
P3–P1	1.00	−1.61	0.87	0.15	−1.00	1.00	1.00	0.00	0.00
P3–P2	2.00	−0.81	0.07	0.15	−1.00	0.00	0.95	1.00	0.67
P3–P4	0.00	0.00	0.00	−0.85	−1.00	0.00	0.00	−0.50	−0.33
P3–P5	2.00	0.80	−1.00	−0.85	−1.00	−1.00	0.00	−0.50	−0.33
P3–P6	−1.00	−1.50	−2.50	−2.85	−3.00	−2.40	−2.05	−2.00	−2.00
P3–P7	0.00	−0.02	−1.41	−1.00	−1.00	−1.00	−1.42	−2.00	−2.00

where: P1–P7, solar collectors; C1, impact on the natural environment; C2, total surface (m²); C3, absorber surface/or aperture (m²); C4, optical efficiency (%); C5, thickness of glass or glass tube (mm); C6, maximum volume of heated water (l); C7, absorber tube layout or number of vacuum tubes (pieces); C8, diameter of connections or vacuum tubes (mm); C9, housing color; B, beneficial criterion; NB, non-beneficial criterion.

.

Next, for each pair of solar collector criteria and in view of each criterion, an individual index of preference is determined. This consists of matching the preference function to results from the comparison of the solar collector criteria. Formula (7) is used for this. Then, multiple preferences indexes are determined for each pair of solar collector criteria, as in Formula (8). The fragment of results obtained is shown in

Table 10. Fragment of preference indices and multi-criteria preference indices determined for solar collectors in the PROMETHEE II method.

$\mathbf{Weight}\left({\mathbf{w}}_{\mathbf{i}}\right)$	0.10	0.06	0.13	0.13	0.16	0.16	0.10	0.10	0.06	$\begin{array}{c}\mathsf{\pi }\left({\mathbf{a}}_{\mathbf{i}},{\mathbf{a}}_{\mathbf{j}}\right)\\ ={\displaystyle \sum _{\mathbf{k}=1}^{\mathbf{m}}}{\mathbf{w}}_{\mathbf{i}}{\mathbf{H}}^{\mathit{c}}\left({\mathbf{a}}_{\mathbf{i}},{\mathbf{a}}_{\mathbf{j}}\right)\end{array}$
Beneficial or Non-Beneficial	NB	NB	B	B	B	B	B	B	B
Criterion	C1	C2	C3	C4	C5	C6	C7	C8	C9
P1–P2	0.10	0.05	0.00	0.00	0.00	0.00	0.00	0.10	0.04	0.29
P1–P3	0.19	0.10	0.00	0.00	0.16	0.00	0.00	0.00	0.00	0.46
P1–P4	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.05	0.04	0.09
P1–P5	0.10	0.05	0.00	0.00	0.00	0.00	0.00	0.05	0.04	0.24
P1–P6	0.00	0.03	0.00	0.00	0.00	0.00	0.00	0.10	0.06	0.19
P1–P7	0.29	0.06	0.00	0.11	0.16	0.00	0.00	0.00	0.00	0.62
P2–P1	0.00	0.00	0.10	0.00	0.00	0.16	0.01	0.00	0.00	0.27
P2–P3	0.10	0.04	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.14
P2–P4	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
P2–P5	0.10	0.05	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.15
P2–P6	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
P2–P7	0.29	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.35
P3–P1	0.00	0.00	0.11	0.02	0.00	0.16	0.10	0.00	0.00	0.39
P3–P2	0.00	0.00	0.01	0.02	0.00	0.00	0.09	0.10	0.04	0.26
P3–P4	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
P3–P5	0.10	0.05	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.15
P3–P6	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
P3–P7	0.29	0.06	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.35

where: P1–P7, solar collectors; C1, impact on the natural environment; C2, total surface (m²); C3, absorber surface/or aperture (m²); C4, optical efficiency (%); C5, thickness of glass or glass tube (mm); C6, maximum volume of heated water (l); C7, absorber tube layout or number of vacuum tubes (pieces); C8, diameter of connections or vacuum tubes (mm); C9, housing color; B, beneficial criterion; NB, non-beneficial criterion.

.

Then, flows are determined: positive ${\mathsf{\phi }}^{+}\left({\mathrm{a}}_{\mathrm{i}}\right)$, negative ${\mathsf{\phi }}^{-}\left({\mathrm{a}}_{\mathrm{i}}\right)$, and net $\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$. The flows are determined for each solar collector according to Formulas (9)–(11). The results are shown in

Table 11. Positive and negative flows of solar collector in PROMETHEE II method.

Solar Collector	P1	P2	P3	P4	P5	P6	P7	${\mathsf{\phi }}^{+}\left({\mathbf{a}}_{\mathbf{i}}\right)$
P1	-	0.29	0.46	0.09	0.24	0.19	0.62	0.32
P2	0.27	-	0.14	0.00	0.15	0.00	0.35	0.15
P3	0.39	0.26	-	0.00	0.15	0.00	0.35	0.19
P4	0.00	0.20	0.46	-	0.15	0.00	0.35	0.19
P5	0.29	0.07	0.33	0.29	-	0.00	0.35	0.22
P6	0.13	0.12	0.43	0.13	0.12	-	0.67	0.27
P7	0.09	0.18	0.04	0.19	0.13	0.20	-	0.14
${\mathsf{\phi }}^{-}\left({\mathrm{a}}_{\mathrm{i}}\right)$	0.20	0.19	0.31	0.12	0.16	0.07	0.45	-

and

Table 12. Ranking of solar collectors in PROMETHEE II method.

Solar Collector	${\mathsf{\phi }}^{+}\left({\mathbf{a}}_{\mathbf{i}}\right)$	${\mathsf{\phi }}^{-}\left({\mathbf{a}}_{\mathbf{i}}\right)$	$\mathsf{\phi }\left({\mathbf{a}}_{\mathbf{i}}\right)$	Ranking	Decision
P1	0.32	0.20	0.12	2
P2	0.15	0.19	−0.03	5
P3	0.19	0.31	−0.12	6
P4	0.19	0.12	0.08	3
P5	0.22	0.16	0.07	4
P6	0.27	0.07	0.20	1	The best solar collector
P7	0.14	0.45	−0.31	7	The worst solar collector

.

According to net flows, the ranking of solar collectors is determined. The best collector for the customer is marked as P6. It has the first position in the ranking. The choice of this collector results from the assessment of its quality (determined according to the actual parameters of the criteria) and the importance of these criteria for the customer.

Stage 6.

Qualitative-price analysis

It is assumed that customer selects the product in view of the quality of the product, its impact on the natural environment, and the price of purchase. This is achieved by combining values from the ranking of the selected solar collectors (considering their quality and impact on the natural environment) with the current price of purchase. In this aim, the price of purchase of solar collectors for a single piece is determined in euros. The values from the ranking of selected solar collectors with their current price of purchase are shown in

Table 13. Prices and values of quality level of solar collectors.

ACJ	P1	P2	P3	P4	P5	P6	P7
P (cost, EUR)	482.02	454.90	589.84	309.82	401.71	286.85	368.39
$\mathsf{\phi }\left({\mathrm{a}}_{\mathrm{i}}\right)$	0.12	−0.03	−0.12	0.08	0.07	0.20	−0.31

.

The result of the matrix analysis of data is shown in Figure 4.

The matrix analysis of data does not change, in this case, the selection preferences. In PROMETHEE II, the ranking shows that the best is collector P6, and also the same collector is the best according to the matrix analysis. This situation is possible because this product is by far the cheapest among those analyzed. If this product is not analyzed, the next groups dedicated to this client in order of selection preference is as follows: panels P1, P4, and P5 and only then P2, P7, and P3.

Stage 7.

Predicting direction of products improvement

At this stage, it is possible to predict the direction of improving solar collectors considering customer expectations. This prediction should be realized based on the solar collector’s weights (${\mathrm{w}}_{\mathrm{i}}$). The criteria weights should be obtained each time from the customers, and the criteria weights obtained from the customers when using the developed model should be processed for a specified period of time [31]. According to the authors of studies, it is preferred to obtain expectations from, e.g., 100 customers. Then, it is necessary to calculate the arithmetic mean value-obtained weights according to Formula (12). The greater the value of the arithmetic mean of the criteria weights, the more preferred the process of improving these criteria. After determining, e.g., the main (or several of the most important) criteria, it is possible to realize improvement activities. This process depends on the individual preferences of the enterprise, e.g., production possibilities, sources, and others.

4. Discussion

Selection and also improvement of the quality of products according to customers’ expectations is still a challenge [7,9]. It is crucial to define design and improvement activities mainly for dynamically developing products [55,56,57]. One of these is photovoltaic panels and also solar collectors [58,59,60]. Although these products were analyzed, the model that simultaneously predicts their selection and the direction of their development was not developed [10,11,12]. This means there is a lack of a model that would allow the simultaneous inclusion of experts’ opinions, customer expectations, and also the real parameters of product criteria, price of purchase, and impact on the natural environment. Herein, the predicted direction of product improvement will be realized according to customers’ expectations towards the importance of product criteria.

Therefore, the purpose was to develop a model supporting the choice and prediction of products considering customers’ expectations towards the quality of products and also simultaneously considering the price and sustainable development criteria (impact on the natural environment). It was realized based on real product parameters, the current price of purchase, individual preference of the customer, and expert opinion and also considering the impact on the natural environment. The model was developed by sequentially integrating selected instruments of decision support and quality assessment of products. These techniques included brainstorming (BM), SMARTER method, rule 7 ± 2, a questionnaire with the Likert scale, AHP method, and PROMETHEE II method. Qualitative price analysis was also used.

A test of the model was carried out for solar collectors. The most advantageous both in terms of quality and purchase price was shown to be the solar collector with the conventional designation of P6. After this model, we observed slight differences between collectors P6, P4, and P1 (in qualitative price ranking). It was observed that the same collector varied greatly in quality (in qualitative ranking, PROMETHEE II); i.e., both collectors P1 and P4 had a much lower level of quality compared to the P6 collector. Therefore, in the proposed approach, it was possible to predict the customer’s choice of the P6 collector. It is necessary to remember that the final decision belongs to the customer and results from his individual preference and expectations. For this reason, the rankings obtained in future analyses for other customers can be different, but these differences will result from the current parameters of the product criteria, the real price of purchase, and the impact on the natural environment.

The test of the model shows that the product that satisfies the customer can be selected, and simultaneously, the model can predict the direction of product development. This result was realized according to individual customer expectations, experts’ opinions, and also current and real criteria and price of purchase. The main benefits of the model are, among others, as follows:

• Choice of product as expected by the customer;
• Prediction of product improvement direction according to customer requirements;
• Possibilities of the product choice by criteria including the quality of the product (resulting from customer expectations and real parameters of the product), and its price of purchase and impact on the natural environment;
• Ensuring that analyses are carried out on the actual values of the product criteria parameters and also the current price of purchase and data expressed in a qualitative way (verbal), e.g., impact on the natural environment;
• Reducing the waste of enterprise resources by methodically identifying appropriate product improvement activities;
• Low-cost model, which could be useful for meeting customer expectations, and also will be useful for enterprises in striving to improve products in order to achieve customer satisfaction (in the future).

In turn, the main disadvantages of the proposed model are, for example, the possibility of verification expectations only for individual customers, the need to obtain expectations from customers for a given period of time, and the possibility of analysis of products only based on current product criteria. A certain limitation is also the need to carry out calculations, which can be relatively time-consuming.

Therefore, future research will be based on developing the model in computer programs such as an intelligent models, which is compatible for obtaining customers’ expectations, dynamically operating according to the methods used in this model (mainly MCDM), and allowing making decision by experts. Moreover, it is planned to simultaneously adjust the model to process expectations from a large number of customers. Future research will be concentrated on using neural networks in this area, for example, SOFNN-HPS, and GK-ARFNN, which, after preliminary review, were not used in this approach.

5. Conclusions

Striving for a satisfactory quality of products should be inseparable from striving to prevent negative climate changes. this is possible by popularizing and improving products applied as RES. Those most preferred by the customer are solar collectors. Despite their popularity, there is still a problem with adjusting these products to customers’ expectations. Hence, the purpose of the study was to develop a model supporting choice and prediction of the quality of a product considering customers’ expectations towards the quality of products but also simultaneously considering the real price of purchase and sustainable development criteria (i.e., impact on the natural environment).

The model was developed by selecting integrated sequential instruments for decision support and methods to assess the quality of products. These techniques were brainstorming (BM), SMARTER method, rule 7 $\pm$ $2$, a questionnaire with Likert scale, AHP method, and PROMETHEE II method. A test of the model was carried out for seven solar collectors from UE producers. Verification was carried out for the nine main criteria of these collectors, i.e., impact on the natural environment, total surface, absorber surface/or aperture, optical efficiency, thickness of glass or glass tube, maximum volume of heated water, absorber tube layout or number of vacuum tubes, diameter of connections or vacuum tubes, and housing color. The ranking obtained was compared with the price of purchase.

This test showed that the most preferred product in terms of quality and price of purchase was solar collector P6. However, the final decision depends on the customer. After the model test, it was concluded that a product that satisfies the customer can be selected, and at the same time, the direction of product development can be predicted. At the same time, it will be implemented according to individual customer expectations, expert opinion, and also on the basis of current and actual parameters of the product criteria and its purchase price.

The originality of this research is in the integration of the main criteria for the selection of the product by the customer, i.e., quality, impact on natural environment, and price. The novelty of the study is in the ranking of selected products by considering qualitative and environmental criteria, limiting the customer’s necessary knowledge about the analyzed products to determine the weights of criteria, and visualization of the qualitative–environmental relationship. The model test was carried out for popular solar collectors.

The developed model will be useful both for the choice of an adequate product for the customer and also to determine design and improvement actions for production enterprises, e.g., producing a new product or significantly modifying a product currently on the market.