Methodology of Multiple-Criteria Decision Making for Selecting a Refrigerant to Be Used in Commercial Refrigeration Equipment

Abstract

This paper presents the application of the multiple-criteria decision-making (SAW) method for selecting the optimum refrigerant for the refrigeration systems of commercial cooling equipment used in gastronomy furniture, which is paramount in storing food under optimal conditions. The analysis focused on comparing different refrigerants, including natural refrigerants such as R744 (carbon dioxide) and R290 (propane) and synthetic refrigerants such as R455A, R449A, and R452A. As a result of the analysis using the SAW method, the refrigerant R455A was found to be the best solution. This choice resulted from the consideration of various decision criteria, such as energy efficiency, environmental impact, operating costs, and technology availability. R455A stands out as a synthetic refrigerant that provides high energy efficiency with minimal environmental impact. Its use supports sustainability goals by reducing greenhouse gas emissions and electricity consumption, which is crucial given the modern regulatory requirements and environmental standards. This study offers a practical decision-making tool for commercial refrigeration equipment designers and manufacturers, supporting them while selecting the optimal technological solutions. The choice of refrigerant R455A addresses the need to integrate energy efficiency, environmental protection, and cost-effectiveness in the process of designing modern refrigeration systems for catering furniture.

1. Introduction

Modern catering furniture does not only fulfill a practical function, but is also becoming increasingly technologically advanced. Refrigeration systems are its key component and are fundamental to maintaining the appropriate food storage conditions. Choosing the right refrigerant for these systems is a strategic decision that has a significant impact on the energy efficiency, environmental performance, and overall operating costs of catering furniture [1,2,3,4,5,6,7,8,9,10].

The decision regarding the choice of refrigerant is particularly important in the context of the ever-more-stringent energy efficiency and sustainability requirements. Contemporary regulations and environmental requirements challenge the designers and manufacturers of commercial refrigeration equipment to choose refrigerants that not only provide an adequate cooling capacity, but also are environmentally friendly.

Multi-criteria decision-making methodology is essential in the process of selecting the optimum refrigerant. Multi-criteria analysis allows for the consideration of various aspects, such as energy efficiency, safety of operation, environmental impact, operating costs, and technology availability.

This article presents the methodology of multi-criteria analysis as a tool to support the decision-making process in the selection of refrigerants for gastronomy equipment. The various decision-making criteria are discussed, practical examples are provided, and the benefits of applying this methodology to design and manufacturing practice are presented. By analyzing the various aspects and challenges of refrigerant selection, this article aims to provide the reader with a comprehensive tool for making knowledgeable and information-based decisions.

2. Research Subject and Methodology

2.1. Choice of Decision-Making Support Method

Operational research is one of the fields of science that performs tasks in the field of multi-criteria decision-making support [11,12,13]. Multi-criteria decision-making methods are used in the implementation of tasks aimed at solving demanding problems that frequently involve contradictory criteria. The tool presented here supports the decision-making process regarding the selection of the optimal refrigerant.

Among the various known methods of decision-making support, the American and the French ones constitute two major approaches [12,14,15]. In the course of the decision-making process, different criteria might occur that cannot be directly compared to one another. Different methods involve different solutions, which leads to different courses of the decision-making process itself. The various methods of the above approaches vary in the way they operate on criteria that cannot be directly compared with each other.

According to the so-called American school, whose methods are based on a synthetic criterion, individual criteria are classified into a single optimal utility function. Such methods as AHP, SMART, SAW, MUZ, and UTA may serve as examples of this approach [12,13].

The other approach refers to the so-called French school, which classifies incomparable decision options using the superiority relation. This allows us to obtain results even though the decision maker comparing the two variants cannot positively indicate the superiority of one of them. Classes of interactions are thus created. This is characteristic of the Promethee, as well as the Electre, group of methods [12,13].

There is also another approach that is a combination of the two above methods, with the Pragma, Idra, and Mappac methods [12,13].

Nowadays, decision-making support methods are often used, as they greatly advance and facilitate the decision-making process. What is important, however, is to properly match the problem addressed with the appropriate method [14,15,16,17].

To optimally select a modern refrigerant and take into account the above aspects, it was assumed that the task could be categorized as a variant ordering problem. For further research purposes, the weighted-sum method SAW (simple additive weighting) was selected due to its popularity for its simplicity, flexibility, and ease of implementation. It renders it possible to compare decision-making options based on various criteria by summing the weighted scores of evaluations. It is intuitive and can be used in many different situations without the need for advanced mathematical analysis, which makes it attractive to a wide range of users, especially when simplicity of calculation is crucial.

2.2. Simple Additive Weighting Method

The simple additive weighting method (SAW) is one of the most frequently used methods of multi-criteria optimization [14,17,18]. With this method, it is possible to convert a multi-criteria problem into a single-criteria one by determining the weights of each criterion based on user preferences. In this method, a proxy criterion is introduced, which is a weighted sum of criteria. The SAW method can be expressed by the function defined in Equation (1) [14], as follows:

$${\mathrm{F}}_{\mathrm{i}}\left(\mathrm{x}\right)={\displaystyle \sum }_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{w}}_{\mathrm{j}}{\mathrm{f}}_{\mathrm{j}}\left(\mathrm{x}\right)$$

(1)

where

F_i—objective function

w_j $\in \left[0,1\right] \mathrm{and} {\displaystyle \sum }_{\mathrm{j}=1}^{\mathrm{m}}{\mathrm{w}}_{\mathrm{j}}=1$—weight index

m—number of accounted criteria

i—ith factor

j—jth criterion

Usually, the weights of individual criteria symbolize the importance of a given criterion in a particular problem. However, there is an approach that, by using criteria weights, normalizes the value of individual conditions. There are numerous methods of normalizing criteria and determining their weights w_i.

One of the most commonly used methods of normalizing the variables for evaluating a finite number of options to choose from is the method of null unitarization. In this method, to normalize and aggregate the objective function, all variables used in evaluating the individual criteria are divided into the following three classes:

• Stimulants—variables whose increase is associated with an increase in the evaluation of the phenomenon, whereas a decrease represents a decrease in the evaluation thereof.
• Destimulants—variables whose increase is associated with a decrease in the evaluation of the phenomenon, while a decrease is associated with an increase in the evaluation thereof.
• Nominants—those variables that have a certain most favorable value, and all other values, both higher and lower than the set value, worsen the evaluation of a given parameter.

3. Conducting the Decision-Making Process

The presented method of multi-criteria decision making was used to select an alternative refrigerant operating in refrigeration systems of commercial refrigeration equipment. It was assumed that the lowest value describing a given criterion is the best choice, which means that the lowest sum of the final score represents the objective function. To perform a multi-criteria evaluation of the selected refrigerants, decision-making criteria for these refrigerants were selected. The criteria selected include those that can be easily represented numerically, however, some cannot be represented numerically. The latter should be presented descriptively and then quantified to compare and evaluate the criteria against one another. Based on the analysis, it was found that the most representative way of presenting the value of criteria that cannot be represented numerically can be carried out through presentation on a five-point scale. A value of one represents the highest rating, while a value of five represents the lowest one.

Table 1. A five-step scale of criteria evaluation (own compilation based on [19]).

Quantitative Description	Qualitative Description
5	Bad
4	Not bad
3	Average
2	Good
1	Very good

explains the reasoning behind the rating scale.

A description of the selected decision-making criteria is presented below, as follows:

• The cost of purchasing 1 kg of refrigerant (EUR)—One of the most important economic and directly measurable criteria, expressed in a currency unit. With this criterion, it is assumed that, once purchased, the refrigerant does not undergo leakage.
• Safety Group [20]—The standard separates the refrigerant safety groups defined based on flammability and toxicity and determines the impacts on human health and safety, according to qualitative and toxicity criteria.

To enable optimization using unmeasured values, the qualitative criteria must be transformed into quantitative criteria. The transformation of the criterion in question is shown in

Table 2. The safety group presented qualitatively and quantitatively (own compilation based on [19,20]).

Quantitative Description		Qualitative Description
Higher flammability	A3	4
Lower flammability	A2	3
Slight flammability	A2L	2
Non-flammable	A1	1

.

• GWP—Greenhouse effect potential related to carbon dioxide, for which GWP = 1.
• Condensation pressure at 30 °C (bar)—One of the operating parameters that determines the operation of the refrigeration system, as well as the materials used and its design. The lower the operating pressures, the lower the resistance the compressor must overcome, and the fewer demanding design elements can be used.
• Evaporation pressure at −10 °C (bar)—Accordingly as for Criterion 4.

The parameters of condensation at 30 °C and evaporation at −10 °C were selected because they represent the standard operating conditions for commercial refrigeration systems, particularly in gastronomy equipment. These parameters reflect the typical operational loads that affect energy efficiency, cooling capacity, and overall system performance. Choosing these values allows for a comparison of different refrigerants under realistic working conditions, which is crucial for evaluating their efficiency and compliance with environmental and regulatory requirements. By assessing refrigerants at these operational points, this study ensures that the chosen solutions are aligned with industry standards and can meet modern sustainability and performance expectations.

Table 3. The values of the decision criteria for the selected variants (own compilation based on [19]).

		Criterion 1	Criterion 2	Criterion 3	Criterion 4	Criterion 5
		The cost of purchasing 1 kg of refrigerant (EUR) *	Safety group according to PN-EN 378 [20]	GWP (-)	Condensation pressure at 30 °C (bar)	Evaporation pressure at −10 °C (bar)
Variant 1	R452A	48	1	2140	14.9	4
Variant 2	R449A	43	1	1397	14.5	3.6
Variant 3	R455A	35	2	146	15.6	3.4
Variant 4	R290	27	4	3	10.7	3.4
Variant 5	R744	12	1	1	72	26.4

* July 2024.

summarizes the values of the five decision criteria for the five variants.

Table 3 shows the decision criteria values for multi-criteria evaluation. The evaluation values for the measurable criteria can be obtained from the manufacturer’s data. However, the rating values of the qualitative criterion were determined using the adopted rating scale presented in Table 2.

Table 4. Vector of weights of main criteria (own compilation based on [19]).

Criterion	Weight
1	0.20
2	0.25
3	0.25
4	0.15
5	0.15

shows the degrees of importance for each criterion. To meet the legal requirements and ensure user safety, the importance of the GWP coefficient and the relevance of the degree of flammability were highlighted. To minimize costs, the criterion determining the economic factor was also highlighted.

As already mentioned, the smallest input values represent the best choice. Therefore, in the next step, the transformation of the table with the values of the decision criteria is omitted, and the given values are immediately identified as the input matrix of the P solutions shown in

Table 5. Input solution matrix for multi-criteria evaluation P (own compilation based on [19]).

	48	1	2140	14.9	4
	43	1	1397	14.5	3.6
[P] =	35	2	146	15.6	3.4
	27	4	3	10.7	3.4
	12	1	1	72	26.4

.

Then, it is necessary to calculate the expressions of the normalized matrix P* shown in Table 6, according to Equation (2), as follows:

$$\left[{\mathrm{P}}_{\mathrm{ij}}^{\ast }\right]={\displaystyle \frac{{\mathrm{P}}_{\mathrm{ij}}}{\sqrt{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{P}}_{\mathrm{ij}}^2}}}$$

(2)

where

i = 1, …, m; j = 1, …, n; (m—number of variants, n—number of criteria)

Table 6. The normalized matrix P* (own compilation based on [19]).

	0.607	0.209	0.836	0.193	0.146
	0.544	0.209	0.546	0.188	0.132
[P*] =	0.443	0.417	0.057	0.202	0.124
	0.341	0.834	0.001	0.138	0.124
	0.152	0.209	0.000	0.932	0.965

Table 6. The normalized matrix P* (own compilation based on [19]).

	0.607	0.209	0.836	0.193	0.146
	0.544	0.209	0.546	0.188	0.132
[P*] =	0.443	0.417	0.057	0.202	0.124
	0.341	0.834	0.001	0.138	0.124
	0.152	0.209	0.000	0.932	0.965

The next step is to compile a matrix of normalized P* solutions with the assigned weights. The summary is shown in

Table 7. Normalized input matrix of P* solutions with their assigned weights (own compilation based on [19]).

	Criterion 1	Criterion 2	Criterion 3	Criterion 4	Criterion 5
Variant 1	0.607	0.209	0.836	0.193	0.146
Variant 2	0.544	0.209	0.546	0.188	0.132
Variant 3	0.443	0.417	0.057	0.202	0.124
Variant 4	0.341	0.834	0.001	0.138	0.124
Variant 5	0.152	0.209	0.000	0.932	0.965
Weight w	0.20	0.25	0.25	0.15	0.15

.

To obtain a solution to the problem, the value of each criterion of a given variant must be multiplied by the weight assigned to it, according to Equation (3), as follows:

$${\mathrm{V}}_{\mathrm{ij}}={\mathrm{P}}_{\mathrm{ij}}^{\ast }·{\mathrm{w}}_{\mathrm{j}}$$

(3)

where

${\mathrm{P}}_{\mathrm{ij}}^{\ast }$—the normalized value of the ith variant, jth criterion

w_ij—the weight of the ith variant, jth criterion

Table 8. Results of multivariate evaluation using the weighted-sum method (own compilation based on [19]).

	Criterion 1	Criterion 2	Criterion 3	Criterion 4	Criterion 5	Total
Variant 1	0.1214	0.0521	0.2090	0.0289	0.0219	0.4334
Variant 2	0.1088	0.0521	0.1364	0.0281	0.0197	0.3452
Variant 3	0.0885	0.1043	0.0143	0.0303	0.0186	0.2560
Variant 4	0.0683	0.2085	0.0003	0.0208	0.0186	0.3165
Variant 5	0.0304	0.0521	0.0001	0.1397	0.1447	0.3670

shows the results of the multivariate evaluation using the SAW weighted-sum method.

Carrying out a process of multivariate selection of the optimal refrigerant for refrigeration systems of gastronomy furniture is a key step in designing modern systems that must simultaneously meet the high requirements of energy efficiency, operational safety, and compliance with environmental standards. This article presents an analysis based on the multi-criteria decision-making (SAW) method, which allows a systematic comparison and evaluation of the different refrigerants used in the commercial refrigeration equipment used in gastronomy.

The first option, based on the R452A refrigerant, was found to be the least suitable for application. Its high global warming potential (GWP) and purchase costs constitute serious constraints when choosing an ecological and economical solution. Despite its low GWP, Variant 5, which uses R744 (carbon dioxide), was given a less favorable rating due to its high operating pressures, which may require specialized technical solutions and pose greater risks in handling.

Variant 2, on the other hand, using the R449A refrigerant, stands out as a well-balanced solution that has earned praise for its energy efficiency and low operating costs. The other highly rated variants are Variants 3 and 4, which are based on R455A and R290 refrigerants, respectively. R455A is the preferred choice, due to its favorable energy balance and low environmental impact.

Evaluating the process of multi-variant selection of the optimal refrigerant has helped to determine which refrigerant is the best choice for use in refrigeration furniture.

The worst rating was given to Variant 1 (R452A refrigerant), due to its high GWP coefficient, as well as its high purchase price. The second worst was Variant 5 (R744—carbon dioxide), due to its high operating pressures. The next refrigerant, already clearly deviating from the previous one in terms of the established criteria, was refrigerant R449A (Variant 2). In the top ranking, Variants 3 and 4 (R455A and R290, respectively) were ranked similarly, with Variant 5 (R455A refrigerant) receiving a better final score.

4. Discussion

The articles discussed below offer detailed approaches to multi-criteria decision making (MCDM) in the context of refrigerant selection and related technical issues. Each of these articles brings unique insights and methodologies that can be applied in a variety of industrial and research contexts.

The paper by Hontoria et al. [21] presents a methodology that identifies the most important variables affecting pressure drop and heat transfer during the condensation of various refrigerant gases in mini-channel heat exchangers. In this study, the SIMUS (Sequential Interactive Modeling for Urban Systems) method is used, which allows for a significant reduction in computational costs compared to neural networks or other modeling systems. This study pointed to 6 key variables out of 39 that best define the minimum pressure drop and maximum heat transfer. The most important variable was the saturation pressure of the refrigerant entering the condenser. This methodology not only improves the energy efficiency of refrigeration systems, but also helps to reduce the carbon footprint. When applied, this methodology can be particularly effective in designing modern and more environmentally friendly refrigeration systems.

Zarate [22] presents the results of comparative experiments conducted in France, Canada, and Brazil using a group decision support system (GDSS) called GRUS. The experiments were designed to assess the participants’ comfort when using shared and private criteria in group decision making. The results showed that there was a need to use both private and shared criteria and also indicated the difficulty with using the GDSS in the absence of a facilitator.

The study by Haqqani et al. [23] focuses on prioritizing the properties of air as a natural refrigerant using the DEMATEL methodology. The authors emphasize that properties such as ozone depletion potential and refrigerant cost are key. The results show that air, as a natural refrigerant, can be a competitive alternative, especially in the context of its low environmental impact and its widespread availability.

The paper by Besagni et al. [24] analyses the choice of refrigerants for ejector refrigeration systems using an integrated CFD (Computational Fluid Dynamics) and LPM (Lumped-Parameter Model) approach. The authors evaluated the energy performance of systems with different refrigerants, considering both fluid dynamics phenomena at the component level and the level of the entire system. The results indicate the importance of precise refrigerant selection to optimize the performance of refrigeration systems.

Jesus et al. [25] describe the development of a computer tool that assists in the decision-making process used for selecting sustainable refrigerants. The tool takes into account minimal environmental impact while ensuring adequate thermal and energy efficiency. Case studies conducted in the agro-food sector confirm the tool’s effectiveness and flexibility, enabling companies to select refrigerants with reduced or zero ozone depletion potential and global warming impact.

5. Conclusions

This article presents a multi-variant analysis of the optimal refrigerant selection for catering refrigeration systems, taking into account energy efficiency, safety of use, and compliance with environmental standards. The multi-criteria decision-making support (SAW) method was used to compare five different refrigerants, for which the following conclusions were obtained:

• R452A: Received the worst rating due to high global warming potential (GWP) and high purchase costs.
• R744 (carbon dioxide): Despite its low GWP, high operating pressures and handling risks make it not the best choice.
• R449A: Rated as a well-balanced solution, characterized by good energy efficiency and low operating costs.
• R455A: Considered the preferred choice due to its favorable energy balance and very low harmful impact on the environment.
• R290 (propane): Also highly rated, but its flammability poses a significant safety challenge, requiring additional precautions and safeguards.

The selection of the optimal refrigerant that meets the current market requirements revealed that, in addition to natural refrigerants, there are also synthetic refrigerants that can widely replace R404A. A multi-criteria analysis, carried out using appropriate decision criteria, showed that the best choice for refrigerated furniture is the R455A refrigerant, while R290, despite its favorable energy properties, must be used with special precautions, due to its flammability. The R452A refrigerant received the lowest score in this analysis.

However, it should be remembered that, despite the conclusive result of the multi-criteria analysis, the final decision regarding the selection of the optimal refrigerant for use in the refrigeration systems of refrigerated commercial gastronomy furniture belongs to the decision maker. Decision-making support programs, such as the SAW method, serve as an auxiliary tool that provides objective data and indicators, but the final decision should also consider other factors, such as specific technical conditions, user preferences, and company policies.

The application of multi-criteria analysis methods is an important step in the process of designing and selecting refrigeration technologies aimed at achieving optimal results in terms of economic, environmental, and operational performance.

In the presented paper, the innovation lies not only in the application of the simple additive weighting (SAW) method for refrigerant selection, but also in how this method is integrated with contemporary industry demands, such as sustainability and regulatory compliance. While SAW itself is a well-established and straightforward multi-criteria decision-making technique, the novel aspect of this study is its practical adaptation to the specific context of commercial cooling systems for gastronomy furniture, a sector where energy efficiency, environmental protection, and operational costs are critical.

The inclusion of refrigerants like R455A, which is a relatively new low global warming potential (GWP) synthetic refrigerant, adds to the innovative edge of this analysis. R455A is not only energy efficient, but also complies with the increasingly stringent environmental regulations, such as the European Union’s F-Gas regulations and other global agreements aimed at reducing the use of high-GWP refrigerants. By prioritizing this refrigerant, this paper anticipates future industry trends where compliance with environmental standards will be just as important as technical performance.

Moreover, compared to previous works that applied more complex decision-making frameworks, such as the fuzzy AHP model used by Seyhan et al. [26] or the hybrid DEA-TOPSIS model employed by Arabi et al. [27], this study innovatively simplifies the decision-making process while still addressing key concerns like sustainability. The use of SAW makes the tool highly accessible to refrigeration system designers and manufacturers, enabling them to make informed, cost-effective, and environmentally conscious decisions without the need for advanced computational resources or complex methodologies.

The choice of R455A also signals an innovative shift towards refrigerants that can bridge the gap between high energy efficiency and minimal environmental impact, reflecting the evolving needs of modern refrigeration systems in the catering industry. This makes this paper particularly relevant, as it not only applies existing methods in a new context, but also aligns the selection process with forward-looking technological and regulatory frameworks, supporting sustainable development goals in cooling technologies.