An integrated multi-criteria decision-making framework for a medical device selection in the healthcare industry

Abstract Medical devices used in healthcare organizations are costly, and the process of selecting these devices requires considering multiple criteria such as effectiveness and ease of use. Careful selection of these devices is daunting since it entails the evaluation of various measures. This research investigates the selection process of the same type of medical devices, especially when alternatives are available, and the organization needs to make a good selection. A Multi-Criteria Decision-Making (MCDM) framework based on the integration of the Analytical Hierarchy Process (AHP) and ELimination Et Choice Translating Reality (ELECTRE) method is developed. The framework model includes 10 criteria, which are selected based on real-life inputs from professional physicians. Seven Ultrasound machines (referred to as alternatives) are evaluated using the developed framework. A case study is conducted on the best selection practice of an Ultrasound machine in a gynecology clinic based in the Kingdom of Jordan. Results revealed that the best and worst alternatives of ultrasound machines are identified and compared with all other options.

ABOUT THE AUTHOR Mohammad A. Shbool is an assistant professor of industrial engineering at The University of Jordan in Amman, Jordan. He received his Ph.D. in industrial engineering from the University of Arkansas -Fayetteville, USA, in 2016. He mainly teaches Simulation, Logistic Engineering & Supply Chain Management, and Engineering Statistics classes for IE students. Dr. Shbool is mainly interested in doing research in Simulation Modeling (discrete, Agent-based, & system dynamics), multi-criteria decision analysis, and Machine Learning applied to healthcare and manufacturing systems. He published a journal article in healthcare decision-making entitled "Decision Making Framework for Evaluating Physicians Preference Items Using Multi-Objective Decision Analysis Principles." Dr. Shbool is an EFQM (European Foundation for Quality Management) certified, and he is a member of both the IISE Institution and Alpha Pi Mu American honor society. Many MCDM techniques have been successfully utilized in the era of decision-making as selection and ranking problems. The integration between two or more techniques has also been investigated and implemented in different fields. However, the current work provides a hybrid framework that integrates both AHP and ELECTRE techniques to select medical devices such as Ultrasound Machines efficiently. This paper details the decision-making process in conjunction with physicians' input and expertise to validate the model and generate the best final ranking of high-quality different specifications ultrasound machines in Jordan. The hybrid approach can provide physicians, hospitals, and healthcare supply chain professionals with a generic decisionmaking tool that can be used to select medical devices.

PUBLIC INTEREST STATEMENT
Many MCDM techniques have been successfully utilized in the era of decision-making as selection and ranking problems. The integration between two or more techniques has also been investigated and implemented in different fields. However, the current work provides a hybrid framework that integrates both AHP and ELECTRE techniques to select medical devices such as Ultrasound Machines efficiently. This paper details the decision-making process in conjunction with physicians' input and expertise to validate the model and generate the best final ranking of high-quality different specifications ultrasound machines in Jordan. The hybrid approach can provide physicians, hospitals, and healthcare supply chain professionals with a generic decisionmaking tool that can be used to select medical devices. framework. A case study is conducted on the best selection practice of an Ultrasound machine in a gynecology clinic based in the Kingdom of Jordan. Results revealed that the best and worst alternatives of ultrasound machines are identified and compared with all other options.

Introduction
In the last and current centuries, the global economy, pushed by innovations and progress in technology, has shown remarkable growth in the medical devices industry, which resulted in high competency among companies and manufacturers. Diversity of brands of products, different quality levels, and prices have made it difficult for customers to purchase a product. Buyers have always been facing the dilemma of selecting the best alternative at a reasonable price. With multiple criteria to be considered when alternatives exist, making a choice becomes complicated. This sort of problem complexity comes from the conflicting objectives, implying the need for a systematic procedure that tackles decision problems, guaranteeing the least amount of after-decision regrets. Therefore, Multi-Criteria Decision-Making (MCDM) methods have emerged to support decisions and enhance the selected solution's reliability and credibility (Marsh et al., 2017).
In the healthcare industry, systems have always been an area of great interest in research and development. This interest attributes to the high expenditure of this industry and lack of performance measures compared to other leading industries such as retail and manufacturing. Authors in (Shbool, 2016) focused on healthcare expenditures and causes of physicians' preferences in medical item selection. Multi-objective decision-making on physicians' preference items based on value modeling principles is investigated by (Shbool & Rossetti, 2017), and an extension of the model is provided in (Shbool & Rossetti, 2020).
One of the problems that healthcare providers face is the selection of medical devices. The decisionmaker, either an individual or a group, needs to decide which device is the best to purchase. The diversity of alternatives (models of the same functional equipment) available from manufacturers imposes a burden on the shoulders of decision-makers to decide the most suitable device. This problem becomes complex when many criteria should be considered when making such a decision, in which confliction of criteria is the central theme. This problem is significant for two main reasons; first, selecting items based on a structured method can cut costs. Second, the right decision may increase the acquisition rate of patients due to excellent device characteristics. Therefore, healthcare providers must spend more effort making accurate decisions, which should be based on a structured methodology, that otherwise would increase the risk of after-decision regrets. Therefore, this research considers selecting a medical device out of many similar alternatives as a multi-criteria decision-making problem. This problem is to identify the best selection of Ultrasound device alternative out of many other competitive options of the same product. This paper aims to develop an MCDM framework that combines both the Analytical Hierarchy Process (AHP) and ELimination Et Choice Translating Reality (ELECTRE) method for the best selection practice of a medical device.
The main contributions of this study can be summarized as follows: (1) To propose an MCDM framework based on integrating AHP and ELECTRE methods for best practice in selecting medical devices subject to conflict criteria.
(2) To formulate new relevant criteria necessary to the selection process of medical devices with professional physicians working in this field.
An illustration of selecting an Ultrasound device in a gynecology clinic will be presented to provide a complete structure of an MCDM framework.

Previous work
In this section, applications of MCDM techniques, including AHP, ELECTRE, and their hybrids in different healthcare areas, particularly in resource selection, are presented and categorized based on the environment type (deterministic and uncertain/vague).
Multi-Criteria Decision Analysis (MCDA) methods were reviewed by (Glaize et al., 2019) to provide practical insights on how MCDA methods are applied in different healthcare areas in deterministic environments. Glaize et al. (2019) provided a structure for and practical insights on how MCDA methods are applied in different healthcare areas, including medical device selection. (Ivlev et al., 2015) presented a new MCDM model for medical device selection under conditions of uncertainty. Ivlev et al. (2016) identified the most suitable Magnetic Resonance Imaging (MRI) system for regional hospitals in the Czech Republic. They defined the most appropriate MCDA model for medical equipment selection by comparing various MCDA methods such as AHP and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE II), and Simple Additive Weighting (SAW) method.
The AHP technique as one of the MCDA tools was used in a novel evaluation framework to select the optimal medical device by overcoming the limitations of previously confined assessments to the medical device cycle and the purpose of the specific assessment (Park et al., 2019). It has been shown that AHP can also be used in assessing selected medical devices and materials for grants by the Korean Ministry of Health and Welfare (Cho & Kim, 2003). Considering the time dependence of criteria, Improta et al. (2019) developed dynamic AHP by considering the evaluations associated with criteria as a function of time. They developed a system dynamic model for each criterion to capture the time behavior of the criteria. They implemented the proposed dynamic AHP framework in Health Technology Assessment. It is worth mentioning that the AHP was developed by (Saaty, 1980) based on the pairwise comparison of the relative importance of the on-hand criteria.
The ELECTRE as an outranking MCDA method that uses a weighted sum technique of multicriteria based on agreement and disagreement indexes of the pairwise comparisons on each criterion has also been used. This method was initially introduced by (Roy, 1968), which was then analyzed and tailored by other researchers to other versions, including the ELECTRE method, ELECTRE I and subsequent extensions II, III, IV, and IS are outranking methods. These methods were developed to solve choice problems (Ishizaka & Nemery, 2013). A comprehensive review of the literature of ELECTRE methods and applications in various areas was made by (Govindan & Jepsen, 2016). Many studies applied the ELECTRE method in the research, which indicates this method's effectiveness. Examples of using ELECTRE in different areas are found in (Bari & Leung, 2007) and (Afshari et al., 2010). The ELECTRE methods have been successfully implemented in solving problems in various areas such as environmental management, energy, water management, transportation, military, and other topics (Figueira et al., 2005).
Under uncertain environments, MCDA tools were also used in medical device selection, including but not limited to (Buyukozkan & Gocer, 2019), who presented a novel approach for evaluating the smart medical device selection process in an uncertain decision environment. The intuitionistic fuzzy Choquet integral (IFCI) approach was applied to treat the uncertainty and vagueness. A fuzzy MCDM approach was proposed by (Tadic et al., 2014) to evaluate one kind of medical device supplier. A novel approach, including Neutrosophic with TOPSIS, was proposed by (Abdel-Basset et al., 2019) to estimate the smart medical devices (SMDs) selection process in a vague decision environment. Frazão et al. (2018) concluded that AHP and fuzzy logic dominate other methods in the literature. This conclusion was also confirmed by (IVLEV et al., 2014), who used the AHP approach to select sizeable medical equipment in resource-limited settings. Carnero and Gomez (2019) used both the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) and FAHP (Fuzzy AHP) techniques for the optimal selection of medical gas supply devices. Both AHP and fuzzy VIKOR (VIekriterijumsko KOmpromisno Rangiranje) methods were utilized by (Emec et al., 2019) for the best selection of protein isolation devices used in a scientific research laboratory. The VIKOR-based fuzzy MCDM method was used by (Liu et al., 2013) to assess alternatives available for medical waste disposal. A hybrid fuzzy MCDM approach composed of the fuzzy AHP method and the fuzzy TOPSIS method was used for medical device manufacturer's selection (Lee et al., 2017). A multi-objective decision-making approach based on fuzzy AHP and fuzzy TOPSIS under a fuzzy multi-criteria decision-making environment was used to improve the supplier selection process in the healthcare sector (Goh et al., 2018).
Hybrid MCDM techniques in different environments were developed for medical device selection. An effective and efficient MCDM tool consisted of three different methods of AHP, Multi-Attribute Range Evaluations (MARE), and ELECTRE III was suggested to address equipment selection problems (Hodgett, 2016). Budak et al. (2016) proposed integrated TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) with an intuitionistic fuzzy set to select the appropriate Real-Time Location System technology for a hospital-based multi-criteria structure. A hybrid model consisting of the Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method was developed by Barrios et al. (2016) to appropriate medical equipment. HMCDM (Hybrid MCDCM) methods were developed, mixing AHP, TOPSIS, ELECTRE, GRA (Grey Relational Analysis), and SAW methods for selecting the most suitable supplier in the healthcare sector (Akcan & Güldeş, 2019).

Figure 1. Schematic view of the hybrid framework.
Moreover, AHP was also applied in modeling and solving many other real-life problems, including but not limited to assessing the energy credits to enhance the Egyptian Green Pyramid rating system. AHP provided a logical framework to determine the relative weight for the energy sector of each system (Abdel Aleem et al., 2015). A framework was proposed by (Elbasuony et al., 2018) to assess the overall PQ performance of different hybrid smart grid-connected DG systems, considering different interface-bus types and PQ criteria in various scenarios under normal operating conditions and a three-phase fault condition. A weighted sum strategy using the analytic hierarchy process (AHP) was used to convert the multi-objective problem into a normalized single-objective one to find the best solution of an Economic Technical Environmental Dispatch (ETED) problem (Rawa et al., 2021). (Abbas et al., 2018) developed a fuzzy knowledge-based model to select the best container storage location in a container yard with uncertain container departure times.
No previous work was found in the literature that used MCDM models, including both AHP and ELECTRE methods, to optimize the selection process of medical devices subject to conflicting criteria. Hence, this work aims to provide a structured hybrid framework for selecting the medical devices using both the AHP and ELECTRE methods together on a real-life medical device selection problem. AHP was used in this research to obtain criteria weights, while ELECTRE was used to select the best alternative based on their performance concerning the weighted criteria.

Research methodology
During recent decades, drastic medical devices and technological advancement raised the bar for aliveness, which is also considered a driver for increased healthcare expenditure (Willemé & Dumont, 2015). Healthcare problems have become more complex. Therefore, there is a solid need to elevate the decision-making process by incorporating Multi-Criteria Decision analytical approaches into the healthcare domain.
As cited before, this work's decision-making framework targets medical device selection in healthcare clinics. The problem is examined as a multi-criteria decision-making problem, where criteria were elicited from physicians who use such devices. The ELECTRE method will be explained step by step as summarized in (Yücel & Görener, 2016) and (Abdolazimi et al., 2015). Figure 1 is a schematic view of the developed methodology. The whole framework is explained in the following subsection in two parts, AHP and ELECTRE. Each step includes necessary formulas as well as corresponding calculations. The AHP method itself will be implemented to derive weights of the criteria, and consequently, it will be terminated at some point. When compromise is needed (importance is neither one of two defined degrees)

Reciprocals of the above nonzero
The judgment value corresponds to the reverse relationship If v is the judgment value when i is compared to j, then 1/v is the judgment value when j is compared to i.
Constructing a Hierarchical Structure is considered the core step. In this first step, the problem is decomposed into different levels to build the hierarchical structure. The core function of the hierarchy is the criteria.

The AHP steps
The first stage is to solicit weights of the criteria selected for evaluation; AHP was utilized in this study for this purpose. In the AHP part, the pairwise comparison will be conducted in the second step by stakeholders. Pairwise comparison is the heart of the AHP method to develop the judgment matrix. The criteria are compared two at a time by specifying a relative importance/preference on a scale of 1 to 9. Different judgment scales have been reviewed by (Ishizaka & Labib, 2011) besides the original linear scale proposed by (Saaty, 1980). The linear scale moderately keeps a balance between the two outputs of AHP, consistency of judicial decisions, and priority allocation. Pairwise comparison is either subjective based on stakeholders'/experts'/decision-makers' opinions and knowledge or objective based on quantitative measures. The judgment scale used in this research is shown in Table 1.
In general, for n criteria, the pairwise comparisons are shown in a square and reciprocal (n × n) matrix as shown in Equation (1) (Gorener, 2012). A total of n nÀ 1 ð Þ 2 comparisons are to be carried out, representing how each criterion (listed as row heading) is essentially relative to each of the remaining criteria (listed as column heading).
From the pairwise comparison matrix, the normalized relative weights are estimated in step 3 by finding the sum of each column S j (column j) and dividing each relative weight (a ij ) by the sum of that column; see Equation (2) (Saaty & Tran, 2007) below.
Relative weight vector (w) can be set up from the normalized principal Eigenvector (a.k.a priority vector); that is, the first criterion's weight is simply the average of normalized weights. Relative weights for the ten criteria were calculated according to Equation (3) (Saaty & Tran, 2007). Estimating the Input Consistency Index is the fourth step. In this step, the whole process is based on judgments of priorities by pairwise comparisons. For example, if physicians preferred criterion 1 over 2 (C 1 > C 2 ) And criterion 2 over 3 (C 2 > C 3 ) and they have been asked to compare criterion 1 with 3, the expected answer should be (C 1 > C 3 ). This logic entails consistency, and it emerges from the transitive property. Measuring input judgments' consistency is based on the principal Eigenvalue (λ max ) that can be calculated using Equation (4) (Gorener, 2012).

The ELECTRE steps
The second stage in the framework evaluates and ranks alternatives based on criteria weights; ELECTRE was utilized. In the ELECTRE part, Metrics (value measures) will be defined in step 5. This scale establishes the range of the valuation measure that determines each criterion for scoring in the decision matrix. It is like a rubric that describes what each score value means on this value measure on a scale explicitly defined for this value measure. Determining alternatives that should undergo the evaluation process is done in step 6.
The decision matrix will be formulated in step 7. It presents the criteria (n) as columns and (m) rows for the alternatives, with cells representing the alternatives scoring on the criteria. The general matrix represents the standard decision matrix that determines the process baseline in Equation (6) (Akcan & Güldeş, 2019;Supraja & Kousalya, 2016;Yücel & Görener, 2016).
Where v is the column weighted normalized value for all alternatives on criterion j, and x is the normalized column in the decision matrix on criterion j.
Determining the Concordance Sets is step 10. This step compares each pair of the alternatives in each criterion using the weighted normalized matrix. This process is done as follows: for every possible pair of alternatives A p and A q p; q ¼ 1 . . . m; and p�q ð Þ, if alternative p is better than or equal to q on that specific criterion, it is listed under the concordance set as follows in Equation (9) (Akcan & Güldeş, 2019;Supraja & Kousalya, 2016;Yücel & Görener, 2016).
where v pj is the weighted normalized score of alternative p on criterion j Thus, C(p, q) represents the set of attributes where A p is better than or equal to A q A p ! A q À � . After determining the concordance set, the concordance index C pq is generated by adding weights for the criteria in the concordance set according to Equation (10) (Akcan & Güldeş, 2019;Supraja & Kousalya, 2016;Yücel & Görener, 2016).
Determining the Discordance Sets will be in step 11. The discordance set, D(p,q), is the collection of remaining criteria not included in the concordance set, i.e., D p; q ð Þ ¼ j; "j�j � f g. In other words, all criteria for which A p is worse than A q compose D (p, q): The degree of disagreement in A p ! A q À � is called the discordance index D pq and can be defined using Equation (12) (Supraja & Kousalya, 2016;Yücel & Görener, 2016).
Outranking Relationships will be determined in step 12. Every pair is compared, and the outranking relationships are built according to Equation (14) (Supraja & Kousalya, 2016;Yücel & Görener, 2016). For example, A 1 beats A 3 based on the concordance index, while based on the discordance, it does not so that the A 1 A 3 cell will be indicated with "False." The full ranking list of all alternatives is determined in step 13 by calculating net concordance and discordance matrices, Equations (15) and (16) (Supraja & Kousalya, 2016;Yücel & Görener, 2016). Then, sort the alternatives in descending order in terms of the net concordance, and another list sorted in ascending order in terms of the net discordance.

Case study
The on-hand problem is selecting a medical device in general and in the specific Ultrasound device. The goal will be to choose the device that outranks all other devices on the listed criteria. This goal leads to the next (first) step; defining criteria based on which the devices will be evaluated and compared.
The researchers suggested the criteria based on some readings and, more importantly, from 20 physicians after visiting their gynecology clinics based in Jordan. The physicians agreed on some of the proposed criteria and added them to the list, which reached ten criteria. They were able to provide information about seven Ultrasound Machines for this case study. Table 3 summarizes the physicians' list who participated in this study based on their name's initials (Coded for data privacy purposes).
Seven ultrasound machines are mainly used in this paper. These machines used in Jordan are coded for legal declaration issues. The codes of these machines are GV, MM, AP, SS, GL, ST, and MD. From now on, alternatives will be referred to as A i and criteria as C j for simplicity. For example, A 1 is the first ultrasound machine brand (GV), and C 1 is the "Imaging" criterion.  A list of 10 criteria, shown in Table 4 (C 1 -C 10 ), were defined using the opinion and assessment of the professional physicians who took part in this study. Detailed explanations on how to build a value hierarchy and the process of building value measures (step 5) can be found in (Parnell et al., 2013). In this work, criteria listing was done in two phases; in the first phase, physicians were asked about relevant criteria when selecting the device. The second phase was to get consensus on any irrelevant criterion or merge any two criteria due to dependency. By applying Step 1, the hierarchical structure was constructed.
The judgment matrix was obtained by applying Step 2. The criteria are compared two at a time by specifying a relative importance/preference on a scale of 1 to 9. In our problem, an aggregate of 10 criteria was considered resulting in 45 comparisons. Relative weights were calculated by applying Step 3; Table 5 shows the final results. Input consistency index was measured as in Step 4. In our medical devices' selection problem, λ max ¼ 10:3, Thus CI ¼ 10:38À 10 10À 1 ¼ 0:0381 ! CR ¼ 0:0381 1:49 ¼ 2:55% Which is < 10%, Thus physicians' subjective judgments of the 10 criteria preferences are consistent.

After applying
Step 5, a detailed listing of criteria and their value measures with corresponding scales rubrics were obtained, as shown in Table 4. For example, criterion C1 (Imaging) has a scale of 5 value measures on which each option will be categorized. Suppose a Gynecology has a device X with 2D colored imaging capability; it should be assigned a value of 2 regarding this criterion. The physicians determined these scales.
The framework of this research was illustrated with an example of medical devices, precisely Ultrasound machines. By applying Step 6, Seven Ultrasound functional equivalent devices were proposed as alternatives for evaluation.
The Decisions matrix, the result of step 7, was obtained by scoring the seven Ultrasound devices on the ten criteria. Scores were gathered from the participated physicians and organized in a decision matrix, as shown in Table 6.
Step 8 was applied to obtain the Normalized decision matrix; results are shown in Table 7.
The weighted normalized decision matrix was obtained by applying Step 9; each alternative's normalized score on each criterion was multiplied by that criterion weight. Resulted matrix is shown in Table 8. Concordance sets C(p, q), as shown in Table 9, were obtained by applying Step 10. Every possible pair is listed with corresponding criteria for which the predecessor alternative dominates the successor. The sum of weights in the concordance sets is referred to as the concordance index. Concordance indices are shown in Table 10. Table 10 represent the alternatives concordance index that is greater than the average concordance index. From Table 10, � C ¼ 0:5966 and highlighted cells indicate that C pq � C.

Highlighted cells in
In Step 11, the discordance set, D(p,q), was determined by determining all criteria for which A p is worse than A p . The discordance indexes D pq , which represent the degree of disagreement in Table 11. The average discordance value is used to determine outranking sets, i.e., the alternatives for which the discordance index is less than average.
Outranking relationships are determined by applying Step 12. Table 12 shows the result outranking relations, where "True" means that the alternative in the leftmost column outranks the corresponding alternative in the top row. Alternative p outranks alternative p if and only if their concordance index is greater than average and discordance index is greater than average. For example, A 4 dominates A 1 based on both concordance as well as discordance, so the A 4 A 1 cell is indicated as "TRUE." The outranking relationships matrix shown in Table 12 is used to build the outranking diagram depicted in Figure 2. Each "True" is represented by an arrow starting from the alternative in the leftmost column, pointing to the top row's alternative. For example, an arrow should be drawn from A 1 to A 5 , meaning that A 1 outperforms A 5 . In cases where no one outranks the other in both concordance and discordance, i.e., False for A p →A q and False for A q →A p as well, then no arrow will be drawn between this pair. For example, neither A 1 outperforms A 3 nor A 3 outperforms A 1 .
The dominant alternative that outranks all other alternatives is the best selection, which is, in our case, the Ultrasound device alternative A4. The least preferable alternative is alternative A5. These two devices' brands are the most common ultrasound machines used by physicians in gynecologist clinics in Jordan. A full ranking of all alternatives was done, as seen in the next step.

Discussion
Healthcare providers always face the hurdle of selecting a medical device that fulfills their expectations on several conflicting constraints. Still, making decisions based on just subjective evaluations may lead to a non-optimal choice. The net result summarized in Table 13 shows that alternative 4 is the dominating one since it outranks every other alternative in terms of concordance and discordance. The ranking is based on concordance and discordance, as can be seen, that 1 st , 3 rd , 5 th , 6 th , and seven th ranks agreed upon by concordance and discordance. This result gives the decision-maker confidence when selecting the best alternative and leaving the worst selection.
The resulting ranking shows that physicians, based on their criteria selection, used A7 instead of A4. Implementing structured multi-criteria techniques helped in the manipulation of the criteria confliction. The result was discussed with physicians; they showed interest and appreciation for the framework and agreed upon it. We consider this as a validation of the model.

Comparison study
In order to establish the effectiveness of this hybrid framework compared with AHP, a comparison study is essential to justify the superiority of the hybrid framework compared with AHP. This study also helps in validating the performance of the provided solution of the hybrid framework. Table 14 presents the comparison study results highlighting the effectiveness of each used method individually and combined.  The results show that the best alternative is A4 based on AHP and the hybrid framework method. The two methods also agreed on the last three alternatives. This outcome validates the hybrid framework outputs in terms of the ranking of the alternatives. However, the hybrid framework provided a more detailed ranking on the 2 nd , 3 rd , and 4 th positions, and hence, the alternatives ranking was different both methods. This shows the strength of the hybrid framework in guiding more informed decisions represented by the achieved alternatives ranking. The provided alternatives were discussed with the related physicians who participated in this study. They adviced the alternatives provided by the Hybrid approach are more applicable in the selection process of medical devices.

Conclusion and future work
In this research, a decision framework for medical device selection was illustrated through a specific example on Ultrasound machines. Professional physicians participated in this study to build the model and provide input. Two MCDM techniques were employed in one framework to provide a final ranking of the seven alternatives based on ten criteria accurately determined for Ultrasound machines. The full ranking of the candidate alternatives enables buyers (Physicians or healthcare organizations) to induce a better objective decision. The physicians who took part in this study were asked which device they already have and why; three of them said they have the alternative 7 (A7) in the original list (Unranked). This device had the third rank agreed upon by the concordance as well as discordance sets. Physicians' justification for this choice is that they decided based on their subject evaluations as another kind of decision.
This research was vital for two core reasons; first, it put already presented MCDM techniques in the healthcare context and implements them to the medical devices' selection theme. Second, this research could be used as a reference tutorial on applying a detailed explanation to other similar problems.
However, the limitation of this method is that it needs a large amount of data to identify the best consistent weights and subsequently reduce the error in estimation and hence the after decision-making regrets. In addition, the applicability and usability of this method need to involve a proper sample size and type of physicians that should be identified using statistical sampling techniques to obtain consistent opinions about the achieved alternatives and their best weights values. The proposed framework is applicable only for deterministic environments, making this the main drawback if a vague environment is encountered in terms of medical device selection.
Future work requires involving a representative sample of physicians to reflect fair opinions regarding the criteria used in medical device selection. Other ELECTRE methods (II, III) could be applied for other alternative selection comparison purposes from the technique perspective. The researchers suggest expanding current research on medical device selection by adopting fuzziness in the proposed framework to capture the uncertainty that might be inherited in some of the medical selection problem features. As well, different weights estimation methods could be employed.