An integrated artificial intelligence model for efficiency assessment in pharmaceutical companies during the COVID-19 pandemic

The spread of coronavirus disease around the world has had an immense impact on most economic sectors. Yet amid the turmoil and chaos from the worldwide pandemic, one industry is thriving noticeably. The coronavirus disease is a once in a lifetime business opportunity for pharmaceutical companies. This study presents an artificial intelligence method composed of optimization and machine learning. Data envelopment analysis (DEA) is used to measure productivities and efficiencies of pharmaceutical companies during the COVID-19 pandemic using the additive model in window analysis, the BCC (Banker-Charnes-Cooper) model, and the CCR (Charnes-Cooper-Rhodes) model. The three models are assessed using DataStream financial information with research and development (R&D) investment. The results indicated the additive model's superiority in window analysis, followed by the BCC and CCR models. In the end, some of well-known data mining algorithms, based on the suggested data, have been evaluated in various tools to find the most efficient tool and algorithm.


Introduction
Over the last half-century, there has been a steady rise in the number of disasters, including pandemics, which have had considerable impacts on societies and economics [1,2] . Recently, COVID-19 showed that many countries worldwide are vulnerable to pandemics [3,4] . In addition, many health sectors, particularly pharmaceutical companies, have been impacted by the adverse consequences of COVID-19. Furthermore, during the financial turmoil and worldwide health concerns due to Covid-19, pharmaceutical companies' performance is on the line, and their impact on the fight against the disease will not be simply overlooked. In emergency situations, decision-makers often fail in immediate action to cope with the challenging conditions [5,6] . Although making an appropriate decision is urgent, the process is often too challenging [7] . So far, a wide range of decision-making tools and methods have been used to reach the most desirable decision [8][9][10][11][12][13][14][15][16][17] . However, the research in this area is scarce and has not been conducted in responding to pandemics.
As a nonparametric frontier method, data envelopment analysis (DEA) measures a particular unit's effectiveness by its gap from a train-

Literature review
Researchers attempted to measure the relative efficiency of 2492 Indian pharmaceutical companies from 1991 to 2005. They noticed positive variations in technical efficiency in large companies into which innovation has been introduced. Among them, R&D speculation has the least share in the growth of TFP [23] . In a recent study [24] , the effects of efficiency on a firm's productivity have been determined by assessing DTE by US pharmaceutical companies. The results indicated a significant positive correlation between efficiency and firm productivity. Al-Refaie et al. [25] demonstrate the application of window analysis and MPI on DEA to assess the scorching procedure's efficiency in drug manufacturing. The results also suggested ways to improve efficiency, properties can be utilized, and manufacturing can be operated efficiently. In a similar study, public pharmaceutical companies' efficiency was calculated using a fuzzy hybrid multicriteria decision-making (MCDM) approach [26,27] . An experimental study measured the efficiency of Indian pharmaceutical companies during the recession using DEA methods [28] . A similar study calculated the comparative efficiency of 37 large pharmaceutical companies from 2008 to 2013 by employing the DEA methods. They shared information from a number of foundations in different countries [29] .
Moreover, they assessed the efficiency and productivity of Indian pharmaceutical companies based on resources, stressing that assets should be applied efficiently to guarantee the sustainable development of establishments [30] . The input and output targets, slacks, and technical efficiency of 50 large pharmaceutical companies were evaluated from 2010 to 2011, suggesting that inefficiency could be attributed to unproductive decision-makers or low-quality operation [31] . A similar study evaluated the productivity and technical efficiency of 81 pharmaceutical companies [32] .
Earlier studies focused on information gathering by assessing 160 pharmaceutical companies' efficiency from 1994 to 2001, indicating significant positive earnings. They can be fully ascribed to earlier access to R&D information in target companies and a more substantial situation in which information is exchanged. They concluded that companies would fail inside productivity [33] . Another similar study attributed the value of an R&D plan to two major factors, the properties of R&D projects and pharmaceutical laboratories. They indicated a reduction in the R & D project's value by directing other R & D toward similar markets and schemes requiring a similar level of progression [34] . The relationships between efficiency, marketplace assembly, and performance were evaluated in a Nigerian pharmaceutical industry study. They should have been determined by obstructing drug import in pharmaceutical commerce [35] .
The majority of literature involving the assessment of efficiency or productivity in the pharmaceutical part has been devoted to developing countries in Asia. For example, Honjo and Haneda [36] conducted one of the earliest studies in this regard. They evaluated the efficiency of fourteen pharmaceutical companies in Japan from 1977 to 1991 based on DEA, including a single input and two outputs. You et al. [37] measured American and Korean pharmaceutical companies' efficiency by applying four different DEA-based efficiency types using regression methods. They also attempted to evaluate the effects of economies of scale, R&D speculation, and possession assembly. Mao et al. [38] employed DEA to assess the business performance of 34 pharmaceutical firms in China and calculate three inputs (i.e., administrative expenses, gross assets, and workforce size), and a single output (i.e., operating revenue). The results indicated a low overall efficiency for this Chinese sector. A similar study sought to rank Indian pharmaceutical companies by using the above method [23] .
Nevertheless, recent years have witnessed a dramatic reduction in pharmaceutical novelty productivity. The connections cannot be regulated merely by the simultaneous presence of movements above [39][40][41][42][43][44][45] . We can exploit a variety of computational and ranking techniques to address other relevant studies, including the application of the DEA and metaheuristic methods in health care [39][40][41][42][43][44][45] . This section will introduce three robust data-mining tools [46] : (I) Knime is a widely used open-source data mining, concepts, and informing graphic worktable executed by many administrations. This tool is based on the well-observed and frequently used Eclipse IDE platform, turning it into an expansion to the data-mining platform. (II) Orange is a Python-based software. This tool has a front-end graphic program design for the analysis of experimental data. Different mechanisms are referred to as widgets ranging from preprocessing, uncomplicated data conception, and subdivision assortment to the experimental assessment of predictive modeling and learning algorithms. (III) WEKA is a frequently used data mining tool with many advanced Java machine learning algorithms. It encompasses tools for association rules, classification, clustering, data preprocessing, regression, and visualization.
Different DEA models are typically used in various studies to compare, evaluate, and rank energy efficiency. Maybe some future works also utilize machine learning and optimizers to assess the efficacy of various expert systems [47][48][49][50][51][52][53][54][55][56][57][58][59]62] . These methods utilize stochastic approaches within the local and global schemes that make a soft method for multi-aspect problems [60,61] . Accordingly, the efficiency of a company can be well understood by thoroughly comparing several types of efficiency. Furthermore, pharmaceutical practitioners attach considerable importance to the comparison above as they seek to evaluate efficiency and productivity in its proper procedure. In addition, a windows analysis has been applied to compare three exclusive models with unique features, allowing the comparison of various efficient and inefficient DMUs. In the end, pharmaceutical managers can be provided with useful information to choose the best model by trying to determine the superior model. An innovation of this study is that it compares different pharmaceutical companies based on various developing countries using optimal classification algorithms and tools by simultaneously considering large laboratories. Therefore, managers may find it helpful to evaluate the superior model, eliminate irrelevant data, and conduct highly effective processes. Finally, the major contributions of the current study can be summarized as: (I) A novel combination of DEA window analysis and data mining algorithms and tools have been proposed, which will be a new concept in future research. (II) Three well-known DEA CCR, BCC, and additive models are compared with DEA SOLVER, and window analysis is applied to compare the efficiency during different periods. (III) DEA suggested inputs and outputs play the role of particular attributes for data mining tools and algorithms, and ultimately, efficient DMUs are employed for class yes and no, respectively. (IV) Finally, the highest efficient model, algorithm and company are introduced. Hence, this study's result can improve decision-makers final decisions.

Research methodology
This research proposes a relative DEA framework to assess 38 pharmaceutical companies' efficiency using the data collected from February to July 2020. Table 1 presents the following suggested inputs and outputs: CC R IO model, as follows, is used to calculate the efficiency of an assumed DMU. (1) Subject to: BCC model altered the constant return to scale (CRS) impression to variable return to scale (VRS). The BC C IO is exemplified as: Subject to: Additive model represents the extra inputs and lack of outputs at the same time. The constant return to scale (CRS) for an additive model (additive CRS) is given as: Subject to: , After adding the ∑ =1 = 1 constrain to the abovementioned additive CRS, VRS model is presented as: Subject to: ,  Attaining the maximum input and minimum output of the recommended DMUs is one of the main roles of the additive model. So, based on the Fig. 1 it is required to bring ′ and ′′ DMUs onto the efficient frontier to be efficient. In Fig. 1 , the * , must be employed to F inputs and get Fˆ' value (onto AC efficient frontier).
Therefore, to get the highest efficiency score, additive model is recommended in the current research ′ signifies radial, efficient DMU. In addition, in radial models, the decreasing quantities of both inputs and outputs have the same value. Alternatively, in non-radial models, the decreasing amount may have different values, and this is one of the advantages of non-radial models. For non-radial or additive models, two independent steps should be considered: I Decreasing the first input by 1 − = II Decreasing the second input by 2 − = ′′ Therefore, ′′ signifies the non-radial efficient DMU and Fig. 1 shows the suggested inputs and outputs.
Inputs are considered in this study, including ( = 1 , . . ., ) which is the number of employees between February-July.
( = 1 , . . ., ) which is the total assets, such as equipment, construction, and inventory cost between February-July. ℎ ( ℎ = 1 , . . ., ) which is the R&D expenditure between February-July. While outputs are suggested in this research, including ( = 1 , . . ., ) which is the company's Net operating income is based on the current results after the tax, remuneration, and devaluation between February-July. ( = 1 , . . ., ) which is the company's market value based on the current worth and expectation for the future worth between February-July. ( = 1 , . . ., ) which is the company's total revenues between February-July. Fig. 2 shows the inputs and outputs considered in this research.
Explanation of parameters and their units are presented in Table 2: Table 2 Explanation of parameters and their units.

Dimensionless parameters Units
Decision-making units Vector of input (Total assets of the company) surplus Vector of input (R&D expenditure of the company) surplus Vector of output (Net operating income of the company) shortfall Vector of output (Market value of the company) shortfall Vector of output (Total revenues of the company) shortfall Non-negative scalar (dual variables that categorize the benchmarks for inefficient parts) ℎ input (Number of employees) for ℎ DMU ℎ input (Total assets of the company) for ℎ DMU Primal model in ; Subject to: Primal model in ∶ Subject to: , ℎ , , , , Subject to: Dual proposed model in CC R IO : Subject to: Subject to: Dual proposed model in additive model VRS ∶ Subject to:

Window analysis
Window analysis was mainly recommended by [62] for efficiency evaluation. The input-oriented window analysis established by CRS are as follows [63] : Subject to: . 3. Assessment procedure of the combination of optimization with machine learning.

Table 3
Values of parameters.

Parameters Amount
For the window analysis, the following formula is related: where N represents DMUs or pharmaceutical companies, T is the time, K is the window's length, and W is the number of windows. Table 3 shows the aforementioned parameters in this study

Data mining tools and algorithms
Three well-known data mining classification algorithms have which are K-nearest neighbors' algorithm (k-NN), Decision tree and Naïve Bayes, have been applied in this study. Numeric accuracy calculation was compared according to the following formula: Finally, Fig. 3 shows the assessment procedure based on the optimization method coupling with machine learning.

Discussion in window analysis model and classification algorithms
At first, the window analysis evaluation for pharmaceutical companies was applied.
The main calculation for the basic parameters has been applied in window analysis.
Based on Eq. (70) for K calculation, the following numbers should be applied: According to Fig. 4 , the 29th and 32nd companies have the highest efficiency. While the 26th company has the second-highest efficiency. In addition, the 7th company has the lowest possible efficiency.
Based on the additive model for According to the additive model for Table 5 , companies 29 and 32 with efficiency record of 1 for all months have the highest efficiency score. Furthermore, company 35 (0.924, 0.958, 1.000, 1.000, 1.000,  1.000), and company 37 (0.612, 0.958, 1.000, 1.000, 1.000, 1.000) have  a rising efficiency report. In addition, there is no descending trend of efficiency from the beginning (February) to the end (July).
Based on the BCC model for Fig. 5 , Companies 29 and 32 with efficiency record of 1 have the highest score. In addition, company 26, with efficiency record of0.997, has the second-highest efficiency. Moreover, company 7, with efficiency record of0.894, has the lowest efficiency.
Based on the BCC model for Table 6 , companies 29 and 32, with efficiency record of 1 for all windows, have the highest record. While companies 13,15,17,19,22,26,30,34,35,36, and 37 have a rising efficiency report. In addition, company 16 has a falling efficiency report.
According to the BCC model for Table 7 , companies 29 and 32 with efficiency record of 1 for all months have the highest efficiency score. In contrast, companies 35 and 37 companies have had a rising efficiency report. In addition, there is no falling efficiency report.
Based on the CCR model for Fig. 6 , companies 29 and 32, with efficiency record of 1, have the highest score. While company 26, with efficiency record of 0.997, has the second-highest efficiency. Moreover, company 7, with efficiency record of 0.8875, has the lowest efficiency Based on the CCR model for Table 8 , companies 29 and 32, with efficiency record of1 for all windows, have the highest efficiency. While According to the CCR model for Table 9 , companies 29 and 32, with efficiency record of 1 for all months, have the highest efficiency score. While companies 35 and 37 have a rising efficiency report. Moreover, there is no falling efficiency report Therefore, based on the abovementioned results: The additive model is the best-suggested model, and companies' number 29 and 32 get the best results. On the other hand, company number 7 get the minimum efficiency record Table 3 . Table 10 represents the accuracy of data mining algorithms. According to Table 10: • WEKA: Received maximum efficiency prediction for decision tree.

. Classification algorithms
• Orange: Received maximum efficiency prediction for Naïve Bayes.
• Finally, all the proposed tools get the highest efficiency rank in a particular algorithm.  . 6. Average of total efficiency for the CCR model.

Conclusion
This study described the operation procedure of companies in the presence of similar companies during the first six months of the COVID-19 pandemic. Companies with higher scores may succeed in improving their efficiency. A significant positive relationship was indicated between available information and available data. The status quo of any firm can be evaluated by measuring its efficiency. Thus, inefficient companies can refer to their efficient counterparts to be able to improve their efficiency. The additive model outperformed BBC and CCR models in terms of positive effects on efficiency. It is particularly advantageous because it reduces input and output values at the same time. A practitioner may succeed in comparing uncertain cases in terms of efficiency and, thus, instructing by resorting to the geometric mean, outcomes, predictions, and the proposed approach derived from windows and period in window analysis. The application of the Malmquist Productivity Index (MPI) and the comparison of efficiencies will prove useful in future studies. Moreover, the final comparison can be conducted intriguingly by utilizing fuzzy and random data for window analysis. The proposed window analysis technique is based on a moving average, can be em-    ployed to determine per efficiency trends with the passage of time. Thus, the manager can take advantage of the outcomes and predictions to obtain greater relative efficiency. They can also compare different companies based on efficiency in the present year and over the past several years. Ultimately, they can exploit optimal machine learning algorithms and tools to select the right choice.

Declaration of Competing Interest
The authors declare no conflict of interest.