Multiattribute Decision-Making of TQM Performance of Hospitals Using TQM Digraphs

Total quality management (TQM) is a dynamic philosophy that incorporates gradual and uninterrupted improvements. The total quality is accomplished if all the desired goals including quality of product, reputation in market, services, low cost of product, employee and customer satisfaction, optimum utilization of resources, work environment, and so on are attained. As far as the Pakistani perspective is concerned, TQM as a strategic tool is not appropriately used to optimize its performance. Public healthcare in Pakistan is one of the most ignored sectors with regard to its service quality implementation and delivery. The public sector hospitals are one of the major primary healthcare providers, but the facilities they provide do not meet the desired requirement. This study addresses six TQM attributes to analyze the TQM performance of various public sector teaching hospitals in the province Punjab of Pakistan. The data was obtained from medical experts. The TQM performance to study the behavior of TQM implementation in hospitals is evaluated using TQM digraphs. The hospitals are ranked according to the TQM performance index, which is obtained from TQM digraphs. The technique to find the most effective attribute for a hospital is also proposed. The TQM digraph approach not only focuses on the significance of attributes independently but also incorporates the relative importance of one attribute over another. Also, this approach is very flexible that can incorporate new attributes and market variation so that continuous improvement may be possible. Moreover, the results obtained in this approach are not limited to beneficial for benchmarking of teaching hospitals in Punjab on the TQM basis, but these can also help indicate the particular attribute that is more needed to be improved for a particular hospital to increase its TQM performance.


Introduction
Health is in fact a basic requirement for any society and can be considered as the backbone of economic stability. Literature acknowledges the fact that improvement in health status is considered necessary for improving human welfare and human capital. Health not only enhances workers' productivity by increasing their physical capabilities but also enhances their mental capacities such as their reasoning and cognitive abilities that in turn play a pivotal role in sustainable economic growth [1]. Good health depends on a strong infrastructure of the healthcare system. For many underdeveloped countries including Pakistan, the healthcare issue is not considered just to overcome diseases, but it becomes more crucial and challenging in terms of e ciency and performance quality due to their limited resources.

Healthcare in Pakistan.
Healthcare expenditure in Pakistan is increasing signi cantly and turning into big investments for escalation of quality of healthcare services across the country. Pakistan's national health policymakers are keen to devise and review the health services structure at di erent levels in changing environments and time frames. e objective behind is to attain and sustain the optimal level of e ciency and relative productivity in the delivery of healthcare services. Healthcare expenditure in Pakistan is increasing signi cantly and turning into big investments for escalation of quality of healthcare services across the country. e healthcare system of Pakistan comprises public and private health systems. Private hospitals are providing world-standard healthcare system owing to their huge resources and facilities. e private health sector comprises non-governmental organizations (NGOs), charitable organizations, trusts, and corporate health sectors. e increase in the private healthcare system is due to the massive difference between the contribution of health services of public and private health sectors. Most of the patients prefer to visit private hospitals because public hospitals cannot fulfill the criteria of services [2]. e inefficiency of the public health sector provides a chance for the private health sector to expand healthcare services to commercialization and commoditization of the medical sector [3]. According to the Economic Survey of Pakistan (2018-2019), only 1.1% of its GDP is allocated for healthcare expenditures by the government. e district health system under the district government is now liable for planning, development, and management along with the implementation of healthcare delivery from DHQ hospitals right down to the outreach programs. Despite the detailed and complex network of healthcare delivery, Pakistan has fallen short to bring about an enhancement in health status, especially of rural population. e health system of Pakistan is described by insufficient expenditure, low-quality service, and poor utilization of services. e three most popular reasons for these are unavailable facilities, non-availability of medicines, and low-skilled staff. In the public sector, 947 hospitals, 4,800 dispensaries, and 1,084 MCH center are mostly located in urban and semiurban areas; on the other hand, 581 RHCs and 5,798 BHUs are providing services to the population of rural areas. e total number of availability of beds is approximately 101,047. e inadequate number of health workers in Pakistan is summarized in Table 1 (Economic Survey of Pakistan (2018-2019).

Healthcare in Punjab.
Among the other provinces of Pakistan, Punjab has achieved substantial progress in the field of health. Punjab has become a model for other provinces in the context of low maternal and infant rate and low birth and death rate. e Punjab province comprises 2,455 basic health units (BHUs) and 293 rural health centers (RHCs) in an open area. ere are 42 public sector teaching hospitals in 13 districts (9 divisions) of Punjab, and among 42, 3 are purely dental hospitals. e detailed listing of the remaining 39 hospitals is given in Table 2.

Total Quality Management (TQM)
Total quality management (TQM) is an effective philosophy that integrates subtle and continuous development. It can be seen as a corporate-level philosophy such that each employee must focus his input on improving the commercial movements of a company [4]. e total quality is accomplished if all the desired goals including quality of product, process, reputation in market, services, material, low cost of product, employee satisfaction, policies, customer satisfaction, optimum utilization of resources, work environment and functional area, and so on of an organization are attained.
ese objectives can be obtained by planning, setting targets, affecting agents, improving support systems, applying different techniques, considering human factors, using modern tools, and so on. Mersha [5] emphasized that most crucial and needed objective, i.e., customer satisfaction, can be attained through continuous improvement, maximum participation and involvement of all stakeholders of the company. According to Dale and Cooper [6], TQM measures must include the participation of every person in the organization, teamwork, customer satisfaction, and training programs. Taveiraa et al. [7] suggested that the efficiency of TQM in an organization might depend on the human factor. Motivated by its inspiring outcomes in different service sectors as well as in manufacturing organizations, TQM is also applied in healthcare organizations. Short and Rahim [8] suggested that before the implementation of TQM in any healthcare organization, the rules, procedures, and structures need to be redefined. Another study by Muhhurrum et al. [9] indicated that patients' needs must be taken into account while implementing TQM. e study of Indian hospitals emphasized that cultural, political leadership, and attitude of the healthcare professionals are obstacles to the implementation of TQM, and these factors need to be resolved [10]. Several attempts have been made to implement TQM factors in the healthcare system across the world, but almost no significant attempt has been done so far in the Pakistani healthcare system [11,12]. Irfan et al. ( , 2011a emphasized that private hospitals are providing a better quality of healthcare services in contrast to public sector hospitals. Irfan et al. [13] conducted a study on Pakistani public sector hospitals and stated that the wellmannered implementation of TQM can significantly increase the productivity of processes in Pakistani hospitals. e literature indicates that management practices and their basic principle affect directly to the patients' satisfaction [14]. Talib et al. [15] employed four TQM practices in the service environment, and in [16], it is recognized that these TQM practices are among the best practices for effective implementation of TQM in both service and manufacturing industries. Yasin et al. [17] studied the effectiveness of the implementation of TQM practices in service organizations. Now, it is in dire need of Pakistani health policymakers to implement TQM practices in the Pakistani healthcare system.
Various techniques and models are used for this study, but graph-theoretic approach being a mathematical model produces the scientific and most accurate results, and generalization of these results in different areas of service sectors is extremely helpful. Moreover, this approach is very flexible and can incorporate new attributes and market variations so that continuous improvement may be possible. According to Baykasoglu [18], the most promising feature of this technique is its interfacing behavior and its capability to represent hierarchical models in a better way. He also revealed the applications of GTA in decision-making problems. Grover et al. [19,20] used the graph-theoretic approach for industry evaluation and to investigate the consequences of human factors in the implementation of TQM. Kulkarni [21] also used this technique for performance evaluation of Indian industries. Anand and Bahinipati [22] used the graph-theoretic approach to measure horizontal collaboration intensity in the supply chain. Singh et al. [23] used this graph-theoretic approach in assessing the quality of manufacturing organizations. Jangra et al. [24] used GTA for the performance evaluation of carbide compacting die. e same technique is also used to evaluate the machinability of tungsten carbide composite with wire EDM [25]. e multicriteria decision-making approach in quality assessment is discussed in [26][27][28][29][30]. Different fuzzy graph-theoretic models are also used in several decisionmaking problems [31][32][33][34][35][36][37]. e aim of this study is to evaluate the TQM performance of public sector hospitals of province Punjab of Pakistan using graph-theoretic technique.

TQM Attributes
e TQM attributes that are considered in the performance evaluation of the public sector hospitals in Punjab are briefly discussed.

Top Leadership Commitment.
A solid foundation for implementing TQM operations will be laid by strong leadership. Since everyone's involvement is a requirement for implementing TQM in hospitals, management must exercise leadership skills to influence the behavior of others in hospitals. TQM succeeds in organizations through continuous

Performance Management System.
rough the performance management system, an organization can gain and maintain its competitive advantages and improve its resilience and future prospects. In the healthcare industry, it is based on the number of things such as economy, productivity, and efficacy due to the variation of interests of many stakeholders such as doctors, financers, and trusts. rough this, hospital management can identify the areas for performance improvements, planning systematic performance improvement initiatives, setting targets, and continuously tracking metrics.

Employee Empowerment.
e empowerment of a team can develop the best collaboration among the team, which in turn led to innovation. rough employee empowerment, the individual skills, proficiency, and initiative attitude can be linked to wider social policies of hospitals in a better way. Moreover, this motivates the employees to ascertain the best line of action in every context to acquire the desired goals set forth by the management.

Effective Operational Management.
Proper operations management can help overcome a variety of obstacles so one can provide excellent customer service at every level. e importance of operations management in healthcare cannot be overstated as the healthcare industry is incredibly diverse and operations often require unique solutions based on a variety of factors. Operations management in healthcare refers to overseeing the day-to-day practices of a healthcare facility that impact the client experience and organizational goals.
3.6. Patient Satisfaction. One of the important requirements of TQM is to cultivate customer-oriented operational processes. Filippini and Forza [38] suggested that it is far essential for an organization to preserve close bondage with their clients on the way to recognize their necessities and measure how it has been a success in meeting up to clients' necessities. Client satisfaction is considered as the most important element for healthcare suppliers as well as for patients themselves within the medical care commercial community [39]. Aliman and Mohamad [40] claimed that the quality performance of healthcare units is positively interrelated with patient satisfaction.

Graph-Theoretic Approach (GTA)
e graph-theoretic approach is used to evaluate the TQM performance of public sector hospitals. Graph theory is an elegant way to describe any network or model.
Definition: A graph comprises nodes (representing the basic components of the model), and edges indicate the relation between the nodes. Definition: A directed graph or a digraph is a graph in which the edges have a direction. is is usually indicated with an arrow on the edge, more formally, if v and w are vertices, an edge is an unordered pair {v, w}, while a directed edge, called an arc, is an ordered pair (v, w) or (w, v). e graph-theoretic approach is systematical mathematical modeling that incorporates all the qualitative properties and factors of the given problem into mathematical quantities.
is makes them more effective than other techniques such as flow charts, cause-effect diagrams, and so on. To study the TQM environment, GTA not only emphasizes on the numerical values of TQM factors in the TQM environment but also includes the influencing relation of one factor over another. In this approach, the qualitative information of the TQM evaluation process is converted into a numerical quantity known as the hospital TQM performance index (HTQMPI).
is index is not only used to evaluate the quality performance of hospitals under study but can also be used in ranking these hospitals in terms of TQM attributes.
is method elegantly incorporates the significance of attributes and their relative importance for a given organization.
is graph-theoretic approach comprises the following three main components.

TQM Attributes Digraph D TQM .
It consists of a set of nodes v i with i � 1, · · · M having TQM attribute value A i and a set of arcs with edge weight A ij that indicates the interdependency or relative importance of i-th attribute over j-th attribute. If an attribute A i (node i) is relatively more important than the attribute A j (node j), then a directed arc is drawn from node i to node j with arc weight A ij . en the general TQM variable permanent matrix for M-TQM attributes environment is defined as

TQM Variable
4.3. TQM Performance Index, TQM HPI . e TQM performance index, TQM PI , is a numerical value that is used to evaluate the TQM performance of a hospital. It is obtained through the permanent function of the TQM variable permanent matrix defined as follows: where σ is a permutation on M attributes and A i � A ii . e permanent function of PM TQM for five TQM attributes environment is defined as follows: e above expression is appropriate for TQM evaluation as it involves both the values of attributes and their interrelationship impact. Its numerical value gives the TQM performance index, TQM HPI : Since it contains only positive terms and values of A i , A ij are also non-negative, and its higher value indicates the better performance of an organization.

Quantification of A i 9 s and A ij 9 s
To compute TQM HPI , the values of A i ′ s and A i ′ s need to be calculated. e organizations that are evaluated through TQM attributes provide the data, and then such data are converted into a suitable qualitative scale (0-10). If it is difficult to measure attributes through a qualitative scale, then a questionnaire may be designed to measure their values. In this case, these quantitative values are then normalized so that qualitative and quantitative scales remain the same, that is, 0-10. e values of A i ′ s indicating the relative importance of the TQM factors are also allocated on a scale 0-10. ese values can be assigned according to the rule given in Table 3.

Advantages of Proposed Method
e TQM digraph approach has the following advantages: (i) e benefit of GTA to study TQM environment is that this method not only highlights the importance of all TQM attributes independently but also focuses on the interdependence and relative importance of one attribute over another. (ii) is approach is not limited to pictorial analysis but is also suitable for computer processing as matrices are involved in the proposed technique. (iii) As the obtained results are in the form of numerical values, in this way, the comparison and benchmarking of hospitals are very easy and useful. (iv) e proposed method can integrate multiattributes at a time. (v) e graph-theoretic approach is systematical mathematical modeling that incorporates all the qualitative properties and factors of the given problem into mathematical quantities. is gives superiority to the proposed method over conventional methods such as flow charts, cause-effect diagrams, and so on. (vi) e proposed technique also helps indicate the particular set of attributes that are more influential than other attributes or that are more needed to be improved for a particular hospital to improve its TQM performance subsequently.

Limitations of the Study
One of the limitations of this study is the limited number of hospitals in the Punjab province. ere are total 8,300 public sector healthcare facilities in Punjab, but this study deals only with 39 teaching/public hospitals in Punjab due to the unavailability of data from other healthcare facilities. Another limitation of this study is that the data is collected only from healthcare professionals. is small sample size may limit the generalizability of the results of the study. e more accurate results can be obtained if the sample size is increased by taking data from healthcare professionals as well as from the management team and patients who are the actual stakeholders.

Methodology
A questionnaire addressing six TQM factors was developed. e data were collected from healthcare professionals working in the under studied hospitals. e following main steps for the assortment of best TQM performing public sector hospitals among the hospitals in nine divisions of Punjab, Pakistan, and to determine the influential attribute

Relative importance A ij A ji
Same importance 5 5 i-th attribute is slightly important than j-th 6 4 i-th attribute is very important than j-th 7 3 i-th attribute is most important than j-th 8 2 i-th attribute is extremely important than j-th 9 1 i-th attribute is extraordinary important than j-th 10 0 Mathematical Problems in Engineering 5 that contributed most significantly to the TQM index of hospitals as compared to others are proposed: Step 1: For an assortment of the best TQM performing public sector hospital: ( For the values of relative importance A ij , among the attributes, see Table 3  s, which are attained in step 2 into the expression obtained in step 5. (7) Sort out the hospitals in descending order of the TQM performance index, TQM HPI . e hospital with the highest TQM performance index, TQM HPI , value can be considered the best hospital in terms of TQM implementation.
Step 2: For finding the most influential attribute in a hospital: (1) To find the contribution of an attribute A i in the TQM index, all the terms in the expression (2)

Analysis and Results
Based on the financial, physical, and regional conditions of the public sector hospitals in Punjab, the following six TQM attributes that could affect the TQM performance of the under studying hospitals are selected: e required data were taken from the hospitals through a designed questionnaire. Each attribute in the questionnaire is assessed through eight subquestions, where each subquestion has maximum of five points that further contributed total of 40 points to each attribute. As all six attributes are beneficial in our graph-theoretic model, therefore, their higher values are required. e point values of each attribute A i for i � 1, 2, 3, 4, 5, 6 is calculated for all 39 hospitals. ese values are then converted into the 0−10 scale (normalized) as defined in (5). e values of relative importance A ij of attribute A i over attribute A j from 0 to 10 based on the literature review and the physical situation of these hospitals are then assigned according to Table 3. For instance, TLM is more important than EE so a relatively higher value of 6 of relative importance is given to the TLM over EE, and the low value of 4 of relative importance is given to the EE over the TMS. Likewise, all other relative importance between the other attributes can be illustrated. e values of relative importance among six attributes are given in Table 4. e TQM digraph, where the six nodes represent the selected attributes A i ' and directed edges show the relative importance, is depicted in Figure 1.
e TQM permanent matrix for each hospital using expression (1) is written as e permanent TQM index for each hospital is expressed as:

A ij A ji A k A l A m A n + A ij A jk A ki + A ik A kj A ji A l A m A n + A ij A ji A kl A lk A m A n + A ij A jk A kl A li + A il A lk A kj A ji A m A n + A ij A ji A kl A lm A mk + A km A ml A lk A n + A ij A jk A kl A lm A mi + A im A ml A lk A kj A ji A n + A ij A ji A kl A lk A mn A nm + A ij A jk A kl A li + A il A lk A kj A ji A mn A nm + A ij A jk A ki + A ik A kj A ji + A lm A mn A nl + A ln A nm A ml
e quantitative values of the above six mentioned attributes calculated from the questionnaire are given in Table 5.
e normalized values of these attributes are detailed in Table 6. e values of A i ' s and A ij ' given in Tables 4 and 6, respectively, and the expression given in (9) are used to compute the TQM performance index, TQM HPI , for each hospital.
All the computations are carried out in MATLAB using constructed TQM permanent matrix expressed in (8) Table 7. e TQM index-based ranking of public sector teaching hospitals in Punjab is shown in Figure 2. Now, to nd the TQM index of each attribute of a hospital, the digraph D TQM−A i and permanent matrix PM TQM−A i are constructed using the values of A i s and A ij ′ s from Tables 4 and 6 as detailed in the methodology section. For example, consider Lahore General Hospital and attribute A 1 . e digraph D TQM−A i is given in Figure 3. e matrix PM TQM−A 1 is given as

PM TQM �
e values of TQM PA 1 PI computed from expressed (4) is given as Similarly, other values are computed. e values of TQM PA i PI for each attribute of all hospitals along with the most influential attribute for the hospital are tabulated in Table 8. Now, to find in which hospital a particular attribute is implemented more effectively, the percentage contribution of each attribute in the TQM index of every hospital is computed by using expression (5) and tabulated in Table 9.

Conclusion
A graph-theoretic technique (GTA) is suggested for analyzing the TQM environment in public sector hospitals in the province Punjab of Pakistan. In the proposed technique, rstly, TQM digraph is constructed for each teaching hospital; then corresponding matrices are obtained; and then using those matrices, the TQM performance index is designed. e hospitals with the highest TQM performance index are considered as the best hospital with reference to TQM implementation. All the hospitals with reference to TQM implementation are ranked. According to the obtained results, Services Hospital has the highest TQM index indicating the best implementation of TQM. e obtained ranking is not only based on the values of all attributes (obtained from the questionnaire) but also on the in uencing relations of one attribute over another.
is makes this approach more suitable for TQM study in a speci c province (Punjab) of Pakistan because the interdependency relations of attributes in di erent localities may be changed. Secondly, as the hospitals located in di erent communities have di erent problems, that is why it is not possible for every hospital to incorporate all the TQM attributes e ciently. e proposed technique settled this problem by providing the procedure to indicate the most in uencing TQM attribute for each hospital. is technique not only helps us to evaluate the current TQM performance of hospitals but also helps us to indicate the most e ective and in uencing attribute for each hospital. e betterment in indicated in uencing attribute may lead to a better TQM environment in that hospital. Hence, the results obtained can become the guidelines for health policymakers in Pakistan for better planning and improvements. Furthermore, one can apply this TQM digraph model in wider scope covering the health facilities all over Pakistan instead of one province.

Data Availability
Data used in the study are available on request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.