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

Authors: Ahmad Islam; Abdus Salam
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

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.


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## Body

## 1. 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 efficiency and performance quality due to their limited resources.


### 1.1. Healthcare in Pakistan

Healthcare expenditure in Pakistan is increasing significantly 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 different levels in changing environments and time frames. The objective behind is to attain and sustain the optimal level of efficiency and relative productivity in the delivery of healthcare services. Healthcare expenditure in Pakistan is increasing significantly and turning into big investments for escalation of quality of healthcare services across the country. The 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. The private health sector comprises non-governmental organizations (NGOs), charitable organizations, trusts, and corporate health sectors. The 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]. The 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. The 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. The health system of Pakistan is described by insufficient expenditure, low-quality service, and poor utilization of services. The 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. The total number of availability of beds is approximately 101,047. The inadequate number of health workers in Pakistan is summarized in Table 1 (Economic Survey of Pakistan (2018–2019).Table 1
Registered medical and paramedical personnel.
Health workersNumbers in 2019Doctors233,261Nurses112,123Dentists24,930Midwives41,810Lady health visitors20,565


### 1.2. 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. The Punjab province comprises 2,455 basic health units (BHUs) and 293 rural health centers (RHCs) in an open area. There are 42 public sector teaching hospitals in 13 districts (9 divisions) of Punjab, and among 42, 3 are purely dental hospitals. The detailed listing of the remaining 39 hospitals is given in Table2.Table 2
List of public sector hospitals in Punjab.
Sr. No.HospitalsDistrict1Jinnah Hospital (JH)Lahore2Sheikh Zayed Hospital (SZH)Lahore3Services Hospital (SH)Lahore4Government Nawaz Sharif Hospital (GNSH)Lahore5Lahore General Hospital (LGH)Lahore6Said Mitha Hospital (SMH)Lahore7Government Mozang Teaching Hospital (GMTH)Lahore8Lady Aitchison Hospital (LAH)Lahore9Children Hospital (CHL)Lahore10Lady Willington Hospital (LWH)Lahore11May Hospital (MH)Lahore12Punjab Institute of Cardiology (PIOC)Lahore13Sir Ganga Ram Hospital (SGRH)Lahore14Government Mian Munshi Hospital (GMMH)Lahore15Government Kot Khawaja Saeed Teaching Hospital (GKKSTH)Lahore16Govt Teaching Hospital Shahdra (GTHS)Lahore17Government Sardar Begum Teaching Hospital (GSBTH)Sialkot18Aziz Bhatti Saeed Hospital (ABSH)Gujrat19District Head Quarter Hospital Gujranwala (DHQHG)Gujranwala20Wazirabad Institute of Cardiology (WIC)Wazirabad21District Head Quarter Hospital Rawalpindi (DHQH)Rawalpindi22Holy Family Hospital (HFH)Rawalpindi23Benazir Bhutto Hospital (BBH)Rawalpindi24Rawalpindi Institute of Cardiology (RIOC)Rawalpindi25Allied Hospital (AH)Faisalabad26District Head Quarter Hospital Faisalabad (DHQHF)Faisalabad27Govt General Hospital Ghulam Muhammad Abad (GGHGMA)Faisalabad28Faisalabad Institute of Cardiology (FIC)Faisalabad29Children Hospital, Faisalabad (CHF)Faisalabad30District Head Quarter Hospital Sargodha (DHQHS)Sargodha31District Head Quarter Hospital Sahiwal (DHQHS)Sahiwal32Nishtar Hospital (NH)Multan33Ch. Pervaiz Elahi Institute of Cardiology (CPEIC)Multan34Children Hospital Mulatan (CHM)Multan35Bahawal Victoria Hospital (BVH)Bahawalpur36Cardiology and Cardiac Surgery Hospital (CCSH)Bahawalpur37Civil Hospital Bahawalpur (CHB)Bahawalpur38Sheikh Zayed Medical Hospital (SZMH)Rahim Yar Khan39Teaching Hospital Dera Ghazi Khan (THDGK)D.G. Khan


## 1.1. Healthcare in Pakistan

Healthcare expenditure in Pakistan is increasing significantly 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 different levels in changing environments and time frames. The objective behind is to attain and sustain the optimal level of efficiency and relative productivity in the delivery of healthcare services. Healthcare expenditure in Pakistan is increasing significantly and turning into big investments for escalation of quality of healthcare services across the country. The 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. The private health sector comprises non-governmental organizations (NGOs), charitable organizations, trusts, and corporate health sectors. The 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]. The 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. The 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. The health system of Pakistan is described by insufficient expenditure, low-quality service, and poor utilization of services. The 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. The total number of availability of beds is approximately 101,047. The inadequate number of health workers in Pakistan is summarized in Table 1 (Economic Survey of Pakistan (2018–2019).Table 1
Registered medical and paramedical personnel.
Health workersNumbers in 2019Doctors233,261Nurses112,123Dentists24,930Midwives41,810Lady health visitors20,565


## 1.2. 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. The Punjab province comprises 2,455 basic health units (BHUs) and 293 rural health centers (RHCs) in an open area. There are 42 public sector teaching hospitals in 13 districts (9 divisions) of Punjab, and among 42, 3 are purely dental hospitals. The detailed listing of the remaining 39 hospitals is given in Table2.Table 2
List of public sector hospitals in Punjab.
Sr. No.HospitalsDistrict1Jinnah Hospital (JH)Lahore2Sheikh Zayed Hospital (SZH)Lahore3Services Hospital (SH)Lahore4Government Nawaz Sharif Hospital (GNSH)Lahore5Lahore General Hospital (LGH)Lahore6Said Mitha Hospital (SMH)Lahore7Government Mozang Teaching Hospital (GMTH)Lahore8Lady Aitchison Hospital (LAH)Lahore9Children Hospital (CHL)Lahore10Lady Willington Hospital (LWH)Lahore11May Hospital (MH)Lahore12Punjab Institute of Cardiology (PIOC)Lahore13Sir Ganga Ram Hospital (SGRH)Lahore14Government Mian Munshi Hospital (GMMH)Lahore15Government Kot Khawaja Saeed Teaching Hospital (GKKSTH)Lahore16Govt Teaching Hospital Shahdra (GTHS)Lahore17Government Sardar Begum Teaching Hospital (GSBTH)Sialkot18Aziz Bhatti Saeed Hospital (ABSH)Gujrat19District Head Quarter Hospital Gujranwala (DHQHG)Gujranwala20Wazirabad Institute of Cardiology (WIC)Wazirabad21District Head Quarter Hospital Rawalpindi (DHQH)Rawalpindi22Holy Family Hospital (HFH)Rawalpindi23Benazir Bhutto Hospital (BBH)Rawalpindi24Rawalpindi Institute of Cardiology (RIOC)Rawalpindi25Allied Hospital (AH)Faisalabad26District Head Quarter Hospital Faisalabad (DHQHF)Faisalabad27Govt General Hospital Ghulam Muhammad Abad (GGHGMA)Faisalabad28Faisalabad Institute of Cardiology (FIC)Faisalabad29Children Hospital, Faisalabad (CHF)Faisalabad30District Head Quarter Hospital Sargodha (DHQHS)Sargodha31District Head Quarter Hospital Sahiwal (DHQHS)Sahiwal32Nishtar Hospital (NH)Multan33Ch. Pervaiz Elahi Institute of Cardiology (CPEIC)Multan34Children Hospital Mulatan (CHM)Multan35Bahawal Victoria Hospital (BVH)Bahawalpur36Cardiology and Cardiac Surgery Hospital (CCSH)Bahawalpur37Civil Hospital Bahawalpur (CHB)Bahawalpur38Sheikh Zayed Medical Hospital (SZMH)Rahim Yar Khan39Teaching Hospital Dera Ghazi Khan (THDGK)D.G. Khan


## 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]. The 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. These 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. The 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. (2011, 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 well-mannered implementation of TQM can significantly increase the productivity of processes in Pakistani hospitals. The 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. The same technique is also used to evaluate the machinability of tungsten carbide composite with wire EDM [25]. The multicriteria decision-making approach in quality assessment is discussed in [26–30]. Different fuzzy graph-theoretic models are also used in several decision-making problems [31–37].The aim of this study is to evaluate the TQM performance of public sector hospitals of province Punjab of Pakistan using graph-theoretic technique.


## 3. TQM Attributes

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


### 3.1. 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 purposeful leadership, interteam communication, and full senior management commitment focused on customer satisfaction. Good leadership has the ability to build a strong foundation, develop and lead a long-term vision of the organization, and focus on ever-changing customer needs.


### 3.2. Continuous Improvement

It stands for devotion to the continuous analysis of the administrative and managerial process so that more appropriate methods can be replaced with existing processes. In other words, flaws can be identified so that mistakes can be evaded. In the healthcare industry, through continuous improvement, all the team members (CMOs, doctors, paramedical staff, administrative staff, etc.) of a hospital can be engaged in designing improvement strategies and their implementation.


### 3.3. Performance Management System

Through 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. Through this, hospital management can identify the areas for performance improvements, planning systematic performance improvement initiatives, setting targets, and continuously tracking metrics.


### 3.4. Employee Empowerment

The empowerment of a team can develop the best collaboration among the team, which in turn led to innovation. Through 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.


### 3.5. Effective Operational Management

Proper operations management can help overcome a variety of obstacles so one can provide excellent customer service at every level. The 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.


## 3.1. 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 purposeful leadership, interteam communication, and full senior management commitment focused on customer satisfaction. Good leadership has the ability to build a strong foundation, develop and lead a long-term vision of the organization, and focus on ever-changing customer needs.


## 3.2. Continuous Improvement

It stands for devotion to the continuous analysis of the administrative and managerial process so that more appropriate methods can be replaced with existing processes. In other words, flaws can be identified so that mistakes can be evaded. In the healthcare industry, through continuous improvement, all the team members (CMOs, doctors, paramedical staff, administrative staff, etc.) of a hospital can be engaged in designing improvement strategies and their implementation.


## 3.3. Performance Management System

Through 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. Through this, hospital management can identify the areas for performance improvements, planning systematic performance improvement initiatives, setting targets, and continuously tracking metrics.


## 3.4. Employee Empowerment

The empowerment of a team can develop the best collaboration among the team, which in turn led to innovation. Through 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.


## 3.5. Effective Operational Management

Proper operations management can help overcome a variety of obstacles so one can provide excellent customer service at every level. The 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.


## 4. Graph-Theoretic Approach (GTA)

The 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. This is usually indicated with an arrow on the edge, more formally, ifv 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).The graph-theoretic approach is systematical mathematical modeling that incorporates all the qualitative properties and factors of the given problem into mathematical quantities. This 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). This 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. This method elegantly incorporates the significance of attributes and their relative importance for a given organization. This graph-theoretic approach comprises the following three main components.


### 4.1. TQM Attributes DigraphDTQM

It consists of a set of nodesvi with i=1,⋯M having TQM attribute value Ai and a set of arcs with edge weight Aij that indicates the interdependency or relative importance of i-th attribute over j-th attribute. If an attribute Ai (node i) is relatively more important than the attribute Aj (node j), then a directed arc is drawn from node i to node j with arc weight Aij.


### 4.2. TQM Variable Permanent MatrixPMTQM

Although TQM attributes digraph provides a graphical representation of the attributes and their interdependency relation, it would be difficult to visualize these digraphs if the number of attributes increases. However, this problem can be settled by representing the attribute digraph by anM×M matrix. This matrix sufficiently incorporates all the characteristics of the attribute digraph including the attribute values and their relative importance. Suppose there are M values of attributes A1,…,AM. Then the general TQM variable permanent matrix for M-TQM attributes environment is defined as(1)PMTQM=A1⋯A1M⋮⋱⋮AM1⋯AM.


### 4.3. TQM Performance Index,TQMHPI

The TQM performance index,TQMPI, 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:(2)perPMTQM=∑σ∏iAiσi,where σ is a permutation on M attributes and Ai=Aii. The permanent function of PMTQM for five TQM attributes environment is defined as follows:(3)perPMTQM=∏i=15Ai+∑i∑j∑k∑l∑mAijAjiAkAlAm+AijAjkAki+AikAkjAjiAlAm+AijAjiAklAlkAm+AijAjkAklAli+AilAlkAkjAjiAm+AijAjiAklAlmAmk+AkmAmlAlk+AijAjkAklAlmAmi+AimAmlAlkAkjAji.The 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,TQMHPI:(4)TQMHPI=perPMTQM.Since it contains only positive terms and values ofAi, Aij are also non-negative, and its higher value indicates the better performance of an organization.


## 4.1. TQM Attributes DigraphDTQM

It consists of a set of nodesvi with i=1,⋯M having TQM attribute value Ai and a set of arcs with edge weight Aij that indicates the interdependency or relative importance of i-th attribute over j-th attribute. If an attribute Ai (node i) is relatively more important than the attribute Aj (node j), then a directed arc is drawn from node i to node j with arc weight Aij.


## 4.2. TQM Variable Permanent MatrixPMTQM

Although TQM attributes digraph provides a graphical representation of the attributes and their interdependency relation, it would be difficult to visualize these digraphs if the number of attributes increases. However, this problem can be settled by representing the attribute digraph by anM×M matrix. This matrix sufficiently incorporates all the characteristics of the attribute digraph including the attribute values and their relative importance. Suppose there are M values of attributes A1,…,AM. Then the general TQM variable permanent matrix for M-TQM attributes environment is defined as(1)PMTQM=A1⋯A1M⋮⋱⋮AM1⋯AM.


## 4.3. TQM Performance Index,TQMHPI

The TQM performance index,TQMPI, 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:(2)perPMTQM=∑σ∏iAiσi,where σ is a permutation on M attributes and Ai=Aii. The permanent function of PMTQM for five TQM attributes environment is defined as follows:(3)perPMTQM=∏i=15Ai+∑i∑j∑k∑l∑mAijAjiAkAlAm+AijAjkAki+AikAkjAjiAlAm+AijAjiAklAlkAm+AijAjkAklAli+AilAlkAkjAjiAm+AijAjiAklAlmAmk+AkmAmlAlk+AijAjkAklAlmAmi+AimAmlAlkAkjAji.The 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,TQMHPI:(4)TQMHPI=perPMTQM.Since it contains only positive terms and values ofAi, Aij are also non-negative, and its higher value indicates the better performance of an organization.


## 5. Quantification ofAi′ s and Aij′ s

To computeTQMHPI, the values of Ai′ s and Ai′ s need to be calculated. The 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. The values of Ai′ s indicating the relative importance of the TQM factors are also allocated on a scale 0–10. These values can be assigned according to the rule given in Table 3.Table 3
Values forAij′ s.
Relative importanceAijAjiSame importance55i-th attribute is slightly important than j-th64i-th attribute is very important than j-th73i-th attribute is most important than j-th82i-th attribute is extremely important than j-th91i-th attribute is extraordinary important than j-th100


## 6. Advantages of Proposed Method

The TQM digraph approach has the following advantages:(i)
The 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)
This 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)
The proposed method can integrate multiattributes at a time.(v)
The graph-theoretic approach is systematical mathematical modeling that incorporates all the qualitative properties and factors of the given problem into mathematical quantities. This gives superiority to the proposed method over conventional methods such as flow charts, cause-effect diagrams, and so on.(vi)
The 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.


## 7. Limitations of the Study

One of the limitations of this study is the limited number of hospitals in the Punjab province. There 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. This small sample size may limit the generalizability of the results of the study. The 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.


## 8. Methodology

A questionnaire addressing six TQM factors was developed. The data were collected from healthcare professionals working in the under studied hospitals. The 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 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:(1)
The list of suitable attributes to evaluate the TQM performance of a hospital is identified.(2)
The values of each attributeAi is computed using a questionnaire. These values are then normalized as follows:Letail≤Ai≤aiu, that is, ail and aiu are minimum and maximum values of Ai, respectively. Then for any intermediate value aik of the attribute Ai is normalized as(5)Ai=10×aikau,ifail=0,10×aiu−aikaiu−ail,otherwise.For the values of relative importanceAij, among the attributes, see Table 3 for details.(3)
Construct the TQM attributes digraph for each hospital by taking the selected TQM performance attributes as vertices. The edges and their directions are drawn according to the values ofAij.(4)
Construct the TQM variable permanent matrix for selected TQM attributes for each hospital as given in (1).(5)
Formulate the TQM performance index,TQMHPI, as given in (2).(6)
Evaluate the TQM performance index,TQMHPI, for each hospital by putting the values of Ai′ s and Aij′ 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,TQMHPI.The hospital with the highest TQM performance index,TQMHPI, 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 attributeAi in the TQM index, all the terms in the expression (2) containing Ai are evaluated. For this, construct digraph DTQM−Ai, which is obtained by removing the vertex corresponding to attribute Ai.(2)
The permanent matrixPMTQM−Ai for the digraph DTQM−Ai is constructed from (1) by deleting the i-th row and column.(3)
Formulate the TQM index of attributeAi as follows:(6)TQMAiPI=Ai×perPMTQM−Ai.(4)
EvaluateTQMAiPI for each attribute of every hospital by putting the already calculated values of Ai′ s and Aij′ s, into the expression obtained in the previous step.(5)
Sort out the attributes of each hospital in descending order ofTQMAiPI. The attribute with highest TQMAiPI value is considered as the most influential attribute for that hospital.Step 3: For determining the independent TQM implementation of individual attributes among hospitals:(1)
Formulate the percentage contribution of attributeAi in TQMHPI as(7)TQMPAiPI=100×TQMAiPITQMHPI.(2)
EvaluateTQMPAiPI by putting already computed values of TQMAiPI and TQMHPI in the above expression for each hospital.(3)
The hospital with the highest value ofTQMPAiPI is considered as having the best implementation of attribute TQMPAiPI in that hospital.(4)
Compute the average value ofTQMAiPI. The attribute with highest TQMAiPI is considered as the best implemented TQM attribute all over the province Punjab.


## 9. 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:(i)
A1 − top leader management (TLM)(ii)
A2 − continuous improvement (CI)(iii)
A3 − performance management system (PMS)(iv)
A4 − employee empowerment (EE)(v)
A5 − effective operational management (EOM)(vi)
A6 − patient satisfaction (PS)The 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. The point values of each attributeAi for i=1,2,3,4,5,6 is calculated for all 39 hospitals. These values are then converted into the 0−10 scale (normalized) as defined in (5). The values of relative importance Aij of attribute Ai over attribute Aj 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. The values of relative importance among six attributes are given in Table 4.Table 4
Relative importance among six attributes.
AttributesA1A2A3A4A5A6A1—66464A24—6465A344—456A4666—76A54453—7A665443—The TQM digraph, where the six nodes represent the selected attributesAi' and directed edges show the relative importance, is depicted in Figure 1.Figure 1
The digraphDTQM for six attributes.The TQM permanent matrix for each hospital using expression (1) is written as(8)PMTQM=A1A12A13A14A15A16A21A2A23A24A25A26A31A32A3A34A35A36A41A42A43A4A45A46A51A52A53A54A5A56A61A62A63A64A65A6.The permanent TQM index for each hospital is expressed as:(9)TQMHPI=perPMTQM=∏i=16Ai+∑i∑j∑k∑l∑mAijAjiAkAlAmAn+AijAjkAki+AikAkjAjiAlAmAn+AijAjiAklAlkAmAn+AijAjkAklAli+AilAlkAkjAjiAmAn+AijAjiAklAlmAmk+AkmAmlAlkAn+AijAjkAklAlmAmi+AimAmlAlkAkjAjiAn+AijAjiAklAlkAmnAnm+AijAjkAklAli+AilAlkAkjAjiAmnAnm+AijAjkAki+AikAkjAji+AlmAmnAnl+AlnAnmAml+AijAjkAklAlmAmnAni+AinAnmAmlAlkAki.The quantitative values of the above six mentioned attributes calculated from the questionnaire are given in Table5. The normalized values of these attributes are detailed in Table 6. The values of Ai' s and Aij' given in Tables 4 and 6, respectively, and the expression given in (9) are used to compute the TQM performance index, TQMHPI, for each hospital.Table 5
Numerical values of attributes.
Sr. No.HospitalsA1A2A3A4A5A61JH3028303232282SZH3233363234333SH3436313335354GNSH3531303535335LGH3132303030326SMH2730302828337GMTH2628282626308LAH3028302929289CH30343332353210LWH25262826323011MH33323231353312PIC32352831342813SGRH35333027302514GMMH16161518202015GKKSTH12181616222216GTHS18121415242017GSBTH21192119191818ABSH19191918211719WIC30232223242620DHQHG26222621262321DHQHR25251412161722HFH30282018222423BBH25251310131524RIC32252422252825AH29282322282926DHQHF23242523242527GGHGMA22212621232528FIC29282526252729CH28252728272930DHQHS1512121010831DHQHS1952118201732NH26222023222533CPEIC25282220272634CH25222317232735BVH23261818222436CCSH23252426252837CHB18151810151038SZMH20181018151839THDGK15138131013Table 6
Normalized values of attributes.
Sr. NoHospitalsA1A2A3A4A5A61JH8789972SZH991091093SH10108910104GNSH1088101095LGH8988896SMH7887797GMTH6776688LAH8788879CH899910910LWH67769811MH999810912PIC9107810713SGRH109878614GMMH24334415GKKSTH04325516GTHS32226417GSBTH45544418ABSH35434319WIC86556720DHQHG65646621DHQHR66212322HFH87435623BBH66201324RIC96656725AH77557826DHQHF56656627GGHGMA45645628FIC77666729CH76777830DHQHS12100031DHQHS30534332NH65455633CPEIC67547734CH65535735BVH57435636CCSH56666737CHB33402138SZMH34132439THDGK130102All the computations are carried out in MATLAB using constructed TQM permanent matrix expressed in (8) for each hospital. The values of the permanent index for all hospitals are tabulated in Table 7. The TQM index-based ranking of public sector teaching hospitals in Punjab is shown in Figure 2.Table 7
TQM performance index of public sector hospitals in Punjab.
Sr. NoHospitalsTQMHPI1JH196132642SZH256303283SH264216904GNSH247417885LGH209261366SMH176356107GMTH154176548LAH183442489CHL2396870010LWH1649002611MH2392859412PIOC2157551713SGRH1947862614GMMH764876015GKKSTH730758416GTHS734190617GSBTH905858918ABSH817246219DHQHG1344734820WIC1219729221DHQHR749965222HFH1164377223BBH695356824RIOC1435019725AH1436878826DHQHF1182784427GGHGMA1067082028FIC1445894429CHF1599593730DHQHS432712831DHQHS687361232NH1104544233CPEIOC1299091634CHM1095683135BVH1060113136CACSH1305837637CHB581320038SZMH688516639THDGK4761556Figure 2
TQM index-based ranking of public sector hospitals in Punjab.Now, to find the TQM index of each attribute of a hospital, the digraphDTQM−Ai and permanent matrix PMTQM−Ai are constructed using the values of Ais and Aij′ s from Tables 4 and 6 as detailed in the methodology section. For example, consider Lahore General Hospital and attribute A1. The digraph DTQM−Ai is given in Figure 3.Figure 3
The digraphPMTQM−A1.The matrixPMTQM−A1 is given as(10)PMTQM=A2A23A24A25A26A32A3A34A35A36A42A43A4A45A46A52A53A54A5A56A62A63A64A65A6=9646548456668764538754439.The values ofTQMPA1PI computed from expressed (4) is given as(11)TQMPAiPI=A1∗perPMTQM−A1=8∗6996748=5597984.Similarly, other values are computed. The values ofTQMPAiPI for each attribute of all hospitals along with the most influential attribute for the hospital are tabulated in Table 8.Table 8
TQM performance index of TQM attributes.
HospitalsTQMA1PITQMA2PITQMA2PITQMA4PITQMA5PITQMA6PIIAJH517048047826805263488588722457570484621148EESZH772214478190298371290809755284712807589997PSSH855449086562007539888838945887921608420600EOMGNSH790488069380806961168827314081200007272144EELGH559798461378925692032589280057679365943348CISMH432736546250404634144438249042780644833864PSGMTH314835034485923593282333814832544723797184PSLAH477532844140044862208503475249190404262692EECHL659599272167767232508747320478207606995808EOMLWH341939438840483889718361378846950844118352EOMMH711225072010177218054691684078123206989211EOMPIOC626080567943305380291609480868984005197710EOMSGRH593559056180525215424492681052798084103076TLMGMMH5302369983767811468184901014648950784CIGKKSTH094364873578053777611537601082120EOMGTHS7269185142885152905404901346376906720EOMGSBTH124713214684901473455128246412409121164180PMSABSH860199129885010420408874061095216800868CIDHQHG330209627105122363860246046027626162933616TLMWIC237597620116802421108183340024564482320464EOMDHQHR13750321308018528422290292537280722709TLMHFH278037625578841653392135667220155202194008TLMBBH125659211964244809880255792658320TLMRIOC387069329284262940522266160529857803170006TLMAH324500432921772559935266519533516493497944PSDHQHF206949523293682334480211272023646242231808EOMGGHGMA146164817850402065152156024018145601973064PMSFIC326799233192182972304308964030139203198398CICHF369240933466983757460389894438073213972144PSDHQHS144053273376142796000TLMDHQHS69824401060150718146889896649008PMSNH211027818591801557256194385018936802060676TLMCPEIOC256167629197422263780197608829712482813090CICHM217254617693501843750126339618751652294082PSBVH173773522951321477580121264518016801960098CICACSH233428025213682626704273460826605442821700PSCHB5696405597767224320394752191424TLMSZMH671442879572249969720195485874839040CITHDGK16174544295601682800289672CINow, 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.Table 9
Percentage contribution of each attribute in TQM performance of hospitals.
Hospitals%TQMA1PI%TQMA2PI%TQMA3PI%TQMA4PI%TQMA5PI%TQMA6PIJH262427302924SZH303133323330SH323329323332GNSH322828333329LGH272927282828SMH252626252427GMTH202223222125LAH262427272723CHL283030313329LWH212424222825MH303030293329PIOC293125283224SGRH302927252721GMMH71310111312GKKSTH0131071615GTHS107771812GSBTH141616141413ABSH111613111310DHQHG252018182122WIC191620152019DHQHR181774710HFH242214121719BBH18177049RIOC272020192122AH232318192324DHQHF172020182019GGHGMA141719151718FIC232321212122CHF232123242425DHQHS363000DHQHS1001510139NH191714181719CPEIOC202217152322CHM201617121721BVH162214111718CACSH181920212022CHB101012073SZMH1013410712THDGK390406


## 10. Discussion and Interpretations

One of the findings of our proposed technique of TQM digraph is the ranking of public sector teaching hospitals in Punjab. The results show that Services Hospital in the Lahore district with the highest value ofTQMHPI has the best TQM practices implementation. The top five TQM performance-based hospitals are Services Hospital, Sheikh Zayed Hospital, Government Nawaz Sharif Hospital, Children Hospital, and Mayo Hospital, which are located in Lahore city. Twelve out of 16 teaching hospitals in the Lahore division are ranked from 1 to 12 based on the best TQM practices. Their higher scores in descending order differentiate them in comparison to the other teaching hospitals. The reason behind their good performance might be the impact and focus of healthcare service providing local authorities as well as effective management. The results also indicate that 2 hospitals GTHS and GKKSTH of the Lahore division are ranked among the bottom 10 hospitals with respect to the TQM index, which means these 2 hospitals follow poor TQM practices. The reasons behind the low performance regarding TQM practice might be due to management issues and underutilization of scarce resources due to their geographical location. Moreover, it is evident from the results that the bottom five hospitals with respect to the TQM index are SZMH, DHQHS, CHB, THDGK, and DHQHS. Geographically, these hospitals are located in those districts that are far from the provincial capital (Lahore) and being neglected by the healthcare authorities that might be the reasons behind their poor TQM performance. The obtained results might be guidance for the government of Punjab to look after the most neglected areas of this province regarding healthcare facilities.The other finding of this research elaborates the indication of the most influential attribute affecting the TQM practices that can be witnessed in Table8. It can be seen from Table 8 that continuous improvement is the most influential attribute for Lahore General Hospital, that is, the betterment in this TQM attribute as compared to other attributes will lead to better TQM performance for Lahore General Hospital. Moreover, from Table 7, we can see that value of both CI (A2) and PS (A6) for Lahore General Hospital is the same, that is, 9, but CI is more influential than PS. This can be seen in Figure 4.Figure 4
Comparison of TQM index of attribute and attribute value of LGH.The similar comparison between the TQM index of attribute and an attribute value of Children Hospital of Faisalabad, Children Hospital of Lahore, and Nishtar hospital of Multan is shown in Figures5–7, respectively. In all these figures, we can easily see that the values of attributes are not sufficient to indicate that which TQM attribute should be focused on to improve the TQM performance of a hospital. On the other hand, the TQM index, TQMAiPI, helps identify the attribute that is needed to improve the TQM performance of a hospital. The hospitals located in different communities have been facing different problems so it is not possible for every hospital to incorporate all the TQM attributes efficiently. Healthcare authorities can get benefit from these results of influencing TQM attributes for each hospital in decision-making in order to maximize the performance within the applied resources keeping in view the geographic conditions of poorly performed hospitals with respect to TQM practices. In addition, if the results obtained from this research are applied in true spirit, then it may increase the efficiency of hospitals and healthcare service professionals. The results can also minimize the non-effective resources, and ultimately, it will reduce the potential burden on the healthcare budget.Figure 5
Comparison of TQM index of attribute and attribute value CHF.Figure 6
Comparison of TQM index of attribute and attribute value CHL.Figure 7
Comparison of TQM index of attribute and attribute value NH.The third finding of this research indicates that for which hospital, a particular TQM attribute is contributing up to the maximum level in its TQM performance. From Figures8–13, we can see that top leadership management is effective both in Services Hospital and Government Nawaz Sharif Hospital. Continuous improvement and patient satisfaction have a strong impact on the TQM performance of Services Hospital, whereas the performance management system plays an important role in the TQM performance of Sheikh Zayed Hospital. Employee’s empowerment is more effective in Government Nawaz Sharif Hospital, whereas effective operational management is better implemented in Sheikh Zayed Hospital, Services Hospital, Government Nawaz Sharif Hospital, Children Hospital Lahore, and Mayo hospital. These results help the healthcare authorities to apply check and balance on the other attributes in TQM performance that are not effectively implemented. In this way, they can give direction to the management to focus on the other attributes and ensure the implementation of these on the same analogy of attributes rightly implemented or triggered.Figure 8
Percentage contribution of TLM in TQM index of the hospital.Figure 9
Percentage contribution of CI in TQM index of the hospital.Figure 10
Percentage contribution of PMS in TQM index of the hospital.Figure 11
Percentage contribution of EE in TQM index of the hospital.Figure 12
Percentage contribution of EOM in TQM index of the hospital.Figure 13
Percentage contribution of PS in TQM index of the hospital.The average TQM index of all attributes is depicted in Figure14 that shows that overall in all public sector hospitals in Punjab, effective operational management is implemented in a better way as compared to other attributes.Figure 14
Average contribution of attributes in TQM performance of hospitals.


## 11. 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, firstly, TQM digraph is constructed for each teaching hospital; then corresponding matrices are obtained; and then using those matrices, the TQM performance index is designed. The 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. The obtained ranking is not only based on the values of all attributes (obtained from the questionnaire) but also on the influencing relations of one attribute over another. This makes this approach more suitable for TQM study in a specific province (Punjab) of Pakistan because the interdependency relations of attributes in different localities may be changed. Secondly, as the hospitals located in different communities have different problems, that is why it is not possible for every hospital to incorporate all the TQM attributes efficiently. The proposed technique settled this problem by providing the procedure to indicate the most influencing TQM attribute for each hospital. This technique not only helps us to evaluate the current TQM performance of hospitals but also helps us to indicate the most effective and influencing attribute for each hospital. The betterment in indicated influencing 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.



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*Source: 3119888-2022-05-10.xml*