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ABSTRACT

Queuing theory as a tool for optimising patients flow and resources utilisation in the female section of the OPD at Yusuf Dantsoho memorial hospital Kaduna, the study was conducted for a period of 5 days. Simple queuing theory calculations were done using the data collected in the evaluation of the performance characteristics of the system, i.e. the average utilisation of the servers, the probability that the system would be idle, the average number of patients in the queue and the average time a patient spends in the system. These parameters are used by hospital managers in making better decisions as it relates to the management of queues, long wait times thus resulting in overcrowding at the OPD of most public hospitals, from the study it was established that the average arrival rate equal 34.4998 patients/hour which is greater than the mean service rate (mu) = 18.0867 patients/hour at the records section and 14.5226 patients/hour at the consultation unit, this accounted for the high utilisation at the servers thus leading long queues and subsequently long wait times at the OPD. QM software for windows was used to model 5 cases using a server capacity of 3, 4, 5, 6 and 7 doctors at post in the female section of the OPD and it was established that for optimum performance 5 doctors need to be available for service at the OPD at a time as compared to an average of 3 doctors which is presently obtainable at the female section of the OPD during the study.
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TABLE OF CONTENTS

Cover page ………………………………………………………………………………….. Error! Bookmark not defined.
DECLARATION ……………………………………………………………………………………………………………………….. ii
CERTIFICATION ……………………………………………………………………………………………………………………… iii
DEDICATION …………………………………………………………………………………………………………………………. iv
ACKNOWLEDGEMENT …………………………………………………………………………………………………………….. v
ABSTRACT …………………………………………………………………………………………………………………………….. vi
Contents ……………………………………………………………………………………………………………………………… vii
CHAPTER ONE ……………………………………………………………………………………………………………………….. 1
INTRODUCTION ……………………………………………………………………………………………………………………… 1
1.1 BACKGROUND OF THE STUDY …………………………………………………………………………………………. 1
1.2 STATEMENT OF PROBLEM ……………………………………………………………………………………………… 4
1.3 RESEARCH QUESTIONS …………………………………………………………………………………………………… 4
1.4 AIM/OBJECTIVES …………………………………………………………………………………………………………… 5
1.5 JUSTIFICATION OF STUDY ………………………………………………………………………………………………. 5
1.6 SCOPE OF THE STUDY …………………………………………………………………………………………………….. 6
1.7 LIMITATION OF THE STUDY …………………………………………………………………………………………….. 6
1.8 STRUCTURE OF WORK ……………………………………………………………………………………………………. 7
CHAPTER TWO ………………………………………………………………………………………………………………………. 8
LITERATURE REVIEW ………………………………………………………………………………………………………………. 8
2.1 INTRODUCTION ……………………………………………………………………………………………………….. 8
2.2 RELATED PAST WORKS ……………………………………………………………………………………………… 9
2.3 THE QUEUING SYSTEM ……………………………………………………………………………………………. 13
2.4 BASIC OF QUEUING THEORY …………………………………………………………………………………… 14
2.4.1 THE INPUT AND OUTPUT PROCESSES ………………………………………………………………… 14
2.5 CHARACTERISTIC OF A QUEUING SYSTEM …………………………………………………………………. 15
2.6 EXIT/ DEPARTURE ………………………………………………………………………………………………………. 18
2.7 TYPES OF QUEUING SYSTEM ……………………………………………………………………………………. 18
2.8 PROPERTIES OF SOME SPECIFIC WAITING LINE MODELS ………………………………………………….. 21
2.9 NOTATIONS FOR EQUATIONS ……………………………………………………………………………………….. 22
2.9.1 Infinite queuing model …………………………………………………………………………………….. 22
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2.9.2 Finite queuing model …………………………………………………………………………………………….. 22
2.9.3 Important assumptions for a queuing model ……………………………………………………… 23
2.9.4 Suggestions for managing queues …………………………………………………………………….. 24
CHAPTER THREE …………………………………………………………………………………………………………………… 25
RESEARCH METHODOLOGY …………………………………………………………………………………………………… 25
3.1 Introduction ………………………………………………………………………………………………………….. 25
3.2 Methods of Data Collection …………………………………………………………………………………….. 25
3.2.1 Primary Data ………………………………………………………………………………………………….. 25
3.2.2 Secondary Data ………………………………………………………………………………………………. 26
3.3 Data Collection Process …………………………………………………………………………………………… 26
3.3.1 Yusuf Dantsosho Memorial Hospital ………………………………………………………………….. 26
3.4 Method of Data Analysis …………………………………………………………………………………………. 26
3.4.1 Mathematical/Analytic waiting line analysis. ……………………………………………………… 27
3.4.2 The mean arrival rate …………………………………………………………………………………………….. 27
3.4.3 The mean service rate ……………………………………………………………………………………………. 27
3.4.4 Little`s Formula …………………………………………………………………………………………………….. 27
3.4.5 Operating Characteristics of the Multiple Server Model with Infinite Population ………….. 29
CHAPTER FOUR ……………………………………………………………………………………………………………………. 31
4.1 DATA PRESENTATION AND ANALYSIS ………………………………………………………………………….. 31
4.1.1 Presentation of data collected at the female section of the out-patient department of Yusuf Dantsoho Memorial Hospital from Monday (23rd –May-2016) to Friday (27th –May-2016). 32
4.2 The operating characteristics at the two sections in the Female unit at the OPD of Yusuf Dantsoho Memorial Hospital from Monday to Friday. …………………………………………………………… 50
4.3 Data Collection and Presentation for Questionnaires Administered to Patients ………………….. 59
4.4 USING QUEUING MODEL (QM) FOR WINDOWS SOFTWARE TO MODEL CASES …………………… 62
CHAPTER FIVE ……………………………………………………………………………………………………………………… 65
SUMMARY, CONCLUSION and RECOMENDATION…………………………………………………………………….. 65
5.1 Summary ……………………………………………………………………………………………………………………. 65
5.2 Conclusion ………………………………………………………………………………………………………………….. 66
5.3 Recommendations ………………………………………………………………………………………………………. 67
REFERENCES ………………………………………………………………………………………………………………………… 69
APPENDIX ……………………………………………………………………………………………………………………………. 73
QUESTIONNAIRE ………………………………………………………………………………………………………………….. 73
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CHAPTER ONE

INTRODUCTION
1.1 BACKGROUND OF THE STUDY
Out-patient department (OPD) services are one of the most critical aspects of hospital administration. The OPD reflects the performance of the hospital as the first point of contact between the patient and the hospital staff, therefore ensuring high standard for medical treatment as well as other service will be essential in improving upon the efficacy of the current first line treatment for patients who visit various OPD centres in Nigerian hospitals. Many out-patient department (OPD) centres in Nigeria are confronted with long waiting times, delays and queues of patients.
Typical questions challenging hospital managers include: How should they optimally allocate their limited resources? How much exam rooms do they need? How much physicians and supporting staff do they need? If they increase or decrease the amount of exam rooms and/or staff, how would this affect patient waiting time, the length of a medical treatment and the total time spent in clinic by patient?
The amount of time a patient waits to be seen is one factor which affects the utilisation of health care services; patients perceive long
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waiting times as barrier to actually obtaining services (kurata et al 1992). The degree to which health consumers visit OPD centres are satisfied with the services rendered is strongly related to the quality of waiting experience, therefore effectively managing patient flow in an out-patient unit is a key to achieving operational excellence as well as ensuring clinical quality.
Waiting time can be defined as the time a patient waits in the out-patient department (OPD) unit before been attended to by a physician. Healthcare is riddled with delays. Almost all of us have waited for days or weeks to get an appointment with a physician or schedule a procedure, and upon arrival we wait some more until being seen. In hospitals, it is not unusual to find patients waiting for beds in hallways, and delays for surgery or diagnostic tests are common. Delays are the result of a disparity between demand for a service and the capacity available to meet that demand. Usually this mismatch is temporary and due to natural variability in the timing of demands and in the duration of time needed to provide service. A simple example would be a healthcare clinic where patients walk in without appointments in an unpredictable fashion and require anything from treatment of malaria to the setting of a broken limb. This variability and the interaction between the arrival and service processes make the dynamics of service systems very complex. Consequently, it’s impossible to predict levels of congestion or to
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determine how much capacity is needed to achieve some desired level of performance without the help of a queuing model.
In view of these many challenges confronting the health care sector in a developing country such as Nigeria, the out-patient department/unit is not immune and has its own fair share of challenges, over the years investment have been made by government in improving upon existing hospital facilities and the construction of new ones, but the challenge of overcrowding in out-patient units of most government hospitals still persist and still a source of concern to both hospital management, government and other stake holders.
The health care delivery system in private hospitals are perceived to be better than that of public hospitals, but majority of Nigerians rely on government hospitals for health care service which is as a result of the higher cost in assessing private health care facilities due to low income levels of many Nigerians, therefore a large number of patients patronise public hospitals which results in overcrowding and longer waiting times.
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1.2 STATEMENT OF PROBLEM
Queues and overcrowding in public hospitals in Nigeria has been a challenge to both government and hospital administrators on one hand and patients on the other hand. Several factors have been identified as been responsible for this trend, these factors includes the relatively low cost of service in public hospital as compared to private hospitals, inadequate infrastructure, shortage of health care personnel and the inability of hospital administrators to deploy effective operations management techniques in the management of queues .
1.3 RESEARCH QUESTIONS
This study intends to answer the under-listed question and proffer necessary solutions.
– How to optimally allocate available resources i.e. examination rooms, physicians, and supporting staff which are limited
– Suggest a system to reduce patient wait time in public hospitals.
– Improve access to healthcare in public hospitals.
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1.4 AIM/OBJECTIVES
The main aim of this study is to optimise the female section of the out-patient department (OPD) of Yusuf Dantsoho memorial hospital (public hospital);
(i) To examine using waiting line model patients flow in the out-patient department of Yusuf Dantsoho memorial hospital.
(ii) To determine the performance measures of the OPD.
(iii) To examine the effect of varying these parameters on the system.
1.5 JUSTIFICATION OF STUDY
1 This study will be of immense benefit to hospital administrators in making decisions on how resources can be optimally allocated.
2 This study will go a long way in assisting government in proper policy formulation.
3 The study will have positive impact on the economy, where hitherto time spent on queues can be engaged in productive activities.
4 The study will help in saving lives.
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1.6 SCOPE OF THE STUDY
This study covers the female section of the out-patient department of Yusuf Dantsoho memorial hospital Kaduna, Kaduna state, Nigeria the choice of the female section of the OPD is as a result of long queues and long waiting times experienced by patients before getting service. The scope of this study is limited to obtaining both primary and secondary data. The primary data was sourced by the researcher by monitoring patient (folders) at various sections of the OPD and the secondary data was sourced from the records section, the data collected was for a period of 5 days from Monday 23rd-05-2016 to Friday 27th-05-2016 between the hours of 6.00 am to 12 noon
1.7 LIMITATION OF THE STUDY
The study was confined to the female section of the out-patient department of Yususf Dantsoho memorial hospital Kaduna, this implies that results may be peculiar to the chosen case study and may be of limited generalization except for health care institutions with similar characteristics in terms of patients flow and resources.
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1.8 STRUCTURE OF WORK
The thesis consists of five chapters in which chapter one presents the introduction to the background of the study, objectives of the study, justification of the study, scope and the limitation of the study. Chapter Two consist of the literature on queuing system, types of queuing model and queuing performance parameters. The third chapter concentrates on research methodology. This addresses the issues on the description of case problem, research design, data collection process, instruments and steps adopted for investigation. The data presentation and analysis of primary and secondary data are presented in chapter four which using queuing theory. The last chapter centres on discussion of the result (specific and general results), conclusion, recommendations and suggestion for further studies.

 

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