How large is the Opportunity Cost of Queuing in Service Centres? Evidence from Eastern Nigeria
By
Uzochukwu Amakom
[email protected]
Department of Economics Nnamdi Azikiwe University, Awka, Nigeria
September 2008
Abstract Time is a perishable resource while delay is dangerous and expensive. In the face of the long delays experienced by patrons of service outlets in Nigeria resulting in long queues, it became necessary to study the implications of these long queues in terms of cost since most studies carried out stopped at waiting time estimation. Utilizing data collected from direct observation, personal interviews and questionnaires in service centers within the south east and south-south geopolitical zones of Nigeria formerly known as the Eastern Nigeria, estimates of some queuing situations parameters were obtained, including a forecast of the effect of an increase in the number of service providers on the efficiency of service delivery. The study found out that considerable time are wasted by customers in banks, hospitals and post offices due to inadequate staffing, incompetence of service providers, non compliance with the required queue discipline, lack of automation of necessary facilities, etc and this considerable time has some huge costs. Consequently, from the forecasts about the effect of an increase in the number of service providers, the study found a positive effect that will lead to enhancement of service delivery, reducing unemployment and improvement in national welfare.
1.1
Introduction
Time is a major economic resource, which its use has to be optimized always. More time and money for one thing means less time and money for other things. The time available to any economic agent has alternative uses, for leisure or for work (Ashley 2006). The number of hours devoted to work determines the individual’s wage. Apart from situations of work or leisure, economic agents sometimes commit considerable amounts of their time when they come into service situations for service. Typical of Nigeria, customers wait for hours to get service without the service providers feeling there is an opportunity cost for the wasted time. May be, the lack of economic growth in the country is traceable to this economic waste and the economy will begin to grow if this waste can be minimized. Service delivery in places like Post offices, Hospitals, etc is so vital to communities because lack of essential ingredients to perform exceptionally well imposes a lot of hardship on the users. With good employee attitudes and equipment, services will be provided efficiently which will facilitate business growth and survival. But efficient service delivery is not at the zenith in Nigeria yet hence it will not be out of place to continue to search for how optimal improvements can be made to the welfare of Nigeria by improving service delivery for patrons arriving for services like stamps buying, postal and money order clearances, letter registration, express postages, etc in the post offices; and patients waiting to receive medical attention and treatments, laboratory tests, etc in the hospitals. An arriving customer may find that he has to wait in a line on entering these centers when he finds another customer on line being served. If the rate of service is lower than the rate at which customers arrive, then waiting line develops and Queuing theory can be used to examine and solve the associated problem. In service oriented organizations like Post Offices and Hospitals where attaining organizational goals are largely dependent on the quality of human resources available, and where policies focus on service delivery with the attendant profit motive, there is need to evolve methods that would make for better efficiency in service delivery. Gouldner (1985) had stated that “the task of management in any given organization is to co-ordinate activities for the attainment of organizational objectives and the concomitant need to secure maximum employee co-operation to achieve such goals”. Obviously, this presents serious constraints to almost any effort to improve performance and productivity in any business organization since a service organization, for example, also depends on other factors such as the number and arrangement of service providers to secure efficient service delivery. Failure on the part of the management to effect a smooth flow of its customers would also result in long queues, customers frustration and loss of customers which will lead to eventual erosion in the organization’s profit resulting to an increase in the country’s unemployment crisis courtesy of retrenchment when these Outfits could no longer break even. In other words the welfare of the entire nation is then affected. Queuing, model therefore comes in to properly match the service pattern to the rate of arrival of customers or work to be done. For instance, a patient arriving at the reception in the hospital waits in line for his card/file to be processed and treatment effected, he departs (leaves) the hospital thereafter.
1
Waiting in line or in a queue is now part of everyday life but waiting too long for some type of activity might be inconvenient and some might prove fatal because its cost is always very high and can be a good or bad recommendation to any public outfit. Likewise the cost of improving services thereby reducing waiting time might sometime mean providing an additional service mechanism, which varies greatly depending on the type of services to be rendered. The decision maker or manager of the system that provides the service is concerned both with whether adequate services are being rendered or the clients have to wait too long and with whether the service facilities are used efficiently or the facilities are idle. In some situations, deciding on the number of service providers is made easy by having available a supply of service providers who can be otherwise employed. In other situations, a decision to maintain a particular number of service providers must not be taken lightly. For example, enlarging a clinic represents a commitment in a facility that cannot be alternatively employed. So, it must be established beyond reasonable doubt that the additional facility is warranted. Queuing theory, an operational research optimization technique, helps to bring these variance situations to optimum. 1.2
The Problem
Despite the loss in man-hours due to industrial actions in Nigeria, waiting time in public service centres is increasing by the day resulting to another aspect of loss in man-hours. The situation has kept efficient service delivery at the back door hence it will not be out of place to continue to search for how optimal improvements could be achieved. That was the case in the United States of America staffing system before Churchman (1987) developed a letter staffing system using queuing analysis that achieved an implementation plan which established service levels, line staff interaction, control performance, evaluation and follow-up actions which reduced labor cost by approximately $81 million which resulted to improved service. In Nigeria Loss in man-days from 1970 to 2000 rests on an average of 19 days aside from non-working days (computed from Industrial Relations Statistics, CBN Statistical Bulletin various issues). See the chart below: Man Days Lost and Work Stoppages in Nigeria (1970-2005)
M an-Days Lo st Wo rk Sto ppages
30,000,000 25,000,000 20,000,000
15,000,000 10,000,000 5,000,000 0
Source: CBN annual Reports and Statement of Accounts 2006 and CBN Statistical Bulletin 2006
2
The unsettled industrial relations climate during 1986 to 1998 led to an average of 157 industrial disputes pr anum and lost in man-days1 increasing to 234,307,748 from 461,345 giving an average of 27.39 million man-days lost per year (Ibe, 2000:18). Despite huge losses recorded due to industrial actions, Nigeria patrons are still observed to waste much time while receiving service in public centres like post offices and hospitals. More than six minutes (6) or more are wasted in receiving services from some post offices (Onyia, 1987) while some stay more than 40 minutes in receiving services in some hospitals and banks (Amakom, 2002). These are services that do not require more than three minutes in advanced countries. “Time is Wealth” is a common and popular saying, which implies that patrons could not afford to persistently wait in service outlets to be served without losing enormous amount of income. When there are alternatives to customers they can go to them but in some cases there no viable alternatives. Private couriers are springing up by the day because of the ineffectiveness of the Nigeria postal system while private hospitals are the order of the day since the public hospitals are deteriorating day in day out in service provision. Do we suggest that everyone should go to the private hospitals with its exorbitant charges to receive treatment when we know that more than 70.2 percent of the population are living under one dollar per day in Nigeria (Human Development Report 2002). Improvement of service delivery should not be left out in solving the numerous economic problems in Nigeria. If the length of the queue tremendously increases in magnitude, service delivery will deteriorate and lots of resources will be lost because delays are known to be dangerous and expensive. The situation of waiting in line leading to long queues is ‘sine a quo non’ to balking2 and Reneging3, which is a threat to the efficiency and growth of these outfits (Amakom 2002). In order to arrive at an optimal decision, the management board should need a guide to direct them on the best course of action since unaided mind cannot go far in achieving the overall objective of any establishment. More so, in service oriented outfits, the task is enormous because a little error can lead to insolvency of such establishment causing, in some cases, a general economic problem. Furthermore, there is a problem of risk and uncertainties regarding the behavior of customers and resources such that the management finds it difficult to choose the best decision among the alternative decision possibilities. Previous studies only dealt with the measurement of waiting time without really taking deep in sight on the costs of these waiting times. This study is therefore aim as to providing in sight to the cost of the waiting time and the optimum number of service providers that will lead to improvement in the economic welfare of the service centres and the country at large. This study is therefore directed at surveying and examining critically the problems encountered in public service delivery systems in order to identify the nature of the problems of such service outlets and then establishing how the problems can be solved. 1
Note that man-days lost are calculated using the number of workers involved in the industrial action. Balking refers to a situation where a customer refuses to join the waiting line because it does not suit his/her need or interest. 3 Reneging refers to a situation where a customer enters the line and leaves without completing his/her transactions due to impatience. 2
3
1.3
Objectives of the study
The major objective of this study is to find out the opportunity cost of loss in man hours observed in most public service delivery centre in Nigeria thereby seeking the correct mix of service providers and activities that will speed up serving processes in order to realize an optimal cost and utmost efficiency in service organizations. More specifically, the study seeks to 1. Estimate the mean waiting time of the customers and possible cost associated with waiting time in the service delivery centres; 2. Identify the factors responsible for delayed service delivery; and In the light of the findings suggest ways of providing more efficient services at these outfits.
2.1 Review of Literature Many authors have documented the use of optimization techniques in practical day-to-day or yearly operations using some operational research tools. The scope of this literature will be limited to applications of Queuing modeling approach to real-life situations in order to aid and speed off decision-making process. Decision-making was noted by Wagner (1989) as a process of choosing among alternative courses of action for the purpose of attaining a goal or goals. To Keller (1993) managerial decision-making is synonymous with the whole process of management. He also recommended that managers must become more sophisticated; they must learn how to use new tools and techniques that are being developed in their field. These newly developed tools employ quantitative approach and are grouped into Operations Research (O.R). The O.R approach adopts the view that managers can follow a fairly systematic process for solving problems. Therefore it is possible to use a scientific approach to managerial decision-making. In the words of Wagner (1989), operations research technique is a scientific approach to problem solving for executive management. Churchmen et al (1987) defined O.R as an application of the scientific method to problems arising in the separation of a mathematical model and the solving of these problem by resolving the equations representing the system.. While Wittle (1991) describe O. R as a tool for providing management with the facts and figures needed for making effective decisions? To Taha (1992), O.R seeks the determination of the best course of action of a decision problem under the restriction of limited resources. He also noted that it is often associated with almost exclusively with the use of mathematical techniques to model and analyze decision problems. On that note, Ngene (1997) believed that all mathematical techniques used as, aid to decision making are often called operations research. It is interesting and perhaps of particular importance to note that the origin of queuing theory is to be traced to telephone network congestion problems. It henceforth continued to present challenging problems to the many capable investigators working in the field worldwide. Erlang, a Danish telephone Engineer started his work in 1909 in an attempt to determine the effort of fluctuating demand (arrival) on the utilization of automatic dial equipment. Then in telephony, the basic ideas that were of special interest to the investigator were when a call was host or there was a delay (or mixed cases). If the line is engaged, the caller either waits or his call is lost. This appears to be the two quantities: a lost system and a waiting system. 4
The pioneer of queuing theory Erlang (1909) studied the telephone traffic congestion with the objective of meeting uncertain demand for services at the Copenhagen telephone system and he finally came out with what is today developed and called the Queuing theory. Therefore, waiting line or queuing theory came into existence through A.K Erlang. Since then, it has had extensive application in industry and other areas. It has been applied to variety of business and economic situations, however, chains of supermarkets have used queuing to determine the number of checkout stations needed for the smooth and economic operations of their stores at various times of the day. Queuing is one of the most important topics in operations research today and areas of successful applications include the analysis of telephone system; Bank operations, computer time-sharing, Hospitals, Post-offices, etc. Edie (1974) has used a variety of ideas from the steady state of queuing theory to an optimum schedule for operating different number of booths at different times of the day. His work encouraged savings in toll collection expenses and has yielded adequate services. Brigham (1975) studied the optimum number of clerks to be assigned to tool-crib counters in use in the Boeing factory area. The crib stoned the implements which the machines made use of always. The complaints by the front line supervisors was that their machines waited too long in line before getting a tool at least hence the problem is how many more crib-clerks to be employed to match with the costs and the result gave the optimum number. In yet another study, Sespanlek (1996) used the probability of delay (P>0) for a Poisson input with an exponential service-time distribution in multiple channels and ordered queuing. He obtained the optimum number K, of inspectors required to inspect a product while in process. The service time here included the time it took the inspector to walk to the service station. In his work, Delcourt (1989) studied the problem of how much oil each of a number of pumping stations should handle, taking into consideration an accepted waiting risk and following the fact that as the global demand for oil increases, the tendency is for the pumping machine to work longer. Since machines do not operate at all the time, then the incoming demand suffers long waiting which resulted in an un-accommodated queue. It was required to determine the schedule of time during which the pumps operate accepting some delay in satisfying the demand. Queuing theory has been applied to car (automobile) traffic congestion by Borel (1982). The theory helped in finding a permanent solution to the congestion. Also, in their study, Schiller and Tavin (1979) have used Monte Carlo simulation methods to determine the extent of a new Truck dock facilities that would be required at one consolidated warehouse to handle the volume of traffic formerly accommodated at three warehouses. Tanner (1997) made use of Borel’s (1982) ideas to study the problem of interferences of two queues of traffic approaching a single lane from opposite directions while Ani (1993) attempted to find solution to the long queues, which build up, at the Nsukka General Post-Office. Through the use of Queuing models, he found that the average turn round time in queue could be reduced by: (a) Changing the existing model of single services to multiples services in parallel; and (b) Increasing the number of service providers in the system. 5
Abayomi (1984) examined the traffic situation in and around University of Lagos with a view to suggesting solution to the problem of long queues usually present on the University of Lagos (UNILAG) Campus roads. He also used queuing models to provide results which validated the need for the new one-way order adopted for most areas of the University roads especially in the area of reducing to a considerable extent, the incidence and magnitude of traffic jams experienced during traffic peak hours of 9.40 am to 12 noon on the roads. Stevenson (1992) used a steady state version of the M/M/S model to determine the required number of ambulances in a region while Bell and Allen (1969) developed queuing model for determining the number of ambulances required to respond immediately to 95 or 99 percent of Service requests. The New York State Child Abuse and Maltreatment Register Telephone Reporting System relates telephone system as a queuing model and queuing analysis was used to determine staff and equipment requirement. Ezezue (1984), studied the queuing behaviour of students at the Zik’s Refectory of the University of Nigeria Nsukka and observed a mean-waiting time of 15.95 minutes, a mean inter-arrival time of 0.05 minutes and a mean service time of 19.53 minutes. He attributed this unappreciable incidence in service time to problems of insufficient number of plates, customers on special diets and insufficient quantity of meat. Onyia (1987) also studied the queuing behaviour of customers at the Nsukka General Post Office and he observed a mean waiting-time of the customers in the post office for two days to be 3.42 minutes and 6.35 minutes respectively. Okereke (1985) monitored the queuing behaviour of patients in the outpatients department of the University of Nigeria Medical Center and recommended that the mean Service time computed should be used to establish an appointment system for the Medical Center. This, he argued, would reduce the long waiting time he observed for patients in the center. Nweke (1989) investigated the queuing profile of students at the new refectory to the same University and observed a mean-waiting time for each of the two counters to be 15.57 minutes and 11.95 minutes respectively. She also determined the mean-service time to be 21.19 seconds and 17.64 second respectively. Kostas (1983), relating queue to the operation of a medical first-aid office in a large factory covered by one registered nurse, explained that if service providers (nurses) are not enough, patients will have to wait for treatment and in this respect, queuing problem consist of finding the optimum cost of service and reducing waiting to a minimum. He also developed and used the optimization model below: Minimize E(TC) = E(SC) + E(WC) where E(TC) = Expected Total Cost E(SC) = Expected Service Cost E(WC) = Expected Waiting Cost. Churchman (1987) developed a letter staffing system using queuing analysis to achieve the following objectives. 6
i) ii) iii)
A staff planning system that collected and analyzed data and determined staff requirement. An administration System that administered part-time staff, back up personnel and a management reporting system. An implementation plan that established service levels, line staff interaction, control performance, evaluation and follow-up actions which reduced labor cost by approximately $ 81 million and service was improved.
Bowman et al (1981) developed a model to evaluate the sensitivity of expected passenger queuing at terminals to service frequency and schedule reliability. In his opinion, this model represents an improvement over previous models because it explicitly incorporated a passenger decision-making process, rather than assuming that passengers arrive at random instants in time. In building time models, using data from Chicago area, they assumed that in many circumstances, passengers arrivals may not be random, rather users will, to some extent, co-ordinate their arrivals to coincide with the schedule service in an attempt to reduce their waiting time. They conclude after several tests against traditional models, that passenger’s choice model represent a significant improvement in predictive ability and that the passenger waiting time is much more sensitive to service frequency than previously believed. Most of the studies reviewed stopped at either mean waiting time or a sensitivity analysis of the queuing situation. None of the studies reviewed went further to attach costs to waiting time or a forecast of the number of service providers that should be added to the service delivery centers. This lacuna is what this paper sought to close. 3.1 Methodology Data for this study were collected from twelve and eight General Hospitals and General PostOffices (GPO) respectively in the states of Enugu, Ebonyi, Cross River, Imo, Abia and Anambra of Nigeria using a Stratified sampling technique. The survey was carried out between January and June 2006. The methods employed during data collection were direct observation, personal interview and questionnaire administering. Data were collected for (5) days each for all the observed outlets. The study is limited to the General Out-Patient Department (GOPD) of the hospitals and the Stamp/Letter registration counters of the Post Offices. The observed data were tested for goodness of fit before its usage. Questionnaires were also carefully administered to customers at the places of study. A total of two hundred and fifty seven questionnaires were returned from the Hospitals while one a hundred and fifty four questionnaires were returned from the post offices. Oral interviews were conducted with the officials. 3.2 Assumptions The following assumptions were made of the service outlets, which are in accordance with queue theory. They are: 1. Arrival time λ are random, while Inter - arrival time is Poisson distributed (validated). 2. The service rate, µ, follows an exponential distribution. 7
3. There is no shortage of service materials at any of the service situations, i.e., no shortage of funds in the bank, or shortage of stamps in the post office or drugs in the hospital. 4. The Service providers are working at their full capacity. 5. The queue discipline is First – Come, First – Served (FCFS). There is no priority classification for any arrival. 6. There is no limit to the number of the queue (infinite). 7. Once in the queue, an arrival does not “renege” or leave the line because of no fast progression. 8. Service rate is independent of line length; service providers do not go faster because the line is longer. From the above observations and assumptions, the system should be referred to as an M/M/S system which is a system with many service providers, infinite capacity and a queuing system having a poison input and exponential service time. 3.3
The Model
The model adopted in this study was an extended version of Coffman (1969), Keller (1993), Hillier & Lieberman (1995) and Taha (2000). From the model the average rate at which customers arrive per unit of time was referred to as the arrival rate and can be thus represented by λ while the average rate of services completed in a unit of time was the service rate represented by µ. In order to determine the average Utilization, which is the ratio of the average arrival rate to the average service rate the arrival rate was taken as a reciprocal of the ser vice rate. This is known as the Traffic Intensity represented by (ρ): Traffic Intensity
( ρ ) = λ ..................................................1
µ
The value of the traffic intensity is expected to lie between o and 1. If there is no traffic in the system, the traffic Intensity is O. If, however, the traffic Intensity is I or more the queue will, theoretically, be of infinite length. The study assumed that all service providers have the same mean service time and that the service time for each is exponentially distributed. That is, the service rate for each is Poisson. For a Poisson-Poisson multiple – channel – service facility with mean arrival rate λ, mean service rate µ and the number of service channels c, the queue characteristics are given by some equations below: The probability that the system is completely idle: −1
c ( λ )c λ ) c −1 ( µ µ P0 = +∑ ................2 λ i i =u µ C !(1 − c ) Where Po is the probability that the system is idle λ is the arrival rate? 8
µ is the service rate? C is the number if service providers When ρ replaces λ/µ (2) became: −1
i c −1 ( ρ )c ρ + ∑ Po = ........................3 C !(1 − ρ ) i =0 i c The system is Idle when the probability coefficient is more or I and on the reflex when the coefficient is less than I, the system is busy. The system is always busy if the coefficient is less than 0.3 (Lucey, 1989). When the system is busy, the expected number of customers waiting in line Nq to be served per unit of time was given by: N q = (nq ) N .................................................4
Where N is the total number of customers observed while nq is given by: ( ρ )c +1 nq = * P ...........................5 C.C !(1 − ρ ) 0 c At the same time the expected number in the system Ns waiting to be served was: N s = (ns ) K ................................................6 K is defined as any number waiting in line that implies queue to the observer. ns = (ns + ρ ).......................................................7 Obviously when there exists a number of customers in the queue, there is likely to be an expected number of minutes or hours a customer waits in the queue. Tq represents the expected waiting time in the queue and is given as:
Tq = tq (60 min(1hr ))...................................8 Where tq =
nq
λ−
Note that here λ- (the mean waiting time) denotes N/T where N is the Total number of customers observed and T the Total time taken by all the observed customers to arrive. The expected time lost by a customer while waiting in the queue is thus calculated as against the normal time the service would have taken hence its result is given as n times as against the normal waiting time. The expected time lost denoted by TL is thus given as: Tl = (λ − )tq ................................................9 While the opportunity cost of waiting (Cw ) is given by: Cw = ϑTl ....................................................10 Where ℘ is the average opportunity cost of an idle hour provided by any standard measurement?
9
From the model above the traffic intensity, the probability that the system is idle, the expected number in the waiting line, the expected number in the system, the expected waiting time in the queue, the expected time lost waiting and the average cost per customer for waiting were derived and the summary presented in tables 4.1 - 4.4. 3.4 Modeling for Causes of Waiting Time In order to find out the influence of the observed causes of increase in waiting time using the responses of the customers from the questionnaire carefully administered a model of qualitative choice was employed. Since the dependent variables take the values of 0 and 1(binary, where 1 represents Yes and 0 represents No) the model employed is the Logit Model. The Logit model overcomes the draw back of the linear probability because it is based on the cumulative logistic probability function, which is easier to use computationally (Pindyck and Rubinfeld, 1998; 308). Applying the Logit model, waiting time was modeled as a function of inadequate service facilities, inefficiency of service providers and insufficiency of service providers. Detailed results are presented in section 4.2. 4.1
Results Presentation and Data Analyses
The tables below show the result of the mean waiting time, arrival rate, the service rate and the number of service providers at the service delivery centres observed. Table 1: Summary of the Mean Arrival Rate, Waiting time and Service Rate States
Anambra
Enugu
Ebonyi and Cross River
Abia and Imo
Hospital 1 Hospital 2 Hospital 3 Hospital 1 Hospital 2 Hospital 3 Hospital 1 Hospital 2 Hospital 3 Hospital 1 Hospital 2 Hospital 3 Grand Mean
Average Waiting Time (Minutes) 64 59 73 56 35 62 45 57 53 43 29 51 52.25
Average Number Served (in 1 hr)
Average Number of Arrivals (in 1 hr)
Number of Service Providers
38 41 43 49 34 40 18 19 20 41 25 35 34
57 63 70 73 43 68 29 34 35 59 36 55 52
3 4 4 4 4 4 3 2 2 4 4 3 3
Source: 4Survey by Author.
4
The survey was carried out from the 22nd of October to the 3rd of December in the selected service delivery centres within the eastern part of the country.
10
Table 4.2: Summary of the Mean Arrival Rate, Waiting time and Service Rate States
Average Waiting Time (Minutes)
Anambra Enugu Ebonyi and Cross River Abia and Imo
Post Office 1 Post Office 2 Post Office 1 Post Office 2 Post Office 1 Post Office 2 Post Office 1 Post Office 2 Grand Mean
7 9 5 9 8 6 10 9 7.875
Average Number of Arrivals (in 1 hr) 196 203 221 295 101 96 207 211 191
Average Number Served (in 1 hr) 127 149 164 219 81 64 146 151 138
Number Service Providers
of
5 4 4 6 4 4 5 5 5
Source: Survey by Author. From table 4.2 above, the mean waiting time at the selected Nigerian hospitals is found to be fifty two (52) minutes while that of the post offices is approximately eight (8) minutes. This implies that patients have to wait for up to fifty-two minutes before being attended to in the hospitals and eight minutes in the post offices. These are services that do not take more than four and two minutes in advanced countries. The detail analyses is presented in tables 4.3 and 4.4. Table 4.3: Detailed Hospital Data Analysis Result States
Anambra
Enugu
Ebonyi and Cross River Abia and Imo
Waiti ng Time Hospital 1 Hospital 2 Hospital 3 Hospital 1 Hospital 2 Hospital 3 Hospital 1 Hospital 2 Hospital 3
64 59 73 56 35 62 45 57 53
Number of Service Provide rs © 3 4 4 4 4 4 3 2 2
Hospital 1 Hospital 2 Hospital 3 Grand Mean
43 29 51 52.3
4 4 3 4
Number of arrivals (λ)
Number Served (µ)
Traffic Intensi ty (ρ)
57 63 70 73 43 68 29 34 35
38 41 43 49 34 40 18 19 20
1.5 1.5 1.6 1.5 1.3 1.7 1.6 1.8 1.7
0.24 0.28 0.26 0.29 0.34 0.24 0.21 0.25 0.27
32 18 21 17 13 14 44 40 27
102 60 66 54 42 45 138 120 87
34 18 18 14 18 12 19 29 47
7.6 7.7 10.6 8.5 3.1 8.7 2.7 4 3.8
1338 1355 1866 1496 547 1531 475 704 669
59 36 55 52
41 25 35 34
1.4 1.4 1.5 1.5
0.3 0.3 0.22 0.27
16 16 40 25
51 51 123 78
16 26 43 34
5.2 2.1 5.8 5.8
915 370 1020 1020
Source: Author’s computation.
11
Po
Nq
Ns
Tq
TL
Cw
Table 4.4: Detailed Post Office Data Analysis Result States
Anambra
Enugu
Ebonyi and Cross River Abia and Imo
Number of arrivals (λ)
Number Served (µ)
Traffic Intensi ty (ρ)
7
Number of Service Provide rs © 5
196
127
1.5
0.28
28
42
15
1.7
299
9
4
203
149
1.4
0.29
42
58
13
3
528
5
4
221
164
1.3
0.29
40
54
12
1.5
264
9
6
295
219
1.3
0.29
11
15
4
0.8
141
8
4
101
81
1.2
0.25
32
39
9
1.8
317
6
4
96
64
1.5
0.28
74
111
27
3.9
686
10
5
207
146
1.4
0.27
19
27
6
1.5
264
9
5
211
151
1.4
0.27
29
39
8
2.1
370
7.8
5
191
137
1.4
0.28
34
48
12
2.1
370
Waiti ng Time Post Office1 Post Office2 Post Office1 Post Office2 Post Office1 Post Office2 Post Office1 Post Office2 Grand Mean
Po
Nq
Ns
Tq
TL
Cw
Source: Author’s computation. The traffic Intensity or the Average Utilization which is the ratio of service rate to the arrival rate is more than unity in both the Hospitals and the post offices. In general, the traffic Intensity or the Average utilization should not be greater than 0.8 because it can be shown that the average time in the system increases dramatically above this value. This shows that the systems observed are busy all the time. The only way that the traffic Intensity can be kept at a reasonable figure is to provide adequate service facilities, assuming of course that the arrival rate cannot be controlled (Lucey, 1989). All the customers waiting in the queue to be served have left their various duty posts to receive service in these service delivery centers. Therefore, their inability to be served in good time represents enormous loss of man-hours to the nation since the waste of time in these outfits has a devastating effect (cost) on the productivity of operations where these customers work. On the average in the hospitals the time lost is 5.8 times what it is supposed to be while that of the post offices is about 2.1 times what it is supposed to be. These man-hours lost obviously result in reduced output with its attendant welfare loss in the economy. The cost of waiting for every individual differs depending on what the individual earns every hour. Some might have their cost of waiting in multiples of others people’s value. For the purpose of this study we employ the Nigerian Institute of Social and Economic Research (NISER) (2000) benchmark which suggest that for every idle hour the average opportunity cost estimate is about N176 for an average Nigerian worker. Using the above benchmark, we estimate that a customer loses between N547 and N1,867 at these service centres with an average of N1, 020 at the hospital and N370 at the Post Office courtesy of waiting time. If on the average we have about forty thousand patients in Nigerian hospitals it implies that the economy is losing over fourteen billion Naira or one hundred million US dollars at the end of each year. The said amount should not have 12
been wasted had it been that more hands are employed in these service delivery centres in the face of unemployment, which has hit 80 percent. 4.2
Results from Responses
From the analysis of the questionnaires administered to respondents, the average number of visits by a customer to any of these service outlets and the average duration of waiting are shown in the figure 2 below: Average Responses on Duration of Waiting and Visits
Average number of Visit Per month Average Waiting Time Per Visit
70 Time in Minutes
60 50 40 30 20 10 0 Hospital
Service Centres
Post Office
Source: Author’s computation. From the above figure, the observed waiting time (52.5 minutes) in the hospital is a bit lower than the response from the questionnaires (59 minutes) while that of the Post office is almost the same 7.8 minutes observed as against 8 minutes of respondents view. Further analyses of the questionnaires administered applying the Logit model revealed that inadequate service facilities, inefficiency of service providers and insufficiency of service providers have negative impacts on the waiting time of the customers. Furthermore, insufficiency of service Providers had more impact on waiting time. See the result below:
13
Result 1 Variable C WAITTIME
Coefficient Std. Error 0.692347 0.318605 -1.500973 0.004947
Hannan-Quinn criter. McFadden R-squared Total obs
z-Statistic 2.173059 3.196712
Prob. 0.0298 0.8441
1.316777 0.000117 257
From the above result, waiting time in hospitals and post offices increases when service providers are insufficient. The same applies to inadequate service facilities and inefficiency of service providers. On the reflex, preferential treatment meted out to customers reduces the waiting time of the customers concerned. 4.3
Effects of Increase in the Number of Service providers © on Waiting Time and Cost.
In general, the traffic Intensity or the Average utilization should not be greater than 0.8 because it can be shown that the average time in the system increases dramatically above this value. The only way that the traffic Intensity can be kept at a reasonable figure is to provide adequate service facilities, assuming of course that the arrival rate cannot be controlled (Lucey, 1989). It is an open secret that idle service facilities have some costs. For example, by adding more service points, even though the costs of customer’s waiting-time would be reduced, at the same time the cost of more service points might be astronomical. On the reflex, decreasing the number of service facilities will increase the cost of waiting though it will decrease the cost of idle facilities. The objective of queuing theory, therefore, is to help design a system that will enthrone an efficient service-delivery system that will optimize the sum of the costs of customers waiting and cost of idle facilities. Table 4.5 below shows the effect of an increase in the number of service providers © from three to four, five and six on the expected waiting time, the traffic intensity and the average cost for waiting. The computations assume that the arrival rate and the service rate remain the same. Table 4.5: Effect of increase in the Number of Service Providers Number Number Number Traffic ρo Nq Ns Tq of Service of arrivals Served (µ) Intensity Providers (λ) (ρ) © Hospital 4 52 34 1.5 0.27 25 78 34 Post Office 5 191 137 1.4 0.28 34 48 12 Hospital 5 52 42 1.23 0.26 14 45 19 Post Office 6 191 164 1.16 0.28 23 32 4 Hospital 6 52 51 1.01 0.45 3 9 5 Post Office 7 191 191 1.0 0.50 1 2 2 Source: Computation by Author 14 Service Centres
TL
Cw
5.8 2.1 2.2 0.9 0.8 0.4
1020 370 387 158 140 70
From table 4.5 above, an increase in the number of service providers in both centres yields a corresponding reduction in the expected waiting time, average utilization and average waiting cost. It would appear that the optimal number of service providers in these centres at an average level is six for the hospitals and seven for the post offices. This is so because if an extra service provider is added at this juncture idle time will increase which consequently have some costs too. Therefore at six and seven in hospital and post office respectively opportunity cost of waiting time of customers and the average probability of service providers being idle is optimized. 5.1
Recommendations
In the light of the findings of this study, some recommendations that would help in the management of the service centres within the area of observation and other similar service centres around the country in achieving the overall objectives are highlighted. General Hospitals should increase the average number of their Medical Personnel (Physicians) in the General Out-Patient Department (GOPD) i.e. the general division to at least six while Patrons in the Post offices at the stamp selling and letter registration counters should also be increased to at least seven in all the General Post Offices. Effort should be made to install mechanisms that would not permit people to move backward or forward in queues until they are served and make sure that no service is rendered to anyone not in line. The Nigerian Society should revert to the kind of elementary appreciation of queuing as demonstrated during the Mass Mobilization for Social and Economic Recovery (MAMSER) days and the advantages of orderly queues should be advertised in radios, televisions and posters. Training programmes should be re-designed for the service personnel of these service delivery centres in order to endow them with the necessary knowledge, skills and attitudes that would enable them render efficient and effective service to their numerous customers. Introduction of automated machines like computers, adding machines and counting machines will help in reducing the time involved in service delivery while customers need to exhibit higher queue discipline, which could be done from either the service providers and from the society. Finally, lectures and seminars should be organized to highlight to staff of public service delivery centres on the type of loss (cost) that accrue to both their establishments and the entire nation by directly or indirectly contributing to undue delays in service delivery. They should be encouraged to be time conscious, knowing that they will be contributing to national welfare by minimizing service delays by not trading words with customers or undertaking acts likely to disturb the efficiency of the service delivery mechanism. Enquiry clerks, especially in the hospitals, should be provided to help ignorant customers go through the delicate transactions without disturbing the system and also help the Physicians and Nurses to concentrate on the purely technical aspect of their jobs.
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5.2 Conclusion The study has successfully determined the service providers’ mix of service delivery centers as regards to Hospitals and Post Offices. In conclusion, therefore, the study has revealed that the cost of obtaining Health-Care and Postal services in terms of time committed to them in Nigeria is many multiples of what it is in developed countries. Therefore, there is need for the time spent on Hospitals and Post Offices transactions to be substantially reduced so that these Outfits will be effectively playing the role expected of them in providing prompt services and promoting the economic growth and development of this nation.
To enable these service centres and similar service outlets in the nation to grow in size and strength so as to compete effectively and favorably with others in the same industry both in the country and internationally, their management are advised to religiously implement the recommendations made. There is need for further research in similar and other service centres nation-wide and it should focus on how to further reduce the waiting time because waiting time is a function of the population of patrons and some parameters of the system. Criticisms and contributions will highly be appreciated. Bibliography Abayomi, H. (1988), “Computerization of the Queuing System in University of Lagos Main Cafeteria”, Journal of Economic Studies, Vol. 13, No.5
Amakom, U.S (2002), (Unpublished) “An application of Queuing theory to service delivery in different service facilities” M.sc Thesis, Department of Economics, Nnamdi Azikiwe University Awka, Ani, U. (1992), “An Analysis of long queues in Okpara Avenue Telecommunications Enugu”, Paper delivered at NITEL Seminar held on April 16th. Ashley C (2006). Queuing Cost. http://www.bsbpa.umkc.edu/classes/ashley/Chaptr14/sld005.htm Bailey, C. (1984), “Operations Research, Shaum’s Outline Series”, Pekin: Kin Keong Printing Co. Borel, E. (1982), “Sur L’emploi du Theoryme de Bernoulli”, Application au Probleme de Urguicuent Comptrend, Vol. 214. Bowman et al. (1981), “Applied Probability and Queues”, New York: John Wiley & Sons Ltd. Brigham, G. (1975), “On a Congestion Problem in Aircraft Factory”, Journal on Society Development, Vol.3, No.1 Brockemeyer, E(1974),”Erlangs Paper Translated to English”, Copenhagen: Copenhagen High Publishers. Chiang, A, (1984), “Fundamental Methods of Mathematical Economics”, Singapore: Mc- Graw Hill Books Company. Churchman et al. (1987), “An Introduction to Operational Research”, New York: John Wiley & Sons Inc. 16
Coffman, P et. al (1969), “Queues”, New York: John Wiley & Sons Inc. Delcourt, J.C. (1989),“Equipment Station de Pompage”, Revised Statistical Application, Vol.1, No.2. Eddie,L.C. 1974), “ Traffic Delays at Toll booths” Journal of Operational Research Society. Vol.2, No.4 Eddy, C.N. (1996), “A Century of Banking”, First Bank of Nig PLC, Lagos. Ezezue,U.(1984),“Queuing behaviour of Students at Ziks Refectory”, Journal of Management Studies. Vol.2, No.4. Fred, T. & Williams, K. (1963), “Reducing Voters Waiting”. Journal of Economic,. Vol.10, No.5 Gouldner, K. (1985), “Introduction to Management Sciences”, London: W.C Brown Publishers. Haight, V. (1983), “Operations Research”, London: S.K Jain Publishers. Hillier, S.F and Lieberman, G. J. (1995), “Introduction to Operations Research” Singapore, McGraw-Hill International Ibe, A.C (2000), “The Politics of Economic Policy reforms in Nigeria” Agulu, Levrene Publishers Joseph, M. & Salah, H. (1979), “Principles of Management”, New York: Mc-Graw Hill Inc. Keller, P.F (1993), “An Application of Queuing Theory to a Congestion Problem in an Out-Patient Clinic”, New York: John Wiley & Sons Inc. Kostas, U.N.(1983), “Introduction to theory of Statistics”, Tokyo: Mc-Gram Hill Kogakusha Ltd. Lipsey, G. et. al (1981), “Economics: Sixth Edition”, New York: Harper & Row Publisher Longeneck, C. (1990), “Making Management Decisions”, New Delhi: Oxford & B,H. Lucey, T. (1989), “Quantitative Techniques – An Instructional Manual”, London: DP Publishers Ltd Ngene, S.O. (1997) (Unpublished), “Operations Research Techniques in Managerial Decision Making”: M.sc Thesis, Department of Economics: Nnamdi Azikiwe University, Awka Nigeria Institute of Social and Economic Research (NISER)(2000). Report of a Study of Nigeria’s Manpower Stock, Abuja, Nigeria. Nweke, N. (1989), “ Queuing Profile of Students at the New Refectory”, Journal of Management Studies. Vol.4, No.9. 17
Okereke, H. (1985), “Queuing at the Out- Patient Department of University Nigeria Nsukka Medical Center”, Journal of Statistics. Vol.2, No.6. Onyia, U. (1987) (Unpublished), “Queue at Nsukka General Post Office”, Department of Statistics: UNN. Pindyck, R.S and Rubinfeld, D.L (1998), “Econometric models and Economic Forecasts: Fourth Edition” Singapore, McGraw-HILL International Editions. Robert, B. & Klekamp, R. Operational Research, Vol.28, No.4.
(1990),
“Queue
at
Toll
Booths”,
Journal
of
Schiller, M. & Tavin, I (1997), Simulation Principles, New York: John Wiley & Sons Inc. Sespanlek, L.J(1996),“An Application of Queuing Theory for Determining Manpower Requirements for an In-Line Assembly Inspection”, Economics Journal, Vol. 4. No.2. Taha, H. (1984), Operations Research-An Introduction, New Delhi: Prentice Hall of India Private Ltd. Taha, H. (2000), Operations Research-An Introduction, Sixth Edition, New Delhi: Prentice Hall of India Private Ltd. Tanner, E. (1982), Decision Support and Expert Systems: Management Support Systems, New York: Macmillan Publishers Co. Wagner, H. (1989), Operations Research-An Introduction, New York: Macmillan Publishers Co . Wittle, S.C (1991), Applied Operations Research, New York: John Wiley & Sons Inc.
-----------------(2006) “Queuing Theory - A Straightforward Introduction”. http://www.newdestiny.co.uk/andrew/past_work/queuing_theory/Andy
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