Introduction
This chapter is made up of the following sub-topics: techniques for accomplishing the state objectives, discussion on theoretical framework, gap in the reviewed literature, conclusion and recommendation.
Techniques for accomplishing the stated Objectives
To accomplish the stated objectives, the researcher must evaluate the relevant data to aid our position.
This study made use of secondary data which was obtained from the daily customer data of next time supermarket, as shown in the table below:
The one month daily customer data were shared by the supermarket manager as shown in Table 1.
Table 1. monthly daily customer counts
|
Mon |
Tue |
Wed |
Thu |
Fri |
Sat |
Sun |
|
|
1st Week |
470 |
427 |
429 |
492 |
663 |
973 |
1092 |
|
2nd Week |
456 |
445 |
536 |
489 |
597 |
1115 |
1066 |
|
3rd Week |
421 |
541 |
577 |
679 |
918 |
1319 |
1212 |
|
4th Week |
494 |
559 |
581 |
613 |
697 |
1188 |
1113 |
Calculation
I conducted the research during evening time. There are on average 400 people are coming to the supermarket in 3 hours time window of dinner time. From this we can derive the arrival rate as:
λ = 400 = 2.22 customers/minute
180
We also found out from observation and discussion with manager that each customer spends 55 minutes on average in the supermarket (W), the queue length is around 36 people (Lq) on average and the waiting time is around 15 minutes.
It can be shown that the observed actual waiting time does not differ by much when compared to the theoretical waiting time as shown below:
Wq = 36 customers = 16.22 minutes
2.22
Next, we will calculate the average number of people in the supermarket, that is
L = 2.22 x 55 mins =
122.1 customers
Having calculated the average number of customers in the supermarket, we can also derive the utilization rate and the service rate using
μ = λ (1+L) = 2.22 (+122.1) = 2.24
L 122.1
Hence, p = λ = 2.22 = 0.991
μ 2.24
With the very high utilization rate of 0.991 during evening time, the probability of zero customers in the supermarket is very small as can be derived using
Po = 1 – p = 0.019
The generic formula that can be used to calculate the probability of having n customers in the supermarket is as follows:
Pn = (1 – 0.991) 0.991n = 0.019 (0.991)n
We assume that potential customers will start to balk when they see more than 10 people are already queuing for the supermarket. We also assume that the maximum queue length that a potential customer can tolerate is 40 people. As the capacity of the supermarket when fully occupied is 120 people, we can calculate the probability of 10 people in the queue as the probability when there are 130 people sin the system (i.e 120 in the restaurant and 10 or more queuing) as follows:
Probability of customers going away = P (more than 15 people in the queue) = P (more than 130) people in the restaurant).
P131 – 160 = Σ160 Pn = 0.1534 = 15.34%
n = 131
Discussion on Theoretical Framework
The Little’s theorem was most appropriate for this study. This is because by the little’s theorem the mean queue length or the average number of customers (N) can be determined from the equation N = λT, where lambda (λ) is the average customer arrival rate and T is the average service time for a customer. This can be used to reduce flow time which can lead to reduced costs and higher earrings.
Besides, Little’s law gives a very important relation between the (L), the mean number of customers in the system, E (S) the mean so join time and z, the average number of customers entering the system per unit time.
Generally Little’s law can be applied in nay system in which the mean waiting time, the mean queue length and the mean throughput remains constant.
Queuing theory is useful in the determination of the amount of capacity that is needed (so that waiting times will be reasonable) and the ancient of space to be provided for customer waiting for service.
While Little’s law is convenient to use and gets us a decent approximation to most queuing questions, its clearly not perfect. For example process utilization must be less than 100% or else the line will grow to infinity (this is otherwise known as WIP explosion).
Gap in the Reviewed Literature
The reviewed literature extensively emphasized on the used of mathematical queuing models for solving queuing problems without giving cognizance to human factors.
Besides, the models as founds in Literature are base on certain assumptions about arrival rate and service time, hence the models are over-simplified, hence they are not intended for complex problems especially where there are many decision points and paths to take.
Specifically, considering Mathias work on restaurant queuing model constraints that were faced for the completion of this research were the inaccuracy of result since some of the data use was just based on assumption or approximation. We hope that this research can contribute to the betterment of restaurant in terms of its way of dealing with customers.
As our future works, simulation model for the by developing a simulation model we will be able to confirm the results of the analytical model allows us to add more complexity so that the model can mirror the actual operation of the restaurant more closely.
In the same vain, taking book at Smith’s work on 4-h completion time target in accident and emergency departments, A & E completion time targets appear to have had a beneficial effect in terms of improving services to patients compared to a few years ago, but the application of the targets leaves a considerable margin for doubt as to their integrity and the perverse incentives they create within the system. On a cautionary note, the practicality of a single target fitting all A & E and related services will come under increasing strain, as services are re-focused and become more specialized in terms of complex to revise targets in any case.
Conclusion
Queuing theory is useful in the determination of the amount of capacity that is needed (so that waiting times will be reasonable) and the amount of space to be provided for customers waiting for service.
This study examined the application of queuing theory in next time supermarket. From the result we have obtained, It can be concluded that the arrival rate will be lesser and the service rate will be greater if it is on weekdays since the average number of customers is less as compared to those on weekends.
Recommendations
The management of next time supermarket should integrate queuing model technique in its organizational policy to help in solving problems associated with waiting lines such as the cost to provide waiting space, a possible loss of business, loss of good will and reduction in customers satisfaction. < /span>
Besides, managers carefully assess the costs and benefits of various alternatives for capacity of service system (Stevenson, 2005).
Again, managers of all services consider the possibility of reducing variability in processing times by increasing the degree of standardization of the service being provided.
Moreso, a simulation model should be developed for the supermarket.
REFERENCES
Andreas Willig (1999). A Short introduction to Queuing theory. Technical University Network. Berlin.
Lucy T. (2002). Quantitative Techniques. 6ed. Book power ELST UK
JK Sharma (2007). Operations Research: theory and applications 3 edition. Macmillan India
Stevenson J.W (2005), Operations Management. 8th ed. McGraw-Hill Irwin.
Umoh G.I. (2007). Quantitative Analysis for Modeling and Decision Making.
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