Great Zimbabwe University

Faculty of Agriculture and Natural Sciences Department of Mathematics and Computer Science Student: Sigwadhi Teddy M149125 Research Project (HSOR 460) Proposal Presentation in partial fulfilment of BSc. 4th Year Special Honours Degree in Operations Research and Statistics Supervisor: Mr. R. Mawonike

Research Topic
 Queuing theory based approach to the analysis of sales checkout at Montagu Spar supermarket  Location: Avenues Area, Harare, Zimbabwe

Background of the study
• Zimbabwe is an important emerging country among the developing countries. • The Spar Montagu has been chosen to be the research object primarily because of its clientele which have different buying behaviors. There are a mix of customers, low to high class customers and it has been seen to provide interesting results on the busy and non busy periods. • The main purpose of this project is to study the application of queuing theory and to evaluate the parameters involved in the service unit for the sales checkout operation in Spar Montagu supermarket

Background of the study continued…
• Queuing theory is the theory of waiting lines and service provision • A mathematical model is to be developed to analyse the performance of the checking out service unit • Two parameters need to be determined from the data collected in the supermarket through the mathematical model to the service point. • One parameter is the customer arrival rate to the service point per hour • The other is the rate of service to the customer

Statement of the problem
• The waiting of the customers in the line has been the most challenging issue at supermarkets sales checkout points • The problem is to study what happens during busy and non busy periods of transactions and how many employees would have to be scheduled to minimize waiting time • On the other hand we want to study various alternatives in scheduling and optimizing of employees and their work schedules thereby alleviating the problem of waiting.

Justification of the study
• The problem of waiting in a queue at a sales checkout point is common in the retail industry • The problem is felt especially during the peak periods • This captured my interest to embark on a project to study the problem of waiting in queues at Spar Montagu sales checkout points and to analyse this using statistical techniques mainly queuing theory

Aim of the Study
• The main aim of the research is to measure the expected queue length and so as to be able to determine the service parameter at each sales checkout service unit

Objectives of the study
The objectives of this project are: • To review queuing theory and apply it on the observed data of checking out sales service unit at Spar Montagu Supermarket • To measure the expected queue length in sales checkout service unit (server) • To measure the rate of service at which customers are checked • To get an insight into the busy and non busy periods of the queuing process

Assumptions
i. Arrival rate follows Poisson distribution with mean λ

ii. Service rate follows an exponential distribution with mean μ iii. The service times are independent of the queue length iv. There is no reneging and colluding v. There is positive support for the researcher from Spar Montagu Management

Literature review
• Queuing Theory had its beginning in the research work of a Danish engineer named A, K, Erlang in 1909 Erlang experimented with fluctuating demand in telephone traffic • Lapin (1976) says queues are a phenomenon as old as life. As customers queue for service, they generally do not like to wait long. Operating a service carries a cost and customers waiting also carries a cost. • Organisations need to strike a balance between the cost of operating an expanded facility to reduce customers waiting time and the cost of customers having to wait long. • Azmat Nafees in June 2007 presented a project on queuing theory and its applications analysing the sales checkout operation in ICA supermarket at University of Dalarma, Borlange, Sweden.

Research Methodology
• Secondary data will be obtained from the Spar Montagu department of operations • If there is need for more data to be used in statistical analysis, it will be collected directly by the researcher mostly on Saturday and Sunday because these will be the most convenient days for the researcher • Observation at the sales checkout points will be in hourly periods

Research Methodology continued…
Parameter 1: Rate of arrival To observe customers rate of arrival the following procedure will be followed: i) The time of interest will from 0730hrs to 1930hrs ii) A position at the entrance will be chosen where all customers will be observed and recorded when joining the queue iii) Customers passing will be counted at hourly intervals and recorded

Research Methodology continued…
Parameter 1: Rate of service i) The time of interest was hourly periods ii) The number of customers being served will be observed and recorded

Research Methodology continued…
Data analysis • Having identified the correct model, TORA will be used to compute the measures of performance. • The Kolmogorov-Goodness of fit test will be used to determine whether observed data follows a given distribution for arrival and service rates