Efficiency of Controlled Queue system in Supermarket using Matlab / Simulink

Transcription

1 Volume 114 No , ISSN: (printed version); ISSN: (on-line version) url: ijpam.eu Efficiency of Controlled Queue system in Supermarket using Matlab / Simulink N. Balaji Department of Mathematics SRM University, Kattankulathur balaji.n@ktr.srmuniv.ac.in Abstract In this paper the queue length and waiting time of a customer to be minimized using Matlab Simulink. In regular supermarkets a critical situation arises then queueing model provide a powerful solution using Simulink model. This model allows the prediction and behavior of the queue under different physical experiments. The study indicates as lack of queuing discipline in essentially all of these supermarkets. Many customers were allowed to jump the queue or renege. Hence there is a revamp to improve the service facilities in these supermarkets. The maintenance and replacement costs were rapidly high. The service process seemed to be the continuous one and this could lead to the breakdown of the human resources and even of inanimate inputs. There should also be a dynamic and efficient mechanism by a management of these supermarkets to seek for optimal system utilization. This would help to decrease the tendency for costs associated with system utilization to rise over time. AMS Subject Classification: 00A72, 60K25, 90B22, 65K10, 78M50. Key Words: Queing model, Matlab, Simulink, Supermarket

2 1 Introduction Waiting lines or queues are a common aspect in life, especially in the province of organizations that are for profit making. Queues are common in such places as petrol or filling stations, supermarkets stores, clinics, hospitals, parks, manufacturing firms, to mention a but a few them. An interesting aspect of queuing process resides in the measures of its system s performance, especially regarding average service rate, utilization and the costs implied for a given capacity level. Queuing models provide with a dominant tool for designing and evaluating the performance of queuing, Whenever customers arrive at a service facility. They have to wait before they receive the required service. It means that the customer has to wait for his turn, to get the service in a line. Customers arrive at a service facility with various queues, each with one server (sales checkout counter).the customers choose a queue of a server according to some mechanism. 2 Basic Queuing Process- Multiple Queue service frame work Customers demanding service are generated over time by an input source. The required service is then performed for the customers by the service mechanism, after which the customer leaves the queuing system. There two types of models. One model will be as Single-queue, and another one is Multiple-Server model. The queuing system is when classified as M/M/c with multiple queues where number of customers in the system λ/µ > 1. In most of the supermarkets they follow the multiple service mechanism to acquire an accurate service. To avoid the queue rush we write small coding using Matlab simulation for Entity generation. The multiple channel system presented here again assumes that arrivals follow a Poisson probability distribution and the services time are exponential distributed. Where λ = Average arrival rate, µ = Average service rate, s= number of channels

3 The probability that there is no customers in the system (P 0 ): P 0 = [ s 1 n=0 1 n! ( ) n λ + 1 µ s! ( ) ] s 1 λ sµ µ sµ λ Expected number of customers in the system (L s ): L s = ( ) s λ λµ µ (s 1)!(sµ λ) P λ µ Expected waiting time in the system (W s ): ( ) s λ W s = L µ s λ = µ (s 1)!(sµ λ) P µ 3 MATLAB SIMULINK R2016b To create the simple model, Blocks are the model elements that define mathematics of a system and provide input entity and signal using Simulink R2016b. Simulink is a block diagram environment for multidomain simulation and model-based design. It supports simulation, automatic code generation, and continuous test and verification of embedded blocking systems. Simulink provides a graphical editor, customizable block libraries, and solve for modeling and simulating dynamic systems. It is integrated with MAT- LAB, enabling you to incorporate MATLAB algorithms into models and export results to MATLAB for further analysis. 4 Customer and Services The customers will often leave a store without making a purchase rather than standing a long or slow-moving check-out line. Despite large advancements in technology designed to decrease wait times, queue management remains a challenge for every retailer and shop owner. The truth is that when queues are not well managed, it will definitely result to having unhappy customers, sales decrease, lower customer satisfaction, and loss of customer loyalty. To avoid 3 285

4 certain situations we optimize the waiting time of the customer through design of blocks to be given more service to the customer. The service is provided by a service facility. The customers entry into the service system depends upon the queue conditions. If the time of customers arrival, the server is idle, then the customer is served immediately. Other wise the customer is asked to join in the queue, which can leave several thoughts. By configuration of the service system we mean how the service facilities exist. Service systems are usually classified interms of their number of channels. 5 Checkout Supermarket using Queuing Simulation When the customer entered into the queue for the service of billing, we designed the billing system in Supermarket by considering the constraints like, Quantity, weight, time for the billing service. By restricting the constraints, the queue direct us to which line to select among the three queue lines by the automated coding for the following constraints. With regarding to weight and time we designed the queue into three types for billing. Queue 1 : If Weight > 10 kg and time for billing is < 5 minutes. (i.e) The customers purchasing things in large quantity with maximum items. Queue 2 : If weight is < 10 kg (i.e) The customers purchasing things in large quantity with minimum items. Queue3 : If Weight > 10 kg and time for billing is > 5 minutes. Figure 1: Figure1: Multi service mechanism Model controlled by automated queues in supermarkets 4 286

5 6 Queuing Simulation: The following table shows the behaviour pattern of the customer while entering into the queue in the supermarket in normal conditions. And also can view the service by automated allotment of the server by reduced waiting time using simulation through scope. Entity Arrivals Entity Service /hour µ / Hour λ Server 1 Server 2 Server 3 Runtime Capacity Figure(2) Figure(3) Figure(4) Figure(5) 10 Random Figure(6) 10 Random Figure(7) 10 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 7 Discussion and Recommendations With using Matlab Simulink the pattern behaviour of the customer to reduce the waiting time according to the parameters based on 5 287

6 time, weight, quantity. How to solve the conflict between customers and supermarkets deserves more considerations. Simulation is useful to represent the different pattern of queue behavior and service activities. To crack the waiting time in supermarkets, we make the systematic queue allotment by using different parameters, like primary parameter is quantity and then time. Through an exponential input the entity can be observed through the given figures using Matlab Simulation.Organize managers and employees to learn and train the latest trends to be followed according to the customer behavior supermarkets, concerning their advanced management methods and experiences. The modern technology gives the better service to the customers without spending more time with better effects. References [1] Nasroallah, A., Monte Carlo Simulation of Markov Chain Steady-state Distribution, Extracta Mathematicae, 19(2), (2004), [2] Sheu, C., Babbar S., A managerial assessment of the waitingtime performance for alternative service process designs, Omega, Int. J. Mgmt Sci., 24(6), [3] Ming Sun and Jingye wang, Agent based Simulation framework for Complex Product, Asia simulation conference - 7th International conference on system simulation and scientific computing, [4] Y. L. Deshpande, Roger Jenkins, & Simon Taylor, Use of Simulation to Test Client-Server Models, [5] Sanish A, Application of Queuing Model and simulation to the traffic at New Mangalor Port,, Department of Applied Mechanics and Hydraulics, NITK, Surathkal, Karnataka, (2007), [6] Yuejian Jie, The Optimal Supermarket service, International journal of Business and Management, 5, (2010),