Queuing Theory
Introduction
Being in a queue (waiting line) is an inevitable fact of our daily life, such as waiting for checkout at a supermarket, or waiting to make a bank deposit. Queuing theory, started with research by Agner Krarup Erlang, is used to examine the impact of management decisions on these waiting lines (Anderson et.al, 2009). A basic Queuing Model structure consists of three main characteristics, namely behaviour of arrivals, queue discipline, and service mechanism (Hillier and Lieberman, 2001).
In this assignment, New England Foundry’s queuing problem will be solved in Excel, and then, time and cost savings will be identified.
First of all, current and new situation will be analysed in order to demonstrate the queuing model by using Kendall’s Notation (for the current queuing problem, queuing model is M/M/s). After that, arrival rate, queue size, and service rate will be defined, and added-in Excel file (Queuing models.xlsx). The results will be discussed at the end.
Description
New England Foundry (NEF) produces four different types of woodstoves for home use and additional products that are used with these four stoves.
Due to the increase in energy prices, George Mathison president of the company wants to change the layout to increase the production of their bestselling type of Warmglo III.
NEF has several operations in order to produce woodenstoves which are illustrated as a flow diagram in Figure 1.
Current State Analysis
Current layout offers one counter with two personnel, namely Pete and Bob who are able to serve a total of 10 people per hour (5 per hour each), with an average of 4 people from maintenance and 3 people from molding arriving at the counter per hour randomly (4+3=7). An illustration of current layout can be seen in Figure 2.
Figure 1 Flow Diagram
Figure 2 Current State
This layout caused an additional walking time for a personnel to reach the counter from;
Maintenance department: 3 minutes
Moulding department: 1minute
Being in a queue (waiting line) is an inevitable fact of our daily life, such as waiting for checkout at a supermarket, or waiting to make a bank deposit. Queuing theory, started with research by Agner Krarup Erlang, is used to examine the impact of management decisions on these waiting lines (Anderson et.al, 2009). A basic Queuing Model structure consists of three main characteristics, namely behaviour of arrivals, queue discipline, and service mechanism (Hillier and Lieberman, 2001).
In this assignment, New England Foundry’s queuing problem will be solved in Excel, and then, time and cost savings will be identified.
First of all, current and new situation will be analysed in order to demonstrate the queuing model by using Kendall’s Notation (for the current queuing problem, queuing model is M/M/s). After that, arrival rate, queue size, and service rate will be defined, and added-in Excel file (Queuing models.xlsx). The results will be discussed at the end.
Description
New England Foundry (NEF) produces four different types of woodstoves for home use and additional products that are used with these four stoves.
Due to the increase in energy prices, George Mathison president of the company wants to change the layout to increase the production of their bestselling type of Warmglo III.
NEF has several operations in order to produce woodenstoves which are illustrated as a flow diagram in Figure 1.
Current State Analysis
Current layout offers one counter with two personnel, namely Pete and Bob who are able to serve a total of 10 people per hour (5 per hour each), with an average of 4 people from maintenance and 3 people from molding arriving at the counter per hour randomly (4+3=7). An illustration of current layout can be seen in Figure 2.
Figure 1 Flow Diagram
Figure 2 Current State
This layout caused an additional walking time for a personnel to reach the counter from;
Maintenance department: 3 minutes
Moulding department: 1minute
References: Anderson, D. R., Sweeney, D. J., Williams, T. A., and Wisniewski, M. (2009) An Introduction to Management Science: Quantitative Approaches to Decision Making. London: Change Learning Hillier, F. S. and Lieberman, G. J. (2001) Introduction to Operations Research. New York: McGraw Hill APPENDICES Appendix 1: Solution of NEF Current State Queuing Model in Excel Appendix 2: Solution of NEF New State Queuing Model in Excel for Pete (Molding) Appendix 3: Solution of NEF New State Queuing Model in Excel for Bob (Maintenance)