# Case Study

Topics: Minute, Queueing theory, Sand casting Pages: 5 (1114 words) Published: June 10, 2011
New England Foundry
Assignment – 2

Introduction:-

New England Foundry is woodstove manufacturers for home use. Due to increase in energy prices the demand for wood stoves has increased. The New Foundry is the only in the business of making stove and stove-related products. Its major products are Warmgio I, the Warmglo II, the Warmglo III and Warmglo IV. Presently the company has layout 1. The layout 1 has pattern shop and maintenance department in the same block. The Warmglo III outsells all the other stoves by wide margin because of its typical heat output, accessories and automatic heat variation according to weather conditions. The increase in demand for Warmglo III has made the company to implement new layout in order to decrease production time. The Layouts are described as below

Layout 1: In this layout there are seven departments in which the Pattern and Maintenance shop is situated in the same building. It has two counters and two men(Pete Nawler, Bob Bryan) inorder to provide tools and parts for the maintenance and moulding department people. The capacity of each person is 5/hour. On the average 4 people from maintenance and 3 people from the molding department arrive at the counter. People from maintenance and molding department arrive randomly. Pete and Bob has always followed the FIFO (First In First Out).

Where
No of people arriving at pattern and maintenance (λ) = 7
Service rate of each server (μ) = 5 No of servers in the shop (S) = 2
Time Taken for a person to travel from (t1) =3min Maintenance department to shop
Time Taken for a person to travel from (t1) =1min Molding department to shop

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After observing the operations the pattern shop and maintenance room for several weeks, George, President, decided to make some changes to the layout. The new layout of the factory makes Maintenance and Pattern shop separate. The main advantages for making new layout are

1. It takes only 1Min to travel from Maintenance department to New Maintenance Shop. 2. It allows Bob to serve 6 People from the maintenance department per hour, and Pete to serve 7 people from the molding shop per hour.

Layout 2:

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Where

No of people arriving at pattern and maintenance (λ) = 7

Service rate of Bob Brayan (μ) = 6 No of servers (S) = 2
Time Taken for a person to travel from (t1) =1min Maintenance department to maintenance
Time Taken for a person to travel from (t1) =1min Molding department to Pattern shop

Approach to the problem:-

The present problem is to calculate how much amount of time, money does layout 2 save compare to Layout 1 and finally suggest whether the decision is correct or not. In order to start the Queuing there has to be few assumptions. In this problem there are few assumptions which should be considered while setting in values in the Excel sheet.

Assumptions:-

➢ Arrivals are FIFO. ➢ There is no balking or reneging. ➢ Arrivals are independent. ➢ Arrivals are Poisson. ➢ Service times are independent. ➢ Average service rate exceeds average arrival rate.

The system has Multiple servers, Single Line, Poisson arrival pattern, Exponential service time pattern, and Unlimited Population Size for the first layout. Hence the M/M/s Queuing model is selected. The Operating Characteristic Equations of the above Queuing Model are:- 1. Average server utilization in the system (ρ)

2. Probability of...