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 (? ) = 7 Service rate of each server (? ) = 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 [pic] 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: [pic] Where No of people arriving at pattern and maintenance (? ) = 7 Service rate of Bob Brayan (? ) = 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 (? ) 2. Probability of Zero customers or Units in the system(Po) 3. Average number of customers or units waiting in the line for service(Lq) 4.
Average number of customers or units in the system(L) 5. Average time customers or unit spends waiting in the line for service(Wq) 6. Average time customer or the unit spends in the system(W) 7. Probability n customers or units in the system(Pn) Discussion 1: 1. How much time would the new Layout save (per trip, per hour)? After entering the values of ? , ? , s in the Excel sheet for the first layout the, the average waiting time the system W is 0. 3922 hours, i. e.. 23. 532 mins. If we add the travel time to the waiting time, the maintenance department people will take 23. 32+3+3=29. 52mins (a trip), and for Molding department people take 23. 532+1+1=25. 52mins (a trip). After changing to new layout:- Layout 2 system has single server in each shop. This makes the Queing model M/M/1 instead of M/M/s. When values of ? , ? , s are substituted in the Excel sheet for each system the waiting time (W) in Maintenance shop is 0. 5 hours, i. e.. 30 min and the total time taken (Waiting time in Queue (W) + travelling to and fro) for maintenance department people to take parts is 30+1+1=32 mins. There is an increase in the time of 2 mins when compare to layout 1 for maintenance department people.
The waiting time in the Pattern shop W is 0. 25hours or 15mins. The total time taken (Waiting time in Queue (W) + travelling to and fro) is 15+1+1=17mins. There is certainly decrease in the system when compare to Layout 1. This Layout reduces 8. 5 mins than Layout 1. Discussion 2:- Note:- Trips: The total trips in the system of the given data (4 maintenance,3 molding) If maintenance personal were paid $ 9. 50 per hour and molding personnel were paid $ 11. 75 per hour, how much could be saved per hour with new factory layout? As given the problem the amount paid for each server in the shop Pete Nawler (Molding) = $11. 75/hour ? Bob Bryan (Maintenance)= $9. 5/hour Time increased after implementing new maintenance shop => 32-29. 58 = 2. 48 mins/trips Time decrease after implementing new pattern shop => 25. 52-17 = 8. 52 mins/trips There fore the profit can be calculated as [(8. 52/60)*11. 75] – [(2. 48/60)*9. 5] = $1. 27/trips Conclusion: Therefore implementing new layout will save $1. 27 per trip is relatively small. But it depends on the number of trips per day. The main advantages of new layout are ? Time to travel maintenance shop is reduce to 1 min Can get $1. 2765 profit per trips Although there are few advantages the main disadvantages are ? Initial Cost to implement might be high than profit margin ? Multi-server system is more advantageous than single server system when the demand suddenly varies. ? The efficiency of Pete is 7 which is much more the average arrival rate, which is not so efficient in the system. ———————– Molding shop Maintenance department Pattern and Maintenance shop Pattern shop (Pete) Molding shop Maintenance department Maintenance shop (Bob)