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---- Lean WINGS ----

Project / Case Study
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|Course: |Decision Making under Uncertainty |
|Professor: |Jean-Philippe P. Richard |
|Date: |April 13, 2011 |
|Prepared by: |Timothy Carson |
| |Annie Malpartida |
| |Neville Sicard-Gregory |

Table of Contents

I. References & Related Documents 3
1. Executive Summary 3
1.1. Project Overview 3
1.2. Problem Statement 3
1.3. Project Justification 3
2. Project Definition 4
2.1. Project Objective 4
2.2. Project Success Criteria 4
3. Project Analysis 4
3.1. General Assumptions 4
3.3.7. AS-IS situation 9
3.3.8. 1st Idea 9
3.3.9. 2nd Idea 9
3.3.10. 3rd Idea 9
3.3.11. 4th Idea 9
3.3.12. Combination of Ideas # and # 9
3.3.13. Combination of Ideas # and # 9
3.3.14. OR team TO-BE proposal 9
3.4. Comparative chart 9
4. Recommendations 10

References & Related Documents

|Document |Location |
|AS-IS situation |(embedded files) |
|Idea #1 | |
|Idea #2 | |
|Idea #3 | |
|Idea #4 | |
|Ideas # & # combined | |
|Ideas # & # combined | |
|OR team TO-BE proposal | |

Executive Summary

1 Project Overview

Northern Airplane Company (NAC) is urgently trying to reduce the in-process inventory of its wing manufacturing process. Currently NAC has 8 wing presses that form wings from large sheets of metal that it receives from another department at a mean rate of 6 per hour. All wings arrive to building 1 where they are uniformly assigned to a press at random. NAC currently has 5 old presses housed in building 2 and 3 new presses housed in building 2. The processing time for an older press is exponentially distributed with a mean of 1 hour. At this rate, it has been estimated that 25% of the wings will need to be reworked. On the other hand, the newer presses work faster and more efficient requiring less rework. The processing time for a new press is exponentially distributed with a mean of 45 minutes (3/4 of an hour), with only 10% of wings needing rework. Any wing requiring rework goes to the rework station in building 3 where the time needed for rework is exponentially distributed with a mean of 45 minutes. It has been estimated that 10% of the wings that go through the rework station need to be completely repressed and are sent back to building 1. The wings that do not need to be repressed rejoin the other wings that did not need rework at the finishing station, where the time needed to finish a wing is normally distributed with a mean of 8 minutes and a standard deviation of 1 minute.

2 Problem Statement

NAC is unhappy with the current situation and there is an urgent business need to cut down in-process inventory since it represents expensive handling costs, presently absorbed by the business. Per Jim Wells, VP for manufacturing of the Northern Airplane Company, “we have a few million bucks worth of expensive metal just sitting there”.

Currently it’s visible that metal sheets and wing sections go through unnecessary long queues waiting to be pressed or reworked creating bottlenecks. Lack of organized flow and prioritization of jobs is part of the problem today, especially in rework station. We have been asked to analyze the current situation and develop a recommendation that will cut down on in-process inventory and bring costs down.

3 Project Justification

There is a huge opportunity to significantly reduce the high cost associated with in-process inventory by improving production workflow. The VP of the company has made reducing the in-process inventory a top priority, and rightfully so. For every wing that we reduce from the in-process inventory there is a savings of a couple hundred thousand dollars.

Project Definition

1 Project Objective

As Operations Research analysts, we have been brought in to provide a recommendation to upper management about improving the current situation. We will provide an analysis of the long run averages of the current situation. This will provide a baseline for comparison of the ideas that both Jim and our team have proposed. In the end, we will provide an alternative solution that is more efficient than the current system, leading to a reduction of in-process inventory and associated costs. Specifically we will be looking reduce the inventory waiting in queues in front of each of the presses, rework station, and finishing station thus reducing the inventory waiting to be processed in the entire system. With less inventory siting in queues, we can expect cost per hour of those queues to decrease as well. We also would expect that they average cycle time of a wing to go down with increased system efficiency. These points will help us to identify actual improvements in any of the alternatives that we propose. However, we will also want to monitor the total through put in the system. A reduction in queue length may be negatively offset by a drastic decrease in the total number of units produced.

2 Project Success Criteria

• Reduction of queue size in all stations • Reduction of average total number of units in queue in the entire system • Reduction of average cost of inventory waiting to be processed

Project Analysis

1 General Assumptions

The following assumptions are applicable and have been applied across all models ideas. • The arrival of wings into the system is exponentially distributed with a mean of 6 per hour or every 10 minutes. • The processing time at the re-work station(s) is exponentially distributed with a mean of 45 minutes. 10% of the wings coming out of the re-work station will need to be re-pressed and therefore need to go back through the system. • The processing time at the finishing station is normally distributed with a mean of 8 minutes and a standard deviation of 1 minute. • All queues operate on the First In, First Out queuing order. • It has been estimated that the transportation time between buildings is 5 minutes, while transportation times within a building can be approximated as instantaneous (0 minutes). • We have also assumed that he wing manufacturing processed outlined in this report is a continuous process that operates 24/7 with no breaks and no downtime. As such all simulation models have been run with a 500 hour warm up time and a 4000 hour simulation time. • It has been estimated that there is a cost of $8 per wing for each hour of non-non value added time in the system. This includes all time waiting in queue to be processed as well as transportation time. • Unless otherwise indicated, all processing times are exponentially distributed, and the time given is the mean of that distribution

1. Idea Descriptions 1. AS-IS Situation As described above the current wing manufacturing process includes 3 new presses, 5 old presses, 1 rework station, and 1 finishing station. Wings are distributed uniformly amongst the 8 presses with approximately 12.5% going to each machine

Variables: # of New Presses: 3 New Press Rate: 45 minutes New Press Rework %: 10% # of Old Presses: 5 Old Press Rate: 1 hour Old Press Rework %: 25%

2. Jerry’s 1st Idea Jerry’s first idea was to change the way the metal sheets were assigned to the presses. Since newer machines run faster and require less rework, jerry wanted to assign the metal sheets to newer presses with a higher probability. Jerry was unsure of the exact probabilities so we ran a few different scenarios in order to see the various outcomes. After metal sheets arrive into building 1, they are sent to building 2 or building 3 with the assigned probabilities. Once in a particular building metal sheets are randomly sent to a press in that building with a uniform distribution (20% for each of the old presses in building 2, and 1/3 for each of the new presses in building 3). We created 6 different scenarios for this idea. All data is held constant with the exception of the probabilities of sending wings to either building, with each scenario assigning different probabilities to building 2 and building 3. Each scenario increases the probability associated with sending wings to building 3 from 40% to 90% in order to give an increasingly higher probability to the newer presses.

Variables: # of New Presses: 3 New Press Rate: 45 minutes New Press Rework %: 10% # of Old Presses: 5 Old Press Rate: 1 hour Old Press Rework %: 25%

3. Jerry’s 2nd Idea Jerry’s 2nd idea is similar to his first idea. Sheets of metal are assigned to buildings 2 and 3 in the same fashion as Jerry’s first idea. However, instead of instantly assigning the metal sheet to a press, the sheets are held in queue until a press is free at which point the metal sheet is sent to the first press available. This means that instead of having a queue in front of each individual press the presses in each building will pull from a single queue inside that building. Intuitively this will eliminate the situation in which one press has metal sheets waiting to be processed while there is another machine available to process it into a wing.

Variables: # of New Presses: 3 New Press Rate: 45 minutes New Press Rework %: 10% # of Old Presses: 5 Old Press Rate: 1 hour Old Press Rework %: 25%

4. Jerry’s 3rd Idea Jerry’s third idea is related to reducing the amount of rework that needs to be done on the sheets. Jerry suggested reducing the processing speed from 1 hour to 1.25 hour for old machines reducing the amount of rework to 10%. For new machines the processing speed is reduced from 45 minutes to 1 hour to reduce the rework 5% on the new machines.

Variables: # of New Presses: 3 New Press Rate: 1 hour New Press Rework %: 5% # of Old Presses: 5 Old Press Rate: 1.25 hours Old Press Rework %: 10%

5. Jerry’s 4th Idea Jerry’s fourth idea was also related to rework stations. His idea was to replace one of the old machines in building 2 with a rework station that would be identical to the rework station in building 3. In this new design, all wings that needed to be reworked would do so in the same building in which it was produced. This should reduce the transfer times of the wings produced by the old presses since they would no longer need to be transferred to building 3. With two rework stations we would also expect to see a reduction in the queue length from only having one rework station. The challenge here will be to determine if the reduction in transportation time and rework queue outweigh the loss in production capacity from replacing an old press.

Variables: # of New Presses: 3 New Press Rate: 45 minutes New Press Rework %: 10% # of Old Presses: 4 Old Press Rate: 1 hour Old Press Rework %: 25% # of Rework Stations: 2

6. Idea 5 – Combing 2 of Jerry’s ideas into one After hearing Jerry’s four ideas we were able to instantly come up with an idea that combined two of them into a reasonable option. This idea would reduce the processing speed of the machines as indicated in idea 3 as well as add an additional re-work station in building 2. From the initial problem statement we realized that there seemed to be a large amount of inventory in queue in front of the rework station. Jerry has even voiced his concern as this is a known bottle neck in the system the way it is currently set up. This idea focuses on reducing this large queue by reducing the percentage of wings that need rework and adding a 2nd rework station increasing rework capacity.

Variables: # of New Presses: 3 New Press Rate: 1 hour New Press Rework %: 5% # of Old Presses: 4 Old Press Rate: 1.25 hours Old Press Rework %: 10% # of Rework Stations: 2

7. Idea 6 –First Available Press For this idea we went back to the current situation to see if we could make any improvements just by thinking about how the system operates. This idea will change the way metal sheets are assigned to presses. With the random uniform distribution being used in the current situation, some presses could have a large queue while other machines are completely empty. In order to address this we thought that assigning a wing to the first available press would help to resolve this problem. In this situation, metal sheets would sit in one queue in building 1 and wait for a press to become free, at which point the metal would be sent to that press. In effect, each press would be pulling from 1 large queue.

Variables: # of New Presses: 3 New Press Rate: 45 minutes New Press Rework %: 10% # of Old Presses: 5 Old Press Rate: 1 hour Old Press Rework %: 25% # of Rework Stations: 1

8. Idea 7 – First Available Press & Slower Processing times This idea combines one of our ideas with one of Jerry’s. Here we are still assigning wings to the first available press as they become available. However we are also adding to Jerry’s idea to reduce the processing speed of the presses which will create less need for rework. This idea attempts to address the efficiencies of the queued inventory in front of the presses as well as reduce the amount of rework in order to alleviate the identified bottle neck.

Variables: # of New Presses: 3 New Press Rate: 1 hour New Press Rework %: 10% # of Old Presses: 5 Old Press Rate: 1.25 hours Old Press Rework %: 25% # of Rework Stations: 1

9. Idea 8 – First Available Press & 2nd Rework station This idea is also a combination of our idea and Jerry’s idea. The goal of this idea is the same as Idea 7, but we use a different approach and compare results. In this approach we keep the idea of assigning metal sheets to the first available press. However we do not reduce the processing times of the presses. Instead we add an additional rework station in place of an older press. Again adding a 2nd rework station increases the rework capacity, and will hopefully reduce the queue length in front of the rework station as compared to the current situation.

Variables: # of New Presses: 3 New Press Rate: 45 minutes New Press Rework %: 10% # of Old Presses: 4 Old Press Rate: 1 hour Old Press Rework %: 25% # of Rework Stations: 2

10. Idea 9 – First available Press, Slower Processing, & 2nd Re-work station This idea incorporates three previous ideas into one recommendation. Again focusing on reducing the queue length in front of the rework station, we wanted to reduce the processing times of the presses which would reduce the amount of rework needed as well as add a 2nd rework station which would increase the rework capacity. We coupled this with assigning sheets to the first available machine to see how it fared with our other ideas. By implementing multiple methods to reduce the queue length at the current rework station, we hope to outweigh the loss of one of the old presses.

Variables: # of New Presses: 3 New Press Rate: 1 hour New Press Rework %: 10% # of Old Presses: 4 Old Press Rate: 1.25 hours Old Press Rework %: 25% # of Rework Stations: 2

2. Detailed Analysis

1. AS-IS Situation The as-is situation was analyzed using both Process Model and calculations presented in class. The purpose of this was to compare the results and provide some confidence in the accuracy of the process model results.

Using the inputs provided in section 3.2.1 the new presses and old presses were modeled as M/M/1 ques. In addition the rework station was modeled as a M/M/1 queue however the finishing station was modeled as a M/G/1 queue.

The results from the hand calculations are as follows:

|Variable |New Machines 1-3 |Old Machines 1-5 |Rework Station |Finishing Station |
|L |1.2931 |3.0000 |7.8867 |2.4250 |
|Lq |0.7292 |2.2500 |6.9794 |1.6250 |
|Ls |0.5639 |0.7500 |0.8872 |0.8000 |
|W |1.7241 |4.0000 |6.6667 |0.4042 |
|Wq |0.9723 |3.0000 |5.9148 |0.2708 |
|Ws |0.7519 |1.0000 |0.7519 |0.1333 |

As can be seen from the above hand calculations and the process model results, there are a significant number of wings being held in the queue for the rework station. From the process model results it was shown that the average cost associated with the total amount of time 1 wing spend in the que for the rework and processing is approximately $32.62.

2. Jerry’s 1st Idea In this idea sheets are assigned to presses at varying probabilities as described in section 3.2.2. The probabilities are presented in chart xxx. As can be seen the cost per sheet varied between $22.30 and $2821.60 for a 50/50 and 90/10 distribution for new and old machines respectively. In scenario 2 the faster machines receiving the highest probability of sheets had the greatest reduction in total cost, $22.30

3. Jerry’s 2nd Idea This scenario is described above in section 3.2.3. Scenario two as shown in the results chart produced the most substantial cost savings per wing of any of Jerry’s Ideas. This was due to the fact that after being put into storage for either building one or two that they were being assigned to the next available machine. Scenario two produced wings at a cost of $24.38 as related to total spent in queues.

4. Jerry’s 3rd Idea This idea was to slow down the process time for the machines in an effort to reduce the amount of rework needed on the wings. The assignment of the wings to the machine for processing was an even 1/8 or 12.5%. While this did reduce the rework queue, the cost was relatively per wing at $121.68. This was due to the larger queues for each machine since there was an increase in machine time and an even assignment of probabilities for each machine to be assigned a wing 5. Jerry’s 4th Idea The fourth idea was another one of Jerry’s ideas. This idea involved sending wings to the machines at an even probability; however one old machine in Building II would be replaced with a new rework station. Therefore all items produced in Building 2 would be reworked in building II and all items in Building III would be reworked in building III. The scenario was run in process model and produced a cost of $44.32 per wing. While it seemed logical to add another rework station, the even assignment of sheets to machines for processing just is not efficient and still allowed for a large number of wings to be in queues for each machine

Our Team Ideas The variables for our team’s idea are listed in the chart below:

|Machine |Variable |Idea 5 |Idea 6 |Idea 7 |Idea 8 |Idea 9 |
| |New Press Rate - hour (u): |1.00 |0.75 |1.00 |0.75 |1.00 |
| |New Press Rework %: |5% |10% |5% |10% |5% |
|Old Press |# of Old Presses (S): |4.00 |5.00 |4.00 |5.00 |4.00 |
| |Old Press Rate - hour (u): |1.25 |1.00 |1.25 |1.00 |1.25 |
| |Old Press Rework %: |10% |25% |10% |25% |10% |

6. Idea 5 – Combing 2 of Jerry’s ideas into one This idea was a combination of Jerry’s 3rd and 4th idea. What is proposed here is to assign the wings at an even distribution to the wings for processing, slowing down the machines to take advantage of the less rework and adding a new rework station in building two in place of one of the old machines. As in Jerry’s idea three the slowing down of the machines did produce less rework, however the even distribution of the wings cause a large amount of wings to remain in the press machine’s queue, resulting in a very high cost of $556.97 per wing.

From this idea it was learned that it is clear the metal sheets should be assigned to the machines on a first available basis

7. Idea 6 –First Available Press Based on what we learned in the previous ideas we assigned the wings to the first available machine for processing. We did not slow down the machines nor did we add a second rework station. The only difference between this idea and the current scenario is how the wings are assigned. This resulted in eliminating the queues in front of the presses reducing the cost of a wing to $11.15 However there still was significant bottlenecking at the rework station

8. Idea 7 – First Available Press & Slower Processing times In order to reduce the amount of bottlenecking at the rework station we slowed down the machines. It was shown in previous ideas that this will decrease the amount of rework. It was also thought that if we keep assigning the wings to the first available machine we will continue to eliminate the queues in front of the presses. This idea was successful in reducing both the cost and amount of bottle necking at the rework station even further. The cost per wing dropped to $17.65

9. Idea 8 – First Available Press & 2nd Rework station In this idea the sheets were continued to be assigned to the first available press as they were received and one old machine in Building II was replaced with a new rework station. Therefore all items produced in Building were reworked in building II and all items in Building III were reworked in building II. The machines ran at their normal operating speeds. The scenario as run in process model shows that there a no queues in front of the processing machines and that rework stations both had a very small number of wings on average in queue and a small amount of time spent in those same queues. This produced an average cost of $8.37 per wing in queue. In addition, this idea at 24000 units was one of the largest in terms of number of wings produced

10. Idea 9 – First available Press, Slower Processing, & 2nd Re-work station This idea was proposed to see if the amount of rework could be reduced even further by slowing down the machines and at the same time assigning the sheets to the first available machine and replacing one of the old machines in Building II with a new rework station. As expected the number of wings requiring rework decreased. However, due to the slower machines the number of wings and the amount of time spent in queue before processing significantly increased and this in turn increased cost to $566.03 per wing

2 Comparative chart

Inventory (avg):Inventory (avg) in queue at:4000Quantity ProcessedCycle timeVA timeCostExpected CostAll pressesAll rework stationsWorkflowTotal unitsunits/hr(avg) hrs(avg) hrsp/unit$/hrcontent (Lq)content (Lq)AS-IS24029.506.015.391.2032.62195.9614.967.38Production Manager proposalsIdea 1        Scenario 124034.706.014.941.2130.28181.9413.476.18Scenario 223944.505.994.191.1624.38145.9412.253.16Scenario 323976.805.997.101.1246.75280.2331.012.15Scenario 422989.405.75117.351.09591.853401.57708.471.18Scenario 520563.805.14340.061.051642.338443.142122.540.58Scenario 618128.704.53588.471.012837.2612858.963666.780.28Idea 2         Scenario 123984.706.002.831.1914.6387.720.005.41Scenario 223984.206.002.531.1512.2973.690.003.30Scenario 323979.905.993.441.1218.79112.650.002.16Scenario 422856.705.71115.361.08553.463162.570.001.12Scenario 520562.905.14345.381.051635.488407.550.000.58Scenario 618180.704.55581.051.012788.3012673.310.000.30Idea 324058.406.0116.991.35121.68731.8691.200.21Idea 424008.706.006.541.1844.32266.0228.021.40OR Team proposalsIdea 523007.005.75108.471.33556.973203.55662.520.08Idea 624034.806.012.631.1811.1567.000.005.06Idea 723990.606.003.421.3417.65105.860.000.19Idea 824067.106.022.191.168.3750.360.000.83Idea 922841.005.71118.351.33566.333233.890.000.07OR TO-BE (Idea 8)24067.106.022.191.168.3750.360.000.83Recommended
Recommendations

As shown in the comparative chart, Idea 8 has the lowest amount of wings in queues and is the lowest in terms of cost. It is the recommendation of this team to replace one old machine in Building II a new rework station. Therefore all items produced in Building II should be reworked in building II and all items in Building III should be reworked in building III. In addition wings should be assigned to the first available machines as this will eliminate the need for storage and keeping metals sheets in inventory prior to processing.