Systems Modelling and Simulation Assignment 2015-2016 Brunel University

2015

Systems Modelling and Simulation MN5543 1446800

Brunel University 10/12/2015 1

CONTENT

1.

Introduction .................................................................................................................................. 8

2.

Simulation model of the manufacturing system ........................................................................... 9

3.

2.1.

Sequences of components .................................................................................................... 9

2.2.

Transfer Time ...................................................................................................................... 12

2.3.

Run Setup ............................................................................................................................ 12

2.4.

Resource Schedules ............................................................................................................ 13

2.5.

Resource Failures ................................................................................................................ 14

2.6.

Creating Orders ................................................................................................................... 16

2.7.

Stations and Routes ............................................................................................................ 19

2.8.

Suppliers ............................................................................................................................. 20

Identification the bottleneck process ......................................................................................... 23 3.1.

Proposal for improvement .................................................................................................. 24

3.1.1.

Increase resources in processes 1 and 3 ..................................................................... 25

3.1.2.

New work shift ............................................................................................................ 26

3.1.3.

Bonus .......................................................................................................................... 27

3.2.

Comparison of results ......................................................................................................... 31

3.2.1.

Throughput Time......................................................................................................... 31

3.2.2.

Work in Process ........................................................................................................... 32

3.2.3.

Resource Utilization .................................................................................................... 33

4.

Assembly Station......................................................................................................................... 34

5.

Conveyor System ........................................................................................................................ 38 5.1.

Bonus .................................................................................................................................. 42

CONCLUSION ...................................................................................................................................... 45 REFERENCES........................................................................................................................................ 46

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INDEX OF FIGURES

Figure 1. Flowchart of the manufacturing systems ............................................................................... 9 Figure 2. Component n Process Plan................................................................................................... 10 Figure 3. Steps, Component n Step n .................................................................................................. 11 Figure 4. Assignment of Process Time ................................................................................................ 11 Figure 5. Component Sequence .......................................................................................................... 11 Figure 6. Members of the Component Sequence ............................................................................... 11 Figure 7. Transfer Time ....................................................................................................................... 12 Figure 8. Expression for Transfer Time ............................................................................................... 12 Figure 9. Run Setup ............................................................................................................................. 13 Figure 10. Station n Machine .............................................................................................................. 13 Figure 11. Station Schedule ................................................................................................................ 14 Figure 12. Station Schedule ................................................................................................................ 14 Figure 13. Failures, Station 5 Machine Failure .................................................................................... 15 Figure 14. Failure module, Station 5 Machine Failure......................................................................... 15 Figure 15. Statistic module, Station 5 Machine State ......................................................................... 15 Figure 16. Set Basic Process ................................................................................................................ 16 Figure 17. Picture Name – Members .................................................................................................. 16 Figure 18. Entity Pictures – Members ................................................................................................. 16 Figure 19. Edit entity pictures for components 1, 2, 3, 4 & 5 .............................................................. 17 Figure 20. Link between Type.Component n and Picture.Component n ............................................ 17 Figure 21. Create Orders ..................................................................................................................... 18 Figure 22. Orders Types and Sequences ............................................................................................. 18 Figure 23. Assignments ....................................................................................................................... 18 Figure 24. Station n Station ................................................................................................................. 19 Figure 25. Route from Station n .......................................................................................................... 19 Figure 26. Process n ............................................................................................................................ 20 Figure 27. Station 2 Machine as resource of the Process 2 ................................................................. 20 Figure 28. Process n. Queue, FIFO ...................................................................................................... 20 Figure 29. Supplier n Time .................................................................................................................. 21 Figure 30. Supplier 1 Time .................................................................................................................. 21 Figure 31. Supplier 2 Time .................................................................................................................. 21

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Figure 32. Assignments ....................................................................................................................... 21 Figure 33. Supplier Delay .................................................................................................................... 22 Figure 34. Simulation for the manufacturing system .......................................................................... 22 Figure 35. Animation for the manufacturing system .......................................................................... 23 Figure 36. Identification of the Bottleneck Process ............................................................................ 24 Figure 37. Station 1 Machines ............................................................................................................. 25 Figure 38. Station 2 Machines ............................................................................................................. 25 Figure 39. Capacity factor for new and old machines ......................................................................... 25 Figure 40. Station 1 Machines incorporated in process 1 ................................................................... 26 Figure 41. New Resource Module ....................................................................................................... 26 Figure 42. Priority for components ..................................................................................................... 28 Figure 43. Queue Priority .................................................................................................................... 29 Figure 44. Process Analyser ................................................................................................................ 30 Figure 45. Improved model layout ...................................................................................................... 31 Figure 46. Comparison of throughput times ....................................................................................... 32 Figure 47. Comparison of work in process .......................................................................................... 33 Figure 48. Comparison of instantaneous utilization ........................................................................... 34 Figure 49. Type.Product n & Picture.Product n ................................................................................... 34 Figure 50. Assembly 1 Time ................................................................................................................ 34 Figure 51. Assembly 2 Time ................................................................................................................ 34 Figure 52. Assembly Station ................................................................................................................ 35 Figure 53. Assembly Record ................................................................................................................ 35 Figure 54. Assign Product.................................................................................................................... 35 Figure 55. Assembly Decide ................................................................................................................ 36 Figure 56. Product Match n ................................................................................................................ 36 Figure 57. Product Batch n .................................................................................................................. 36 Figure 58. Assembly Process ............................................................................................................... 37 Figure 59. Route from Assembly Process ............................................................................................ 37 Figure 60. Plan Layout ......................................................................................................................... 38 Figure 61. Loading and unloading times ............................................................................................. 39 Figure 62. Loop Conveyor ................................................................................................................... 39 Figure 63. Loop Conveyor.Segment .................................................................................................... 39 Figure 64. Probability density function ............................................................................................... 40 Figure 65. Probability density function TRIA(20, 30, 40) ..................................................................... 40

4

Figure 66. Next Stations ...................................................................................................................... 41 Figure 67. Start Sequence & Route from Station n ............................................................................. 41 Figure 68. Station n Station ................................................................................................................. 41 Figure 69. Conveyor System Layout .................................................................................................... 42

5

INDEX OF TABLES

Table 1. Component routings and Process times ................................................................................ 10 Table 2. Waiting time (Queue) ............................................................................................................ 23 Table 3. Number waiting (Queue) ....................................................................................................... 23 Table 4. Accumulated wait time (Process) .......................................................................................... 24 Table 5. Difference of schedules ......................................................................................................... 27 Table 6. Total time per component type ............................................................................................ 28 Table 7. Best Combination .................................................................................................................. 30 Table 8. Percentage of improvement of throughput time .................................................................. 32 Table 9. Percentage of improvement of work in process ................................................................... 32 Table 10. Percentage of improvement of instantaneous utilization ................................................... 33 Table 11. Number out of components ............................................................................................... 38 Table 12. Throughput Time ................................................................................................................. 43 Table 13. Work in Process ................................................................................................................... 43 Table 14. Instantaneous Utilization .................................................................................................... 44

6

INDEX OF EQUATIONS

Equation 1. Discrete Probability Distribution ...................................................................................... 18 Equation 2. Supplier Time ................................................................................................................... 21 Equation 3. Process Time for process 1 .............................................................................................. 26 Equation 4. Throughput time in Area.................................................................................................. 28 Equation 5. Queue Priority Equation .................................................................................................. 29 Equation 6. Throughput Time Equation .............................................................................................. 29 Equation 7. Assembly time ................................................................................................................. 37 Equation 8. Distance for the conveyor system.................................................................................... 39 Equation 9. Triangular distribution equation ...................................................................................... 40

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SYSTEMS MODELLING AND SIMULATION ASSIGNMENT 2015-16

1. Introduction

The assignment consists of four main parts. Additionally, two bonuses will be presented, as listed below: Main Parts  Simulation model of the manufacturing system without assembly station  Identify the bottleneck process and present a proposal for improvement  Simulation model of the manufacturing system with assembly station  Introduce a conveyor system Bonus  Queue priorities and the process analyser will be used to improve the original system  A transporter system will be introduced to compare with the conveyor system The Development of the manufacturing system is divided into eight parts. However, its basic operation can be studied according to the Figure 1. Although Company A and B are two different enterprises; the common objective is maximize their profits. In order to achieve that goal, they have created a strategic alliance; Company A does outsourcing with Company B. In other words, the activities of Company B are done in the Company A factory. For that reason, the assembly process and stations are in the same area.

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Figure 1. Flowchart of the manufacturing systems

2. Simulation model of the manufacturing system

2.1. Sequences of components

The company B has 5 machining stations and each component has a separate processing sequence through the system and operation times at each machine are shown in Table 1.

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Components C1

C2

C3

C4

C5

Step 1

Step 2

Step 3

Step 4

Step 5

Station 1

Station 2

Station 3

Station 4

(5,15,20)

(5,8,10)

(15,20,25)

(8,12,16)

Assembly Station

Station 1

Station 5

Station 4

Station 2

Station 3

(6,8,10)

(11,13,15)

(4,6,8)

(6,9,12)

(27,33,39)

Station 2

Station 4

Station 5

(7,9,11)

(7,10,13)

(18,23,28)

Assembly Station

Station 1

Station 2

Station 3

Station 5

Station 4

(5,15,20)

(3,9,15)

(5,10,12)

(3,10,12)

(4,8,12)

Station 2

Station 1

Station 3

(6,10,14)

(6,10,14)

(5,8,15)

Step 6

Assembly Station

Assembly Station

Assembly Station

Table 1. Component routings and Process times

There are five components, therefore five sequences. They are created in the sequence module of the advanced transfer panel. Furthermore, each of them is named “Component n Process Plan”, as illustrated in Figure 2.

Figure 2. Component n Process Plan

The set of steps depends of each component. For instance, component 1 consists of five steps, as shown in the first row of Table 1. These data are introduced as displayed in Figure 3. Additionally, it is important to highlight that the set of steps can end in the Assembly Station or in the exit system. To put it differently, if the model does not contain an Assembly Station, the final step is the exit system. Contrary, if the model contains an Assembly Station the final step is the Assembly Station.

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Figure 3. Steps, Component n Step n

Each step has a process time as shown in Table 1. These times are given in minutes and represent a triangular distribution. For example, the step 1 of the component 1 has a process time TRIA(5, 15, 20) min. It is imperative to point that the Process Time is saved as Attribute, as observed in Figure 4

Figure 4. Assignment of Process Time

Finally, the five sequences will be stored as a set. Arena offers two types of sets: basic set and advanced set, the first one can be found in the Basic Process Panel and the other one can be found in the Advanced Process Panel. For this part of the assignment, the advanced set will be used, due to the Set Type required is the option “Other”. The set name is Component Sequence, as illustrated in Figure 5 and the set members are “Component n Process Plan” as observed in Figure 6

Figure 5. Component Sequence

Figure 6. Members of the Component Sequence

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2.2. Transfer Time

The transfer times between each station is TRIA(1,1.5,2) minutes. This expression can be set up in each station module. However, it is more efficiently if the transfer time is defined as an expression, as indicated in Figure 7 and Figure 8. Alternatively, the transfer time could also have been defined as a variable using the Assign Module.

Figure 7. Transfer Time

Figure 8. Expression for Transfer Time

2.3. Run Setup

The data are “Warm-up Period = 1 day, Replication Length = 2 Months and Number of Replication = 5”. The system does not require initialisation between replications”. It is extremely important to highlight, it might be better to make just one long run and therefore the warm-up only will appear once. Whether this concept is applied, the number of replications would be 1 and the replication length would be 300 days, as shown in Figure 9. This is the same simulation effort as making the five replications of length 60 days each. As defined in article 2.1, there are five stations, consequently five machines. Moreover, these machines work in shifts of eight hours and an hour break between the shifts. For this reason, the number of hours per day is considered equal to 17, as displayed in Figure 9.

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Figure 9. Run Setup

2.4. Resource Schedules

This section consists of three parts. First, it is necessary to create five machines in the Resource Module of the Basic Process Panel; each machine is named Station n Machine. Additionally, work shifts are configured as “Based on Schedule”, the schedule name as “Station Schedule” and the Schedule Rule as “Preempt”, as illustrated in Figure 10. In other words, machine will stop immediately at the end of the current shift and the preempt component will be held back by Arena until the beginning of the next shift and continue with its remaining processing time.

Figure 10. Station n Machine

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The second step is setting up the schedule; it can be done in the Schedule Module of the Basic Process Panel. It is necessary to choose “Capacity” as Type and “Hours” as Time Units”, as shown in Figure 11

Figure 11. Station Schedule

In the tab named Durations, work shifts and break will be configured. As defined in the paragraph 2.3, the capacity for the first work shift (eight hours) is one and the capacity for the break (one hour) is zero. To put it easily, there will be one machine working in each station during the first work shift and none during the break. This statement is depicted in the Figure 12. It is important to mark that Arena starts the first work shift at 0:00 and the after the seventeenth hour the schedule will repeat from beginning.

Figure 12. Station Schedule

2.5. Resource Failures

This section consists of three parts. First is needed to activate the Failure Option in the “Station 5 Machine”, as can be observed in the last row of the Figure 10. The name of the failure is “Station 5 Machine Failure”, as shown in Figure 13. Although others authors recommend the Wait Option for the Failure rule, when the time between capacity decrease (up time) is much larger than duration of the decrease (down time) (Kelton, et al., 2003); in this paper the Preempt Option will be used, since a breakdown is an unexpected event. 14

Moreover the Station 5 Machine can go into failure status at any time, regardless of whether the entity has seized the resource or not.

Figure 13. Failures, Station 5 Machine Failure

The previous action adds a row in the Failure Module labelled “Station 5 Machine Failure”. The up time (duration of the nominal capacity) is EXPO(120) min and the down time (duration of the decrease) is EXPO(4) min, as shown in Figure 14.

Figure 14. Failure module, Station 5 Machine Failure

Finally, it is imperative to request extra information on the Station 5 Machine, specifically the amount of the time the resource is in a failed state. This feature is achieved using the statistical module, as can be seen in Figure 15. It will give statistics based on all the states of the Station 5 Machine (Busy, Idle and Failed). The tab labelled Output File is used to save output data and later be analysed in the Output Analyser. The file needs an extension *.dat, for instance “Station 5 Machine State.dat”. However, the Output Analyser will not be studied in this paper.

Figure 15. Statistic module, Station 5 Machine State

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2.6. Creating Orders

This section is divided into six parts. The objective for the first four steps is relating each component with a particular picture, the aim for the next steps is creating the orders. First, it is necessary to establish two sets. Contrary to the Figure 5, the Basic Set will be configured in this occasion; since “Entity Picture” and “Entity Type” are required as Set Type. The labels are “Component Picture” and “Component Type” respectively, as illustrated in Figure 16.

Figure 16. Set Basic Process

The second step is creating Picture Names and Entity Types. Each set will have five members because there are five components, as can be observed in Figure 17 and Figure 18.

Figure 17. Picture Name – Members

Figure 18. Entity Pictures – Members

The third step is editing the pictures of the components. It can be achieved using the Entity Pictures option. In this example coloured balls have been selected to represent the five components, simply because it is easy to identify them. However it is possible to select any picture from the libraries.

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Figure 19. Edit entity pictures for components 1, 2, 3, 4 & 5

The fourth step is linking each Entity Type with its Initial Picture. It can be done using the Entity Module, as can be observed in Figure 20.

Figure 20. Link between Type.Component n and Picture.Component n

The fifth step is creating the orders. The order sizes and the time period between each order can be configured in the Create Module, as follows: the time period describes an exponential rate of 24 hours and the order sizes follow a triangular distribution of (30,40,50).

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Figure 21. Create Orders

Finally, the percentage of the components in each order will be established in an Assign Module, labelled “Orders Type and Sequences”, as shown in Figure 22.

Figure 22. Orders Types and Sequences

Orders follow a discrete probability distribution with the following data: 26% of C1s, 10% of C2s, 20% of C3s, 14% of C4s and 30% of C5s. Therefore the Equation 1 depicts the cumulative distribution function. 𝐷𝐼𝑆𝐶(0.26 , 1 , 0.36 , 2 , 0.56 , 3 , 0.7 , 4 , 1 , 5) Equation 1. Discrete Probability Distribution

The Equation 1 will be stored in an Attribute named “Component Index” and the three sets created previously: Component Sequence, Component Type and Component Picture will be in function of this attribute, as shown in Figure 23.

Figure 23. Assignments

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2.7. Stations and Routes

This section consists of three stages: Station Module, Process Module and Route Module. The Station Module represents a physical place. For example, work stations or warehouses. The Route Module depicts a physical path between stations. Figure 24 and Figure 25 show the parameters to configure these modules. It should be noted that the Route Time is the “Transfer Time” defined in section 2.2 and “By Sequence” is configured as the Destination Type

Figure 24. Station n Station

Figure 25. Route from Station n

Figure 26 illustrates the Process Modules. There are five Process Modules because there are five resources, defined in the Figure 10. The Process Time established in Figure 4 is used here as Expression.

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Figure 26. Process n

The next step is establishing the resources of each process. The resources were defined in Figure 10. For instance, the “Station 2 Machine” is the Resource Name of the Process 2, as shown in Figure 27

Figure 27. Station 2 Machine as resource of the Process 2

The final step is setting up the queue priorities; it can be done in the Queue Module. The Figure 28 shows the First in First out (FIFO) option. It means that at each of the machine stations, the highest priority is given to the earliest orders.

Figure 28. Process n. Queue, FIFO

2.8. Suppliers

This section is formed by three steps. The first one is storing the supplier times in the Expression Module (Figure 29). Both suppliers follow a triangular distribution, TRIA(1,1.5,2) hours for supplier 1

20

and TRIA(0.5,1,1.5) hours for supplier 2. These data can be saved as Expression Values, as shown in Figure 30 and Figure 31.

Figure 29. Supplier n Time

Figure 30. Supplier 1 Time

Figure 31. Supplier 2 Time

The second step is building the expression. Supplier 1 sends raw material for components 1, 2 and 3. On the other hand, supplier 2 sends raw material for components 4 and 5. The Equation 2 represents the Supplier Time, which varies with the type of component. In Figure 32 can be seen that the expression has been stored as attribute because it is an entity feature.

(𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝐼𝑛𝑑𝑒𝑥 ≤ 3) × 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑟 1 𝑡𝑖𝑚𝑒 + (𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑖𝑛𝑑𝑒𝑥 > 3) × 𝑆𝑢𝑝𝑝𝑙𝑖𝑒𝑟 2 𝑡𝑖𝑚𝑒 Equation 2. Supplier Time

Figure 32. Assignments

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The third step is using a Delay Module to apply the Supplier Delay. It could have also used a Delay Block; however it is important to keep the harmony in the model.

Figure 33. Supplier Delay

This is the last step for the manufacturing system without assembly station. The simulation model with animation and the report file can be edited following the next links.  Simulation model with animation (CD:\ 01 Without Assembly Station\01 Without AS.doe)  Report file (CD:\ 01 Without Assembly Station\01 Without AS.pdf) The simulation model and the animation are presented in Figure 34 and Figure 35 respectively.

Figure 34. Simulation for the manufacturing system

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Figure 35. Animation for the manufacturing system

3. Identification the bottleneck process

Based on (Groover, 2010) the bottleneck is a constraint of the system. It restricts the system throughput. In industry, bottlenecks limit the system performance in terms of capacity, money or time. Thus, in this report, bottlenecks will be defined in terms of time and capacity. Three indicators are used to identify the constraint of the model  Accumulate Wait Time (Process)  Waiting Time (Queue)  Number Waiting (Queue)

Queue Waiting time Percentage Process 1.Queue 3.1254 34% Process 2.Queue 1.9093 21% Process 3.Queue 3.1157 34% Process 4.Queue 0.086 1% Process 5.Queue 1.0503 11% Total 9.2867 100% Table 2. Waiting time (Queue)

Queue Process 1 Process 2 Process 3 Process 4 Process 5 Total

Number Waiting Percentage 4.0374 34% 3.0671 26% 4.0066 34% 0.0967 1% 0.7398 6% 11.9476 100%

Table 3. Number waiting (Queue)

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Process Process 1 Process 2 Process 3 Process 4 Process 5 Total

Accum Wait Time Percentage 12420.6 34% 9611.85 26% 12361.38 33% 337.59 1% 2339.7 6% 37071.12 100%

Table 4. Accumulated wait time (Process)

The results are presented in Figure 36. The Waiting Time, Accum Wait Time and Number Waiting for processes 1 and 3 are around 34%, meanwhile process 2 barely reaches 26%. Consequently, processes 1 and 3 are the bottlenecks of the system.

Figure 36. Identification of the Bottleneck Process

3.1. Proposal for improvement

There are mainly two options to improve the statistics for processes 1 and 3:  Increase the capacity of the resources 1 and 3  Increase resources in the processes 1 and 3 Both options produce the same result. However, in this paper the second option will be studied; just because it permits to create independent work shifts and differentiate the capability of each machine. There are other simpler options to enhance the statistics. For instance, reduce the delays 24

of the suppliers or reorganize the purchase orders. However, this assignment assumes those data are constant.

3.1.1. Increase resources in processes 1 and 3

New machines are 30% faster than the old ones. In other words, Process Time will be improved 30% with this acquisition. Additionally, the characteristics of each machine are:  Doosan Lynx 220LSY, for process 1 (CD:\Doosan Lynx 220LSY.mp4)  Doosan Puma 2100MS, for process 3 (CD:\Doosan Puma 2100MS.mp4) Two sets of resources were created, “Station 1 Machines” and “Station 3 Machines”. Further, each set contains two members, as shown in Figure 37 and Figure 38.

Figure 37. Station 1 Machines

Figure 38. Station 2 Machines

In order to improve the Process Time, a variable named “Factor” was introduced. Initial Value “1” represents the capacity for old machines and Initial Value “0.7” depicts the capacity for new machines, as illustrated in Figure 39.

Figure 39. Capacity factor for new and old machines

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The next step is incorporating the corresponding set in each process. It can be done in the tab Resources of the Process Module. For example Figure 40 shows the set "Station 1 Machines" incorporated in process 1. Moreover, Equation 3 represents the expression for process 1 to calculate the new Process Time.

Figure 40. Station 1 Machines incorporated in process 1

𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑇𝑖𝑚𝑒 𝑓𝑜𝑟 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 1 = 𝑃𝑟𝑜𝑐𝑒𝑠𝑠 𝑇𝑖𝑚𝑒 × 𝐹𝑎𝑐𝑡𝑜𝑟(𝑀𝑎𝑐ℎ𝑖𝑛𝑒 1 𝐼𝑛𝑑𝑒𝑥) Equation 3. Process Time for process 1

3.1.2. New work shift

The new machines will work at a different work shift. To achieve this requirement, a second schedule name “New Schedule” is created, as can be observed in Figure 41. The new machines will start the work shift one hour later, in other words at 01:00 am. The difference between the original schedule and the new one can be observed in Table 5.

Figure 41. New Resource Module

Time Table 00:00 - 01:00 01:00 - 02:00

Station Schedule Shift 1

New Schedule Break Shift 1 26

02:00 - 03:00 03:00 - 04:00 04:00 - 05:00 05:00 - 06:00 06:00 - 07:00 07:00 - 08:00 08:00 - 09:00

Break

09:00 - 10:00

Break

10:00 - 11:00 11:00 - 12:00 12:00 - 13:00 13:00 - 14:00

Shift 2 Shift 2

14:00 - 15:00 15:00 - 16:00 16:00 - 17:00 17:00 - 18:00

Break Table 5. Difference of schedules

3.1.3. Bonus

The system can be improved even more. According to (Groover, 2010) Throughput Time (TT) is the amount of time required for a product to pass through a manufacturing process, thereby being converted from raw materials into finished goods. In other words, TT covers the entire period from when the entity enters to manufacturing until it exits from manufacturing. Furthermore, it includes the following time intervals:  Processing time. This is the time spent transforming raw materials into finished goods.  Inspection time. This is the time spent inspecting raw materials, work-in-process, and finished goods, possibly at multiple stages of the production process.  Transfer time. This is the time required to move items into and out of the manufacturing area, as well as between workstations within the production area.  Wait time. This is the time spent waiting prior to the processing.

Arena adds five values to calculate this parameter, as depicted in Equation 4

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𝑇ℎ𝑟𝑜𝑢𝑔ℎ𝑝𝑢𝑡 𝑇𝑖𝑚𝑒 = 𝑉𝐴 𝑡𝑖𝑚𝑒 + 𝑁𝑉𝐴 𝑡𝑖𝑚𝑒 + 𝑊𝑎𝑖𝑡 𝑇𝑖𝑚𝑒 + 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑇𝑖𝑚𝑒 + 𝑂𝑡ℎ𝑒𝑟 𝑇𝑖𝑚𝑒 Equation 4. Throughput time in Area

Analysing the report offered by Arena, it can be concluded that Wait Time has a weight of 77.4% of the Total Time, as presented in Table 6. In other words, the more the Wait Time is improved, the more the Total Time is reduced.

Entity

VA time

NVA time

Wait Time

Transfer Time

Other Time

Throughput time

Type.Component 1

0.8823

0

8.8005

0.1251

1.5037

11.3116

Type.Component 2

1.1526

0

10.2404

0.1505

1.4943

13.0378

Type.Component 3

0.6997

0

3.9964

0.0998

1.5021

6.298

Type.Component 4

0.7921

0

6.608

0.1503

1.005

8.5554

Type.Component 5

0.4885

0

8.5963

0.1001

0.9973

10.1822

Total

4.0152

0

38.2416

0.6258

6.5024

49.385

Percentage

8.1%

0.0%

77.4%

1.3%

13.2%

100.0%

Table 6. Total time per component type

In the original model, the rule for Queue Priorities was FIFO; in this section the objective is assigning priorities to components to reduce the Wait Time and consequently, the Throughput Time. The First step is creating five variables labelled Priority C1, …, Priority C5, as shown in Figure 42.

Figure 42. Priority for components

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A new Assign Module will be created, named “Assign Priority”. In this module each component will be linked with its priority, according to the Equation 5. It should be observed that the result of that expression is stored in an Attribute named “Priority”. Name: Type: Attribute Name: New Value:

Assign Priority Attribute Priority (Component Index == 1) * Priority C1 + (Component Index == 2) * Priority C2 + (Component Index == 3) * Priority C3 + (Component Index == 4) * Priority C4 + (Component Index == 5) * Priority C5 Equation 5. Queue Priority Equation

The last step is setting up “Lowest Attribute Value” as the rule for the Queue Priority, as shown in Figure 43. It means that the priority will be given to the entity with the lowest attribute. It should be observed that the Attribute Name was defined in the previous step.

Figure 43. Queue Priority

Before searching the best combination is necessary to build the Response Expression. It will be built in the same Assign Module of the previous step, according to the Equation 6. Name: Type: Attribute Name: New Value:

Assign Priority Variable Throughput Time TAVG(Type.Component 1.TotalTime) + TAVG(Type.Component 2.TotalTime) + TAVG(Type.Component 3.TotalTime) + TAVG(Type.Component 4.TotalTime) + TAVG(Type.Component 5.TotalTime) Equation 6. Throughput Time Equation

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The challenge is finding the best priority combination to reduce the Throughput Time. There are five components and five priorities, therefore 120 combinations (5!). Those 120 combinations can be evaluated in the Process Analyser. The Table 7 shows the best combination. The Process Analyser file can be edited in the next link:  Process analyser file (CD:\07 With Assembly Station and Improved\07 With AS and Improved.pan) The Figure 44 shows the Process Analyser with all combinations.

Type.Component 1 Type.Component 2 Type.Component 3 Type.Component 4 Type.Component 5

Queue Priority 2 1 5 4 3

Table 7. Best Combination

Figure 44. Process Analyser

The simulation model with animation and the report file can be edited following the next links.

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 Simulation model with animation (CD:\07 With Assembly Station and Improved\07 With AS and Improved.doe)  Report file (CD:\07 With Assembly Station and Improved\07 With AS and Improved.pdf) The Figure 45 depicts the improved model layout. Contrary to the Figure 35, this new layout has the two new machines.

Figure 45. Improved model layout

3.2. Comparison of results

3.2.1. Throughput Time

The Throughput Time decreased in overall 35%, according to Table 8 and Figure 46. Component 1, 2 and 3 reported an improvement around 30%. However, Component 5 had a dramatically decrement of 63%. On the other hand, Component 3 increases 1%.

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Entity Type.Component 1 Type.Component 2 Type.Component 3 Type.Component 4 Type.Component 5 Total

Throughput time Throughput time Original Improved 11.1321 7.8129 12.8801 8.3039 6.2899 6.3233 8.3722 5.5758 10.0447 3.6907 48.719 31.7066

Percentage of Improvement 30% 36% -1% 33% 63% 35%

Table 8. Percentage of improvement of throughput time

Figure 46. Comparison of throughput times

3.2.2. Work in Process

Similarly to previous article, Work in Process decreased in overall 40% (Table 9 & Figure 47). Component 1, 2 and 3 reported an improvement around 35%. However, Component 5 had a dramatically decrement of 62%.

Entity Type.Component 1 Type.Component 2 Type.Component 3 Type.Component 4 Type.Component 5 Total

Work in Process Original 4.6812 2.0674 1.971 1.9426 4.8034 15.4656

Work in Process Improved 3.1401 1.3351 1.7951 1.223 1.83189 9.32519

Percentage of Improvement 33% 35% 9% 37% 62% 40%

Table 9. Percentage of improvement of work in process

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Figure 47. Comparison of work in process

3.2.3. Resource Utilization

Instantaneous Utilization changed around 11%. The biggest changes are in Station 1 Machine and Station 3 Machine, this modification is due to the addition which took place. The remaining three machines maintain almost the same level of resource utilization; although, they vary near 5%. Table 10 and Figure 48 display these statistics.

Resource Station 1 Machine Machine 1_New Machine 1_Old

Station 2 Machine Station 3 Machine Machine 3_New Machine 3_Old

Station 4 Machine Station 5 Machine Total

Instantaneous Utilization Original 0.2452 0.2392 0.3379 0.1821 0.187 1.1914

Instantaneous Utilization Improved 0.2008

Percentage of Improvement 18%

0.0945

-

0.1063

0.2325 0.2791

3% 17%

0.1245

-

0.1546

0.1727 0.1734 1.0585

5% 7% 11%

Table 10. Percentage of improvement of instantaneous utilization

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Figure 48. Comparison of instantaneous utilization

4. Assembly Station

This section is composed of seven steps. Firstly, is needed to create entities representing to Product 1 and Product 2. This paragraph covers the same four stages done in article 2.6 Creating Orders. Figure 49 displays the result.

Figure 49. Type.Product n & Picture.Product n

The next step is creating the expressions representing the Assembly Time. This paragraph covers the same first stage done in article 2.7. Figure 50 and Figure 51 display the result.

Figure 50. Assembly 1 Time

Figure 51. Assembly 2 Time

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The third step is creating a station labelled “Assembly Station”, as shown in Figure 52. It represents the entrance to the assembly process and the warehouse of components.

Figure 52. Assembly Station

The fourth step is developing a programming logic to divide the statistics before and after the Assembly Station, because the Waiting Time in Queue of components should not be influenced by the Match Queue or Batch Queue. This is due to the assembly process is part of Company A, as explained in article 1 Introduction. This logic can be programming using a combination of Record Module plus Assign Module. “Assembly Record” is the name for the Record Module, as shown in Figure 53. “Assign Product” is the label for the Assign Module, as displayed in Figure 54

Figure 53. Assembly Record

Figure 54. Assign Product

Then, it is necessary to separate the components to store them in the warehouse of components. The Figure 55 shows a Decide Module named “Assembly Decide”. In this module are written four paths, however there is a fifth path; the option “else”.

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Figure 55. Assembly Decide

The warehouse of components can be modelled using a combination of Match Module plus Batch Module. Match Modules gather the components; for instance, Product 1 is formed by Component 1, 2 and 3. For this reason, the tab named number to match is “3”. Similarly, Product 2 consists of Component 4 and 5. Figure 56 displays the parameters for Match Modules.

Figure 56. Product Match n

Batch Modules sends the components together to the assembly process. Additionally, entities named “Type.Product 1” and “Type.Product 2” (created at the beginning of this article) are used as Representative Entity Type. Figure 57 illustrates the parameters for Batch Modules.

Figure 57. Product Batch n

The sixth step is creating a process named “Assembly Process”, as indicated in Figure 58. Equation 7 represents the assembly time, which varies with the type of product.

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𝐴𝑠𝑠𝑒𝑚𝑏𝑙𝑦 𝑇𝑖𝑚𝑒 = (𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑃𝑖𝑐𝑡𝑢𝑟𝑒(𝑇𝑦𝑝𝑒. 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 1)) × 𝐴𝑠𝑠𝑒𝑚𝑏𝑙𝑦 1 𝑇𝑖𝑚𝑒 + (𝐼𝑛𝑖𝑡𝑖𝑎𝑙𝑃𝑖𝑐𝑡𝑢𝑟𝑒(𝑇𝑦𝑝𝑒. 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 2)) × 𝐴𝑠𝑠𝑒𝑚𝑏𝑙𝑦 2 𝑇𝑖𝑚𝑒 Equation 7. Assembly time

Figure 58. Assembly Process

The last step is the Route Module. It is important to point that unlike the Route Modules created in the article 2.7 Stations and Routes; in this step the Destination Type is “Station”, because after this module the products will go directly to the “Exit System Station”. Figure 59 displays this module.

Figure 59. Route from Assembly Process

The simulation model with animation and the report file can be edited following the next links.

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 Simulation model with animation (CD:\02 With Assembly Station\02 With AS.doe)  Report file (CD:\02 With Assembly Station\02 With AS.pdf)

In order to find the best position for the assembly station is necessary to analyse the indicator named Number Out in the tab of process of the report. The assembly process receives components from three processes, as indicated in Table 1. Process 3 and 4 send more quantity of components, around 41% and 36% respectively (Table 11). Consequently, the assembly station should be located between stations 3 and 4, as shown in Figure 60.

Process

Number Out Percentaje

Process 3

3960

41%

Process 4

3447.8

36%

Process 5

2167.6

23%

Total

9575.4

100%

Table 11. Number out of components

Figure 60. Plan Layout

5. Conveyor System

This section consists of fourth steps. Firstly, variables for “Load Time” and “Unload Time” were created, as shown in Figure 61. In addition, the loading and unloading times have a value of 0.25 min. In other words, the conveyor temporarily stops while the load or unload occurs. 38

Figure 61. Loading and unloading times

The conveyor system name is “Loop Conveyor”. Additionally, this type of conveyor is “NonAccumulating”, it means when an entity accesses space, the entire conveyor stops moving. The tab “Max Cells Occupied” represents the maximum number of cells that entity requires to be transported. Furthermore, size of each cell is 3 ft. Parameters can be observed in Figure 62.

Figure 62. Loop Conveyor

The third step is configuring the conveyor segments; it was realized in the Segment Module of the Advanced Transfer Panel, as shown in Figure 63. It is important to note that “Order Release” is the Beginning Station.

Figure 63. Loop Conveyor.Segment

The actual Transfer Time corresponds to a triangular distribution TRIA(1,1.5,2) min. However, considering the Uniform Motion, the expression for distance is obtained using the Equation 8.

𝑑 = 𝑣𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 × 𝑡 𝑑 = 20 × 𝑇𝑟𝑖𝑎 (1,1.5,2) 𝑑 = 𝑇𝑟𝑖𝑎 (20,30,40) Equation 8. Distance for the conveyor system

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Figure 64 and Equation 9 depict the probability density function and triangular distribution equation for distance = TRIA(20,30,40) ft. This expression could have been calculated in Microsoft Excel; in this assignment the Input Analyser was used.

2(𝑥 − 20) (40 − 20)(30 − 20) 2(40 − 𝑥) (40 − 20)(40 − 30) { 0

Figure 64. Probability density function

𝑖𝑓 20 ≤ 𝑥 ≤ 30 𝑖𝑓 30 ≤ 𝑥 ≤ 40 𝑖𝑛 𝑜𝑡ℎ𝑒𝑟 𝑐𝑎𝑠𝑒𝑠

Equation 9. Triangular distribution equation

The software generated 5000 elements. However, just eight of those are necessary and were introduced as measures of length in the Segment Module, as shown in Figure 66. Moreover, Figure 65 shows the input analyser results.

Figure 65. Probability density function TRIA(20, 30, 40)

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Figure 66. Next Stations

The fourth and last step is replacing all Route Modules by Leave Modules, as shown in Figure 67. Similarly, the Stations Modules by Enter Modules, as displayed in Figure 68.

Figure 67. Start Sequence & Route from Station n

Figure 68. Station n Station

The simulation model with animation and the report file can be edited following the next links.  Simulation model with animation (CD:\05 Conveyor\05 Conveyor.doe)  Report file (CD:\05 Conveyor\05 Conveyor.pdf)

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Figure 69. Conveyor System Layout

5.1. Bonus

The conveyor system will be compared and contrasted with a transport system. The Transfer Time is the same as used in conveyor system. Additionally, it was assumed that there are two transport units. The indicators to compare both models are:  Throughput Time  Work in Process  Resource Utilization

The Throughput Time decreased in overall 16%, according to Table 12. Components 2 and 5 reported the best numbers, around 22%. However, Components 1 and 3 only had a slight increase about 7%. Component 4 is the third best with a decent 12%.

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Entity Type.Component 1 Type.Component 2 Type.Component 3 Type.Component 4 Type.Component 5 Total

Throughput time Throughput time Conveyor Transporter 12.206 15.2866 6.7027 9.4319 12.2111 55.8383

11.1097 12.1739 6.3487 8.313 9.2118 47.1571

Diference of Percentage 9% 20% 5% 12% 25% 16%

Table 12. Throughput Time

The Work in Process decreased in overall 31%, according to Table 13. Components 1 and 4 improved around 27%. However, Components 2 and 5 enhanced significantly about 37%. Although, Component 3 reported the lowest number; it is a remarkable improved of 17%.

Entity

WIP Conveyor

WIP Transporter

Diference of Percentage

Type.Component 1 Type.Component 2 Type.Component 3 Type.Component 4 Type.Component 5 Total

5.2069 2.5176 2.0574 2.1162 5.9991 17.8972

3.8526 1.5954 1.7172 1.5247 3.6902 12.3801

26% 37% 17% 28% 38% 31%

Table 13. Work in Process

The Instantaneous Utilization is the steadiest indicator. It reported an average of 20%, according to Table 14. There is barely five points of difference between the highest mark of 22% for Station 3 Machine and the lowest of 17% for Station 5 Machine.

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Resource Station 1 Machine Station 2 Machine Station 3 Machine Station 4 Machine Station 5 Machine Total

Instantaneous Utilization Conveyor 0.2522 0.2427 0.3518 0.1862 0.1872 1.2201

Instantaneous Utilization Transporter 0.1994 0.1967 0.276 0.1509 0.1558 0.9788

Diference of Percentage 21% 19% 22% 19% 17% 20%

Table 14. Instantaneous Utilization

The simulation model with animation and the report file can be edited following the next links.  Simulation model with animation (CD:\04 Transporter\04 Transporter.doe)  Report file (CD:\04 Transporter\04 Transporter.pdf)

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CONCLUSION

This paper represents a manufacturing system. Further, it consists of five process and five components. The Chapter 2 describes sequences, transfer times, schedules, failures, stations and routes. At this part, the manufacturing system has some flaws. For instance, resources to move components from one station to another are unknown. However, in the analysis is possible to draw some conclusions. Machines 1 and 3 receive more components than others. Furthermore, Components 1 & 2 require more time to be processed. These issues can be solved incrementing the process capacity or reorganizing the purchase orders. The second option is the most cheap and intelligent solution. However, Company B is facing an increase in demand. For that reason, the first option was implemented; an extra machine was added to stations 1 and 3. In addition, queue priorities were modified to give preference to Components 1 & 2. These actions led to remarkable improvements; throughput time decreased 35%, work in process 40% and resource utilization around 11%. Although, these numbers are very promising, the imperative conclusion would have been analysing the profits received due to these changes, as Eliyahu Goldratt relates in his book “The Goal”. With the addition of an assembly machine was necessary to develop a business strategy to relate Companies A and B. Company A does outsourcing with Company B. In other words, the activities of Company B are done in the Company A factory. Additionally, the warehouse of components is crucial, due to it can be seen as a new restriction for the system, considering that the number of components stored is between 742 and 958 (This statistic can be read in the label "Product Match 2.Queue2" of "Waiting Time"). The conveyor was contrasted with a transport system. The last one reported important improvements; throughput time decreased 16%, work in process 31% and resource utilization around 20%. This results are due to the conveyor system is "Non-Accumulating". It would be interesting to compare the transport system vs. an “Accumulating” conveyor system.

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REFERENCES

 Groover, M. P., 2010. Fundamentals of Modern Manufacturing: Materials, Processes, and Systems. 4 ed. Bethlehem(Pennsylvania): John Wiley & Sons Inc..  Kelton, D. W., Sadowski, R. P. & Sadowski, D. A., 2003. Simulation with Arena. 4 ed. New York: McGraw-Hill Education.

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