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Development of Simulation Model for Battery Production Floor

DEVELOPMENT OF SIMULATION MODEL FOR BATTERY PRODUCTION FLOOR BASED ON STOCHASTIC MODELED PRODUCTION RAMP AT ELECTRIC VEHICLE MANUFACTURER

Abstract

The world is facing major risks because of increased emissions of carbon dioxide and greenhouse gas emissions. Electric vehicles have been an answer to combat and limit the consequences of such emissions. Still, electric vehicles’ lithium ion batteries manufacturing dynamics have triggered problems in meeting increasing demand. Thus, uncertainty and unpredictability of battery production exist and peak loads have caused an increase in costs. The main contribution for this project is a developed simulation-based approach to enable the understanding of such production process in a cost-efficient manner. The battery production process is investigated and a simulation model was constructed to minimize the waiting time for workstations and minimize the component flowtimes and increase collaboration between workstations. The data used for the simulation consisted of arrival and service times of battery components. Moreover, the simulation tackles scheduling of manufacturing to optimize the productivity and allow integration between workstations. The battery manufacturing process operations’ results are then used to study the scheduling of operations and reduce the waiting time between workstations to improve the service. Moreover, the case of an electric vehicle manufacturer ramping the production output for vehicles from a factory is referenced. The factory’s capacity utilization is mainly considered to maximize revenue.
Table of Contents
INTRODUCTION AND BACKGROUND
1. Project Introduction
2. Literature Review
3. Problem Statement and Approach
Figure 1: 1st Scenario Ramp
Figure 2: 2nd Scenario Ramp
Figure 3: 3rd Scenario Ramp
Figure 4: Battery Manufacturing General Steps
Figure 5: Detailed Battery Manufacturing Process Flow
METHODOLGY AND MODEL FORMULATION
4 Software
5 Distribution
Table 1: Triangular Distribution Parameters and Constraints
6 Data Analysis, Model and Assumptions:
Table 2: Stochastic Bounds Used
Figure 6: MATLAB Simulation Logic Flow Chart
Figure 7: Scenario-1 Simulated Production Output
Figure 8: Scenario-2 Simulated Production Output
Figure 9: Scenario-3 Simulated Production Output
Figure 10: Initial Production Floor Model
Figure 11: Initial Model Sample Results Report 1-4
Figure 12: Initial Model Sample Results Report 2-4
Figure 13: Initial Model Sample Results Report 3-4
Figure 14: Initial Model Sample Results Report 4-4
MODEL SOLUTION AND RESULTS
7 Solution and Results
Figure 15: Addition of Buffers to the New Production Floor Model
Figure 16: New Model Sample Results Report 1-4
Figure 17: New Model Sample Results Report 2-4
Figure 18: New Model Sample Results Report 3-4
Figure 19: New Model Sample Results Report 4-4
Figure 20: Models Average Wait Time Comparison
Figure 21: Models Average System Utilization Comparison
Figure 22: Add-On Processes Addition
CONCLUSION AND FUTURE WORK
8 Conclusion
9 Future Work
REFERENCES
APPENDIX
Table 3:Workstations Service Times
Table 4: Workstations Processing Times.

INTRODUCTION AND BACKGROUND

  1. Project Introduction

 
The world is facing major problems when it comes to the dangers facing the environment and, therefore, electric vehicles have been an answer to limiting the deteriorating environmental consequences of using gas-guzzling gasoline (Petroleum Fuels) powered vehicles. However, the use of electric vehicles has been associated with impracticality and disappointment. Electric vehicles do not have gas tanks or engines that burn through fuel and releases tremendous amounts of emissions through their exhausts that produce tailpipe emissions. Still, electric vehicles still use electricity which comes from different sources ranging from nuclear fission to natural gas or coal. Moreover, electric vehicles are powered by batteries and therefore do not require a combustion engine. This specific project tackles the development of the most important part of electric vehicles; Lithium Ion Batteries. Tesla, an electric car manufacturer, has been a success when it comes to changing peoples’ view of electric vehicles and thus defined a long-range mobility of electric vehicles. Tesla manufactures various electric vehicles. Tesla’s much anticipated Model 3 is expected to launch by the end of 2017. The $35,000 Model 3 is affordable and is intended to be a mass-market electric vehicle. To successfully produce mass-marketed electric vehicles, a decade-old Tesla is facing a lot of challenges meeting production targets.

Simulating battery production ramps as opposed to vehicles production ramps may help Tesla overcome manufacturing challenges. Therefore, a stochastic modeling of production ramp of vehicles was attempted. Then, development of simulation model for battery production floor was achieved. There are many factors that guide high-volume production ramps. Among these factors are assets utilization and throughput. Thus, addition of assets such as facilities and equipment and workforce could prove successful in achieving production ramps targets. In any production ramp, risks often emerge.
This production ramp of an electric vehicle factory was tested in various scenarios to achieve specified production targets. For this reason, the assumption of meeting all demand was made to avoid demand management issues and focus on the volatile variability. The objective was to maximize the revenue at any time point and throughout the production ramp.
In this production ramp, the attempt was to investigate set quantities and times for models already manufactured by Tesla. Then, the 3rd model (Model 3) that Tesla is going to ramp by the end of 2017 was to start about %33 of the total time to complete the production ramps of all three models. Pricing variation was also investigated per the customers’ customization of vehicles. To make this easier for modeling, a consideration of only the average price per model was factored into the final price. This project will delve into the stochastic modeling of production ramps and the development of simulation model for battery production floor.

  1. Literature Review

(Liang & Yao, 2008) discussed production systems with hybrid modeling approach. They used Arena and Simulink to determine discrete behavior of workshop machines and process level continuous characteristics. Production lines with various machines were modeled using Arena to find the waiting times and output per specific product. They also used MATLAB to copy the controller process and specify the processing times and describe the machines’ operations. This allowed them to evaluate different production lines interactions. This served as a study and the results were not specific and/or clear. (Cho , 2005) presented a distributed simulation for the job-shop scheduling problem. Product parts and machines are treated as events and these entities, thus, have states and associated properties. Information are exchanged between them with an established communication structure. They could determine various machine allocations’ arrival time of parts. (Stahl, et al., 2013) offered simulation of a total factory with the goal of calculating material flow in regards to the environment. The approach used took production assets state-based modeling, parts for example, and combined it with the equipment used with it.
The literature surveyed included endless relevant concepts and solutions for modeling and simulating production systems of batteries. Further research went as far as to include product perspective. It has been noted that the product quality must be contained within multiscale simulation which may include physical process of models as discussed in (Brecher, Esser, & Witt , 2009). Product units’ process results depend heavily on specific parameters of the product type. In is discussed that product units as individual entities and not merely events as it is the case in discrete events simulation (Schönemann, 2007).
(Jordan & Graves, 1991) discusses how important it is to have manufacturing flexibility with regards to product demand future uncertainty. Process flexibility is regarded as being able to manufacture various products at the same factory and time allowing the addition of flexibility and resulting in increasing capacity utilization whereas adding just capacity would not yield the same output.
They introduced principles to implement such process flexibility to a network of production facilities. Product mix responded to unexpected future demand. The conclusion of their paper addresses that limited process flexibility in a plant that has a few product-mix would yield the most sales and capacity utilization with regards to total flexibility. Thus, few long product-plant chains linked by product assignment decisions should be introduced to reach optimal manufacturing flexibility. This is important since all products created within a chain would share the same capacity as well. Their introduction of the principle of chaining helped to achieve total flexibility by manufacturing the same products (batteries, for example) in one production facility.
(Escudero, Kamesam, King, & Wets, 1993) Linear programming was used as opposed to mathematical programming to model production and capacity planning in regards to uncertain future demand. They came up with scenarios to simulate uncertainty which then were aggregated to result in a policy. Nonstationary in demand modeling is a result of their work approaches. They also found a multi-period and multi-product production planning of a linear programming model that set the production volume and inventory of products. The expected cost of inventory and lost demand was thus minimized.
(Gfrerer & Zäpfel, 1995) studied multi-period models of aggregated hierarchical production planning with uncertain demand. Their assumption was that actual planning period has a known demand. When it came to future demand, this same demand was only known for upper and lower bounds. Starting to manufacture batteries for electric vehicles responds to demand of these vehicles and their study suggests that for products aggregate demand, the assumption is to make it deterministic at each planning period as opposed to over the whole planning time, which will result in robust production plans.
For this type of undemand uncertainty in an assemble-to-order situation, strategies to control demand fluctuations in the manufacturer’s forecast models, safety stocks level, and machines/assets needed are a must to mitigate such uncertainty. (Hsu & Wang, 2001) took a linear programming model to treat problems relating to production planning. This model works by adjusting production activities and material management in addition to forecasts.  They emphasized how important production planning decisions respond to demand uncertainty. (Kira, Kusy, & Rakita, 1997) address current production planning practices where models do not incorporate demand uncertainty as a solution and therefore deficiency happens.  They stress the importance of considering uncertain demand in production planning and formulation of stochastic linear programming models to propose practical solutions (Alwuhayb, Dubagunta, Gholami, & Verardo, 2017).

  1. Problem Statement and Approach

The previously performed stochastic modeling project served as an inspiration to this project. (Jordan & Graves, 1991) indicated that to understand demand uncertainty, the process flexibility ought to be increased. The electric car manufacturer, in this case, can reach flexibility when different types of batteries are built in the same factory/production facility. To reach this, standardization of components and production processes must occur. When this is achieved, the product mix is free to change as the demand varies. For Model 3, the product mix is only one. However, within the model, there exists 3 variants. The variants are among size of batteries and gear assembly, etc. these variants drive the efficiency of these electric vehicles. Customer customization is also a variant. (Alwuhayb, Dubagunta, Gholami, & Verardo, 2017) addressed three electric vehicle models (Tesla’s models X, S, 3) and attempted to maximize revenues for these models by the following equations:
Objective:Max Revenue=Dx × Px+Ds ×Ps+D3 ×P3= ∑Di ×Pi
Where D is Demand and P is price
Since the study involved all three Tesla models, this project only addresses Model 3 and its constraints are as follows:
For the output:
The overall weekly average demand for Model 3 would be from 0 < K < 4808, assuming the surge capacity would be higher. For the price, it can be no more than $42,700. The productivity is 30 cars per person and the learning curve is set from 0.5-1. Therefore, the learning curve is:
~N 10,3 for the first three quarters of the year~N 9,2.5 for the following three quarters of the year~N 8,2 for the last three quarters of the year
To achieve this, three scenarios were generated to measure the effectiveness of revenue maximization and workforce ramping. The first strategy is to start ramping Model 3 after %33 of ramping the other two models. The ramp plan is for one hundred and seventeen weeks of continuous ramping. This will not allow achieving a steady state throughput forcing Tesla to surpass the indicated output targets. Thus, a higher surge output occurs.

Figure 1: 1st Scenario Ramp [1]

The second strategy is to ramp the two models from the start until we reach sixty-five weeks in. The assumption is by this time; a steady state output is reached. Model 3 ramping will begin after this time and an overlap for a quarter is reached as well. Model 3 surge out is assumed to be more in this scenario than the others.

Figure 2: 2nd Scenario Ramp [1]

Last strategy considers the Models S and X ramping is increased %33 of the total ramp time allowing them to achieve a steady state output before Model 3 starts ramping. In this scenario, Model 3 ramps for about seventy-eight weeks. Thus, the goal is to achieve ramping for models S and X before Model 3 ramps.

Figure 3: 3rd Scenario Ramp [1]

Battery manufacturing is explained in the figure below. Raw materials where lithium and other components (such as nickel, cobalt, and graphite) are mined and specified. Processed materials are the ready to be transformed into cell components and are used to manufacture electrodes (cathode and anode materials). Typically, cells and electrodes are manufactured in the same facility. Cathode, anode, separator, electrolyte, and housing are used to manufacture cells, which are then assembled into a battery pack along with other components such as thermal management and physical protection.

Figure 4: Battery Manufacturing General Steps

A detailed manufacturing process is shown in the following figure:

Figure 5: Detailed Battery Manufacturing Process Flow

For Tesla, the electric car manufacturer, to deliver on its orders for the Model 3, batteries need to be manufactured as fast as possible to deliver cars to the customers. Current system is complex and workstations’ arrangement causes an increase in flow time, which in return affects service time and waiting time as well for all components’ activities in the workstations. Material’s allocation and equipment availability are important to successful scheduling of activities. An apparent issue is that some components are arriving faster than they should creating long queues in which components were processed at different times. There exists another issue where starvation occurs for later stages of the manufacturing process where idle time nears a %100, sometimes. Thus, the start of the process suffers from long queues causing components to process very slowly. This caused the throughput to decline. Components were processed and manufactured at a much faster rate than the final product at the packaging station, where a full product is assembled. There exists another issue where resources are unevenly distributed causing some resources to arrive at a different rate than other resources. A uniform distribution of resources is desired, ultimately. The amount of some components was more than others and that created waste of some components that are not used.

METHODOLGY AND MODEL FORMULATION

  1. Software

Simio is a noncomplex and flexible software that is used to simulate objects (workstations) and processes and is used to improve and predict modeling capabilities of various systems over a time-period while considering resource capability (machines). The Simi software is used often in the manufacturing, healthcare, and transportation industries. it is useful because it shows the impact of performed improvements to processes while not disturbing the original system’s process. Also, its extensive library that consist of many sources and paths, for example, is an advantage to this software.

  1. Distribution

For this production process, triangular distribution is used because the data did not indicate a specific distribution such as exponential distribution and therefore the assumption, per the data, was triangular distribution, which is used when there is no or little data available. However, it is still not an accurate representation of any data set although it is usually used in the first stage of building a model because time is important and an understanding of the system running is under development. Moreover, triangular distribution is continuous and has a probability density function that has a shape as a triangle. It has three values: minimum value a that increases to peak at the mode c and eventually decreases, linearly, to the maximum value b. For the use of this project, the fact that the maximum and minimum values are estimated even if the mean

and standard deviation are not known, is helpful. This distribution also has an upper and lower limit shrinking the possibility of undesired extreme values. One advantage of this distribution is the fact that it is a good model for skewed distributions.
Three parameter values are used as shown in table 1 below.

Parameter Value Used as Constraints
a Minimum value a≤c
b Maximum value b≥c
c Peak value (height of triangle) a≤c≤b

Table 1: Triangular Distribution Parameters and Constraints

The triangular probability density function is as explained by the following equation with a range of
x∈[a,b]:
Px= 2x-ab-ac-a2b-xb-ab-c for a≤x≤cfor c<x≤b
Its distribution function is as follows with a mode of
c∈[a,b]:
Dx= x-a2b-ab-c 1-b-x2b-ab-c for a≤x≤cfor c<x≤b
CITATION Wol l 1033 (MathWorld, 2017)

  1. Data Analysis, Model and Assumptions:

The analytical research included ramping the production of three electric cars. Model 3 is set to start the production in the last quarter of 2017. Each scenario, discussed previously, had a normally distributed learning curve with three quarters. Workforce increased to meet productivity targets. Then stochastic bounds were introduced as follows:

Time Bound: Lower (LB) Bound: Upper (UB)
First 3 Quarters -30% +5%
Next 2 Quarters -20% +5%
Last Quarter -10% +5%
Rest of Quarters Take the value as it is

Table 2: Stochastic Bounds Used

Stochastic bounds were used to promote a high level of encouragement during production while maintaining the belief that overproduction is not realistic. LB starts low to permit the production and workers to get accustomed to the new production system before the bounds, over time, tightens since the workers’ initial productivity is set at 50%. The table shows that when 6 quarters are finished, the output is taken as is because at this point of time, there should be no more deviation since the plant reaches steady state production. Moreover, workers’ learning curve is ultimately reduced as they are reaching their optimal productivity levels. MATLAB was then used to simulate the manufacturing operations and it was fixed as the details of the production plan emerge over time. Hired workforce learning rate uncertainty was also taken into considerations as a normal distribution beginning with mean of 10 and sigma of 3 for the first 3 quarters, mean of 9 and sigma of 2.5 for the next 3 quarters, and mean of 8 and sigma of 2 for the last 3 quarters.
The simulation methodology used is explained in the following flowchart:

Figure 6: MATLAB Simulation Logic Flow Chart [1]

To reach the goal of producing 500,000 electric vehicles by 2018, it has been found that the second scenario resulted in an output of about 494,500 vehicles (Alwuhayb, Dubagunta, Gholami, & Verardo, 2017). All scenarios simulated production is shown in the figures below.

Figure 7: Scenario-1 Simulated Production Output [1]

Figure 8: Scenario-2 Simulated Production Output [1]

Figure 9: Scenario-3 Simulated Production Output [1]

Furthermore, Tesla is building its Gigafactory that has an annual production capacity of 35 gigawatts-hours (GWh). Tesla claims to cut down the per kilowatt-hour (kWh) cost of their battery pack by more than %35 (Tesla Press, 2016). The current price is $190/KWh which means Tesla’s %35 amounts to $124/KWh. Thus, a 55 KWh battery pack, which is the Model 3’s battery, would cost around $6,875 for the 35,000 Model 3 electric vehicle. This new factory would enable Tesla to produce 1.5 Million cars’ batteries per year per completion in 2020 (Wikipedia, 2016). Tesla’s plan to produce 500,000 Model 3 cars out of these 1.5 Million which means it is 27 Million and a half KWh. Therefore, assuming Tesla’s Gigafactory works 365 days for 24 hours, this factory will produce one Model 3 battery per minute per day. For this model, one battery unit will be produced every one hour.
In the simulation model, the assumption that all 30 workstations require no preparation time (Warm-up), have no downtime, and all parts are ready to be assembled along the production line to meet one battery unit per hour per production line. Moreover, time is measured in minutes and unit time refers to a specific unit process. Some entities go through all workstations and some do not. Also, the process is assumed to be automated and therefore the capacity, for simplicity, is assumed to be 1 for each resource. The distance traveled is also assumed to be short and does not require a large amount of time. To indicate the original model’s process complexity and combine similar processes, Simio is used to simulate the model (Figure 10). Then the model is measured to show performance and how components travel over time between workstations. The path length and travel time between workstations and sources was determined, after multiple runs, to be short to achieve the desired output.
This, of course, represents a challenge to meet specified Key Performance Indicators (KPIs) as the system is complex and requires more time and resources than available.

Figure 10: Initial Production Floor Model

Moreover, running the first iteration of the Simio simulation model of the battery production floor showed an instant throughput and queuing problems. Since not all sources go through all workstations (Sources 1-4, for example), some entities were arriving faster than they should to the winding and stacking workstations creating long queues for the other entities to be processed and thus costing longer processing times which is costly and undesired although, for example, raw materials source number 3 is set to start at 13.4 minutes which is when the other sources and entities arrive to a specific workstation. Some of the process latest workstations were starved. This happened because the workstations never actually received any item due to long hours and therefore having a full idle time. Since the production line is simulated for one hour, upon the first iteration, the first workstations were suffering from long queues with entities taking longer time to be processed causing the throughput buffer to be impacted negatively. In this one hour, hundreds of entities were created but only a few reached the last stages of packaging and shipping. Another important observation was that resources were causing an uneven distribution for entities since some were arriving much more often than other resources. To the observant eye, a uniform distribution could be a better fit for all entities. Lastly, waste of entities created also caused an alarm because some components were created than others, sometimes doubled.  A sample of the results are shown in figures 11-14.

Figure 11: Initial Model Sample Results Report 1-4

Figure 12: Initial Model Sample Results Report 2-4

Figure 13: Initial Model Sample Results Report 3-4

Figure 14: Initial Model Sample Results Report 4-4

MODEL SOLUTION AND RESULTS

  1. Solution and Results

The throughput issue faced in the initial model required a solution that would minimize the severity of it. Thus, two buffers were placed (Figure 15) before the winding and stacking workstations and cathode manufacturing, anode manufacturing, and separator manufacturing workstations to handle the number of components arriving from three different stations/sources at different times and delaying them in a timely manner and releasing them into the queue to the next workstations. Thus, this would assure the entities arrive when needed and solving another issue of some components not making it to the later stages of the model without wasting entities and therefore making it to shipping. Buffers are used to hold the work-in-progress until it is needed while also allowing the work to continue flowing by eliminating hold-ups in the line caused by starving or blocking (Shaaban, 2013).

Figure 15: Addition of Buffers to the New Production Floor Model

The long wait problem for entities to be processed and sources to mix into workstations was solved by creating shorter paths between workstations and sources in addition to setting an offset time for some of the sources and entities to not start until they are needed and therefore adjusting the entities arrival times to be more evenly distributed. For example, raw materials source numbers 1-4 is reduced to start at 10.1 minutes which is when the other sources and entities arrive to workstation cathode manufacturing and 2 others. The introduction of the buffer made this possible. This diminished the possibility of some sources arriving to later stages on the back end of the model sooner than others. This setting of starting when needed was applied to all sources in the model rather than just aligning workstations to have a queue and create a uniformly distributed arrival by a simple trick such as this.
System utilization and throughput solution required reversing the assumption made in the initial model of having the capacity as 1 for each resource. Therefore, the capacity was increased for some resources that are suffering from long queues to be 6 to minimize waiting times. In a real battery manufacturing line, 26 resources are needed for each workstation per line per shift (Chung, Elgqvist, & Santhanagopalan, 2015).
Consequently, the increase in capacity was applied to workstations in the front end of the model such as cathode manufacturing, anode manufacturing, and separator manufacturing. Also, workstations’ capacities at the back end of the model were increased as well. Furthermore, throughput decreased from 2 for the initial model to 1 with significant increase of entities entering later stages of the model.
However, the addition of the buffers decreased the scheduled utilization percentage, which calculates the hours for the resource as a percentage of the available capacity. In general, the scheduled utilization of the reported resources decreased by about %11 for welding and %43 for winding resources, for example. The manager should take advantage of this and increase the production line entities to produce more products. A sample of the revised model’s results are shown in figures 16-19.

Figure 16: New Model Sample Results Report 1-4

Figure 17: New Model Sample Results Report 2-4

Figure 18: New Model Sample Results Report 3-4

Figure 19: New Model Sample Results Report 4-4

The initial and new models average wait time and system utilization charts are displayed in the following figures.

Figure 20: Models Average Wait Time Comparison

Figure 21: Models Average System Utilization Comparison

Moreover, add-on processes to add custom logic were added to the model. The addition of decision logic allowed the control of the paths’ flow in the packaging workstation and upon initialization (Figure 22).

Figure 22: Add-On Processes Addition

CONCLUSION AND FUTURE WORK

  1. Conclusion

The revised model is still not perfect and will require future work since some of the components are still arriving faster than the others, although fewer than before. However, the adjustments made by adding the buffers significantly improved the production line performance and therefore created more profit and increased the potential to produce more. It is true that the new profit is impacted by the number of resources hired. Still, the improvements made in the throughput throughout the system should suffice for the cost of the new hires. Future improvement in utilization is needed as well and the manager of the factory should work to improve the utilization by increasing the production without incurring additional overhead costs relating to buying new equipment. The model needs to be simulated for longer periods of time to see where it can be improved as well. Offset times can be removed as well to create a uniform distribution for the entities across the system. Overall, reducing waiting time improved the throughput of the system.

  1. Future Work

The production line can be studied further by collecting data at each workstation with throughput rate and number of parts arriving and departing during the station’s processing. Chi-squared Goodness test can be used to specify its variable distribution by analyzing the arrival and departure data. Workstations performance measures can be investigated such as utilization factor, waiting time spent in the system and queue, and

number of parts to determine the efficiency of each workstation. This is to apply queuing theory analysis to better estimate the resources needed. Moreover, sorting the entities arriving to buffers in accordance with their storage area that will help make the parts flow smoothly. Some entities’ processing times need to be decreased and an investigation into finding the entities that are not processing as normal as the other entities is needed. Thus, this will help store troubled components in a rack that will not disarrange the order of processing.

REFERENCES

Alwuhayb, A., Dubagunta, V., Gholami, A., & Verardo, A. (2017). Stochastic Modeling of Production Ramp at Electric Vehicle Manufacturer. IISE Annual Conference.
Brecher, C., Esser, M., & Witt , S. (2009). Interaction of manufacturing process and machine tool. CIRP, The International Academy for Production Engineering, (pp. 588-609).
Bryan, M., Patil, K., & Sawant, N. (n.d.). Simulation Model For Production Floor.
Cho , S. (2005). A distributed time-driven simulation method for enabling real-time manufacturing shop floor control. Comput. Ind. Eng., 570-600.
Chung, D., Elgqvist, E., & Santhanagopalan, S. (2015). Automotive Lithium-ion Battery (LIB) Supply Chain and U.S. Competitiveness Considerations. Clean Energy Manufacturing Analysis Center (CEMAC).
Escudero, L. F., Kamesam, P. V., King, A. J., & Wets, R. B. (1993). Production Planning via Scenario Modeling. Annals of Operations Research.
Gfrerer, H., & Zäpfel, G. (1995). Hierarchical Model for Production Planning in the Case of Uncertain Demand. European Journal of Operational Research.
Hsu, H., & Wang, W. (2001). Possibilistic Programming in Production Planning of Assemble-to-Order Environments. Fuzzy Sets and Systems.
Jordan, W. C., & Graves, S. C. (1991). Principles on the Benefits of Manufacturing Flexibility. General Motors Research Publication.
Kira, D., Kusy, M., & Rakita, I. (1997). A Stochastic Linear Programming Approach to Hierarchical Production Planning. Journal of the OR Society.
Liang, S., & Yao, X. (2008). Multi-level Modeling for Hybrid Manufacturing Systems Using Arena and MATLAB. Int. J. Simul. Multisci. Des. Optim., 155-160.
Marsudi, M., & Shafeek, H. (2014). The Application of Queuing Theory in Multi-Stage Production Line. International Conference on Industrial Engineering and Operations Management. Bali: IEOM Society.
MathWorld, W. (2017, Feburary 11). mathworld.wolfram.com. Retrieved from http://mathworld.wolfram.com/TriangularDistribution.html
Schönemann, M. (2007). Multiscale Simulation Approach for Battery Production Systems. Springer.
Shaaban, S. (2013). Production Line Efficiency: A Comprehensive Guide for Managers. Business Expert Press.
Simio. (2011). Simio Reference Guide. Retrieved from Simio.com: www.simio.com
Stahl, B., Taisch, M., Cannata, A., Müller, F., Thiede, S., Herrmann, C., . . . A., F. C. (2013). Combined Energy, Material and Building Simulation for Green Factory Planning. 20th CIRP International Conference on Life Cycle Engineering (pp. 491-499). Singapore: Springer.
Tesla Press. (2016). Tesla Gigafactory. Retrieved from Tesla.com: https://www.tesla.com/gigafactory
Wikipedia. (2016). Wikipedia. Retrieved from Wikipedia.com: https://en.wikipedia.org/wiki/Gigafactory_1
 

APPENDIX

Raw Materials (Components) Cathode Mix 
WS1
Cathode Coat 
WS2
Cathode Compress 
WS3
Cathode Dry 
WS4
Cathode Slit 
WS5
Cathode Manufacturing 
WS6
Cathode Electrode 
WS7
Entity 1 3.13 3.13
Entity 2
Entity 3
Entity 4
Entity 5 2 2.57 3.13 3.13 3.13
Entity 6 2 2.57 3.13 3.13 3.13
Entity 7 2.57 3.13 3.13 3.13
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) Anode Mix 
WS8
Anode Coat 
WS9
Anode Compress 
WS10
Anode Dry 
WS11
Anode Slit 
WS12
Anode Manufacturing 
WS13
Anode Electrode 
WS14
Entity 1 3.13 3.13
Entity 2
Entity 3
Entity 4
Entity 5
Entity 6
Entity 7
Entity 8 2 2.57 3.13 3.13 3.13 3.13 3.13
Entity 9 2 2.57 3.13 3.13 3.13
Entity 10 2.57 3.13 3.13 3.13
Entity 11
Entity 12
Entity 13
Raw Materials (Components) Separator 
Manufacturing
WS15
Separator Final 
WS16
Winding WS17 Connect Electrodes WS18 Insert Electrode Jellyroll WS19 Subassembly WS20  
Entity 1 1.5 .75 1.5 3.44 4.44 5
Entity 2
Entity 3
Entity 4
Entity 5
Entity 6
Entity 7
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) Stacking 
WS21
Connect Electrodes 
WS22
Insert Electrode Stack 
WS23
Subassembly_ 
WS24
  
 
 
 
 
 
 
 
 
Entity 1 1.5 3.44 4.44 4.44
Entity 2
Entity 3
Entity 4
Entity 5
Entity 6
Entity 7
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) Weld 
WS25
Vacuum WS26 Seal 
WS27
Formation 
WS28
Storage 
WS29
Testing & 
Packing
WS30
Shipping 
WS31
Entity 1 5 5 3.16 2.83 1.6 5 0
Entity 2
Entity 3
Entity 4
Entity 5
Entity 6
Entity 7
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13

Table 3:Workstations Service Times

Raw Materials (Components) Inventory to WS 1 To WS 1 Flow Time WS 1 Arrival Time WS 1 Departure Time WS 2 Flow Time and Arrival Time WS 2 Departure Time
Entity 1
Entity 2
Entity 3
Entity 4
Entity 5 1.12 1.12 1.13 3.13 3.69 6.82
Entity 6 .56 .56
Entity 7 .56 3.13
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) WS 3 Flow Time and Arrival Time WS 3 
Departure Time
WS 4 Flow Time and Arrival Time WS 4 
Departure Time
WS 5 
 Flow Time and Arrival Time
WS 5 
 Departure Time
Entity 1
Entity 2
Entity 3
Entity 4
Entity 5 6.84 9.97 10 13.13 13.16 16.29
Entity 6
Entity 7
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) WS 6 Flow Time and Arrival Time WS 6 
Departure Time
WS 7 Flow Time and Arrival Time WS 7 
Departure Time
WS 8 
 Flow Time and Arrival Time
WS 8 
 Departure Time
Entity 1
Entity 2
Entity 3
Entity 4
Entity 5 16.32 19.45 19.48 22.61
Entity 6
Entity 7
Entity 8 113 3.13
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) WS 9 Flow Time and Arrival Time WS 9 
Departure Time
WS 10 Flow Time and Arrival Time WS 10 
Departure Time
WS 11 
 Flow Time and Arrival Time
WS 11 
 Departure Time
Entity 1
Entity 2
Entity 3
Entity 4
Entity 5
Entity 6
Entity 7
Entity 8 3.69 6.82 6.84 9.97 10 13.13
Entity 9
Entity 10 .56 3.13
Entity 11
Entity 12
Entity 13
Raw Materials (Components) WS 12 Flow Time and Arrival Time WS 12 
Departure Time
WS 13 Flow Time and Arrival Time WS 13 
Departure Time
WS 14 
 Flow Time and Arrival Time
WS 14 
 Departure Time
Entity 1
Entity 2
Entity 3
Entity 4
Entity 5
Entity 6
Entity 7
Entity 8 13.16 16.29 16.32 19.45 19.48 22.61
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) WS 15 Flow Time and Arrival Time WS 15 
Departure Time
WS 16 Flow Time and Arrival Time WS 16 
Departure Time
WS 17 
 Flow Time and Arrival Time
WS 17 
 Departure Time
Entity 1 14 15.5 15.9 32.45 33 34.5
Entity 2
Entity 3
Entity 4
Entity 5 — 
23 
24.5 
Entity 6
Entity 7
Entity 8
Entity 9
Entity 10
Entity 11
Entity 12
Entity 13
Raw Materials (Components) WS 18 Flow Time and Arrival Time WS 18 
Departure Time
WS 19 Flow Time and Arrival Time WS 19 
Departure Time
WS 20 
 Flow Time and Arrival Time
WS 20 
 Departure Time
Entity 1 33.4 37.4 37.8 42.8 43.2 48.1
Entity 2 33.4 37.4 37.8 42.8 43.2 48.1
Entity 3 33.4 37.4 37.8 42.8 43.2 48.1
Entity 4 33.4 37.4 37.8 42.8 43.2 48.1
Entity 5 24.9 28.9 29.3 34.3 34.7 39.8
Entity 6 24.9 28.9 29.3 34.3 34.7 39.8
Entity 7 24.9 28.9 29.3 34.3 34.7 39.8
Entity 8 24.9 28.9 29.3 34.3 34.7 39.8
Entity 9 24.9 28.9 29.3 34.3 34.7 39.8
Entity 10 24.9 28.9 29.3 34.3 34.7 39.8
Entity 11 24.97 28.41 28.8 34.3 34.7 39.8
Entity 12 28.97 33.41 33.97 38.41
Entity 13 33.97 38.41
Raw Materials (Components) WS 21 Flow Time and Arrival Time WS 21 
Departure Time
WS 22 Flow Time and Arrival Time WS 22 
Departure Time
WS 23 
 Flow Time and Arrival Time
WS 23 
 Departure Time
Entity 1 33 34.5 33.4 37.4 37.8 42.8
Entity 2 33.4 37.4 37.8 42.8
Entity 3 33.4 37.4 37.8 42.8
Entity 4 33.4 37.4 37.8 42.8
Entity 5 23 24.5 24.9 28.9 29.3 34.3
Entity 6 24.9 28.9 29.3 34.3
Entity 7 24.9 28.9 29.3 34.3
Entity 8 24.9 28.9 29.3 34.3
Entity 9 24.9 28.9 29.3 34.3
Entity 10 24.9 28.9 29.3 34.3
Entity 11 28.8 34.3
Entity 12 28.97 33.41
Entity 13
Raw Materials (Components) WS 24 Flow Time and Arrival Time WS 24 
Departure Time
WS 25 Flow Time and Arrival Time WS 25 
Departure Time
WS 26 
 Flow Time and Arrival Time
WS 26 
 Departure Time
Entity 1 43.2 48.1 48.5 53.5 53.7 57.1
Entity 2 43.2 48.1 48.5 53.5 53.7 57.1
Entity 3 43.2 48.1 48.5 53.5 53.7 57.1
Entity 4 43.2 48.1 48.5 53.5 53.7 57.1
Entity 5 34.7 39.8 40.3 45.5  45.7 49.2
Entity 6 34.7 39.8 40.3 45.5  45.7 49.2
Entity 7 34.7 39.8 40.3 45.5  45.7 49.2
Entity 8 34.7 39.8 40.3 45.5  45.7 49.2
Entity 9 34.7 39.8 40.3 45.5  45.7 49.2
Entity 10 34.7 39.8 40.3 45.5  45.7 49.2
Entity 11 34.7 39.8 40.3 45.5  45.7 49.2
Entity 12 33.97 38.41 40.3 45.5  45.7 49.2
Entity 13 33.97 38.41 40.3 45.5  45.7 49.2
Raw Materials (Components) WS 27 Flow Time and Arrival Time WS 27 
Departure Time
WS 28 Flow Time and Arrival Time WS 28 
Departure Time
WS 29 
 Flow Time and Arrival Time
WS 29 
 Departure Time
Entity 1 57.3 60.46 60.48 63.31 63.33 64.93
Entity 2 57.3 60.46 60.48 63.31 63.33 64.93
Entity 3 57.3 60.46 60.48 63.31 63.33 64.93
Entity 4 57.3 60.46 60.48 63.31 63.33 64.93
Entity 5 49.5 52.66 52.69 55.52 55.55 57.15
Entity 6 49.5 52.66 52.69 55.52 55.55 57.15
Entity 7 49.5 52.66 52.69 55.52 55.55 57.15
Entity 8 49.5 52.66 52.69 55.52 55.55 57.15
Entity 9 49.5 52.66 52.69 55.52 55.55 57.15
Entity 10 49.5 52.66 52.69 55.52 55.55 57.15
Entity 11 49.5 52.66 52.69 55.52 55.55 57.15
Entity 12 49.5 52.66 52.69 55.52 55.55 57.15
Entity 13 49.5 52.66 52.69 55.52 55.55 57.15
Raw Materials (Components) WS 30 Flow Time and Arrival Time WS 30 
Departure Time
Entity 1 64.97 69.2
Entity 2 64.97 69.2
Entity 3 64.97 69.2
Entity 4 64.97 69.2
Entity 5 57.55 63.55
Entity 6 57.55 63.55
Entity 7 57.55 63.55
Entity 8 57.55 63.55
Entity 9 57.55 63.55
Entity 10 57.55 63.55
Entity 11 57.55 63.55
Entity 12 57.55 63.55
Entity 13 57.55 63.55

Table 4: Workstations Processing Times.

Note: Some of the data obtained from (Chung, Elgqvist, & Santhanagopalan, 2015)



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