Delft University of Technology
FACULTY MECHANICAL, MARITIME AND MATERIALS ENGINEERING
Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl
This report consists of 33 pages. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning the contents of the advice.
Specialization: e.g. Transport Engineering and Logistics
Report number: 2015.TEL.7940.
Title:
Modelling the learning curve of
operators in a simple assembly
line balancing problem
Author:
L.S.J.C. Lanphen
1369512
Title (in Dutch) Het modelleren van de leercurve van een arbeider in een eenvoudige assemblagelijn balanceer vraagstuk
Assignment: Research Assignment
Confidential: No
Initiator (university): Delft University of Technology Supervisor: Dr.ir. H.P.M. Veeke
S
UMMARY
Since Olds patented the assembly line concept in 1901, it became increasingly popular. An assembly line is a sequence of workstations connected by a material handling system and is used for mass and large-scale series production. At each station certain tasks are performed on the ”product” and these certain tasks fit in the cycle time. The cycle time is the maximum time available for each work cycle. One major decision issue of the assembly line is the balancing problem, which arises when an assembly line needs to be configured or redesigned. The goal is to distribute the total workload among the workstations along the assembly line and minimize the idle time.
The research done on the assembly line balancing problem is mostly devoted to modelling and solving the Simple Assembly Line Balancing Problem (SALBP). Different kind of solutions are suggested in literature to solve the various types of simple assembly line balancing problems. It is found that current literature does not describe the influence of the operators learning curve on the assembly line balancing problem. When the tasks of a station are performed multiple time by an operator, the experience of that operator with those tasks increases and by that decreases the task time with a certain learning curve.
In this research a simulation model is created to create and analyse a digital prototype of an assembly line to predict its performance in the real world. The model helps the user to understand, under what condi-tions, and in which way the assembly line could be improved. The main processes of the model are the station-process and the (re)assigning tasks to a station-process. The (re)assigning tasks to a station-process is a process where the model searches for the optimal cycle time in which the workload is divided as evenly as possible. The station-process is the production process of the products along the stations.
In conclusion a model has been successfully developed that includes the learning curve of an operator in the simple assembly line balancing problem. The developed model is able to select the most optimal cycle time in which the workload is divided as evenly as possible and analyse the effect of the operators learning curve on the assembly line. Nevertheless, further adjustments are required to improve the developed model configuring it to the needs of a specific factory or industry.
Keywords: Simple Assembly Line Balancing Problem, Learning Curve, Simulation Model, Mass-Production, Line Efficiency.
L
IST OF
S
YMBOLS
a first term of the geometric progression
c cycle time
c* optimal cycle time
cst ep iterative step size of cycle time
DP production volume
E line efficiency
Ik idle time of station k
LC lower bound on the cycle time
LR/ LRoper at or learning rate of a specific operator
LRmax maximum learning percentage/ rate of an operator
m number of stations; index k = 1,....,m
n number of tasks; index j = 1,...,n
r common ratio
Sk station load, of station k
tj task time of task j=1,...,n
tmi n minimal task time
tmax maximal task time
tsum total task time
t(Sk) station time of station k
C
ONTENTS
Summary 1 List of Symbols 3 1 Introduction 7 2 Model set-up 9 2.1 Model overview . . . 92.2 Model programming software. . . 9
2.3 Notations . . . 10
2.4 In- & output of the model . . . 10
2.4.1 Inputs . . . 10
2.4.2 Input data set . . . 11
2.4.3 Outputs . . . 11
2.5 Key performance indicators. . . 13
3 Model 15 3.1 Element classes and attributes . . . 15
3.2 Model code . . . 16
3.3 Procedures . . . 17
3.3.1 Initialize procedure . . . 17
3.3.2 Station procedure . . . 19
4 Results 21 4.1 Key performance indicators results . . . 21
4.1.1 (Decreased) Process time . . . 21
4.1.2 Average station idle time of the last product . . . 22
4.1.3 Average station time after reassigning all tasks . . . 23
4.1.4 The line efficiency before and after the interim reassigning of tasks . . . 23
4.2 Additional results . . . 24
4.2.1 Decreased cycle time after reassigning all tasks . . . 24
4.2.2 The minimum and maximum workload at different process moments. . . 25
4.2.3 If interim reassigning all tasks is useful. . . 25
5 Verification & Validation 27 5.1 Model verification. . . 27
5.1.1 Checks . . . 27
5.1.2 Analytical results and event tracing . . . 28
5.2 Model validation . . . 29
6 Conclusion & Recommendations 31 6.1 Conclusion . . . 31
6.2 Recommendation . . . 32
References 33 A Appendix 35 A.1 Production & idle times per product and per learning curve . . . 35
A.2 Line efficiencies per different learning curves . . . 37
A.3 Cycle times before and after reassigning tasks per different learning curves. . . 37
A.4 Hand calculated task times . . . 38
A.5 Event trace . . . 39
1
I
NTRODUCTION
BACKGROUND
Since Olds patented the assembly line concept in 1901, it became increasingly popular [1]. An assembly line is a sequence of workstations connected by a material handling system [5]. Assembly lines are used for mass and large-scale series production and appear from single-model lines to lines with parallel work stations or tasks, customer-oriented mixed model and multi-model lines, U-shaped lines and unpaced lines with intermediate buffers [3]. At each station in de assembly line, certain tasks are performed on the ”product” and these certain tasks fit in the cycle time. The cycle time is the maximum time available for each work cycle. One major decision issue of the assembly line is the balancing problem, which arise when an assembly line needs to be configured or redesigned. The goal is to distribute the total workload among the workstations along the assembly line and minimize the idle time. The decision problem of optimally balancing the work load among the stations with respect to some objectives is known as the Assembly Line Balancing Problem (ALBP) [10].
PROBLEM STATEMENT
The research done on the assembly line balancing problem is mostly devoted to modelling and solving the simple assembly line balancing problem (SALBP). This single-model problem contain the following charac-teristics [10];
Figure 1.1: Learning curve
• Mass-production of one homogeneous product
• Paced line with fixed cycle time (c)
• Deterministic operation time (tj)
• No assignment restrictions besides the precedence constraints
• Serial line layout with m stations
• All stations are equally equipped with respect to machines and workers
• Maximize the line efficiency (E)
Different kind of solutions are suggested in literature to solve the various types of simple assembly line bal-ancing problems. It is found that current literature does not describe the influence of the operators learning curve on the assembly line balancing problem. Performing the tasks of the station takes a task time and re-quires certain equipment of machines and skills of the operator. When a task is performed multiple time by an operator, the experience of that operator with that task increases and by that decreases the task time with a certain learning curve. This curve is presented in Figure 1.1. The learning curve of an person is influenced by multiple factors, namely [2];
8 1.INTRODUCTION
●Initial approach to learning ●Skills and coping strategies
●Age ●Emphasis on (non academic) activities
●Gender ●Preferences for teaching methods
●Intellectual ability/ cognitive development ●Self-direction in learning
●Personality ●Learning habits and preferences
●Emotions (Motivation, enjoyment in learning, un-certainly or low self-esteem or anxiety or failure
●Previous work/ experience)
●Social style
These factors causes that each operator will have a different kind of learning curve, which effects the workload distribution and optimization of the assembly line.
By means of trial and error the assembly line balancing problem can be solved, but this is a very costly process. In this case a simulation model can be a solution to create and analyse a digital prototype of an assembly line to predict its performance in the real world. The model can help the the user to understand whether, under what conditions, and in which way the assembly line could be improved.
RESEARCH OBJECTIVE
The purpose of this research assignment is to create a simulation model that creates a digital prototype of an assembly line and analyses the effects of the operators learning curve on the assembly line. The research goal is defined as following:
2
M
ODEL SET
-
UP
This chapter has the purpose to describe the set-up of the simulation model. An overview of the developed model is presented in section 2.1, the chosen software in section 2.2 and the notations in section 2.3. The models in- and output are discussed in section 2.4, where also a simple test input data set is given, which can be used for the verification of the model. The chapter ends with section 2.5, that describes the key perfor-mance indicators that have been chosen in relation to the problem statement.
2.1.
M
ODEL OVERVIEW
In this section a simplified schematic overview is presented of the models processes to create an understand-ing of the model, where Figure 2.1 is that simplified schematic overview. When startunderstand-ing the model, it will create an assembly line with the elements; stations with operators, tasks and products. When all these el-ements are created, the tasks will be assigned to stations with an as even workload per station as possible. This is done with an iterative process. After all the tasks are assigned, the station process will start and the products will go through the process from station 1 to the last station. When the last product is processed by the last station, the tasks are reassigned to the stations to see if it is required to balance the workload.
Figure 2.1: Overview of the simplified schematic model
2.2.
M
ODEL PROGRAMMING SOFTWARE
To create a simulation model of the Assembly Line Balancing Problem a suitable model programming soft-ware is required. The model needs to work with the assembly line, multiple stations, products and tasks. This creates challenges regarding to the parallel processes. An other requirement of the program is that the model needs to cope with inputs, which are determined by the user.
The simulation program Delphi in combination with TOMAS is been chosen, because it allows object-oriented programming and can simulate parallel processes. Furthermore the user can chose on which set of relevant parameters it want to focus during optimization depending on the goal of the user.
10 2.MODEL SET-UP
2.3.
N
OTATIONS
In literature the same notations are used for the Simple Assembly Line Balancing Problem (SALBP) [10], [5], [9], [3]. In Table 2.1 the notations used in the model are shortly described. The notations are used in the model as abbreviations.
Table 2.1: Simple Assembly Line Balancing Problem notations [10]
Notation Definition
n number of tasks; index j = 1,..., n
m number of stations; index k = 1,...., m
c, c* cycle time, optimal cycle time
LC, UC lower, upper bound on c
tj, tmi n, tmax, tsum task time of task j=1,..., n; minimal, maximal, total task time
Sk, t(Sk) station load, station time of station k; t(Sk) =∑j∈Sktj, k = 1,..., m
Ik idle time of station k; Ik= c - t(Sk)
E Line efficiency [%]
2.4.
I
N
- &
OUTPUT OF THE MODEL
In Figure 2.2 a black box is presented as very simple representative of the model, with its in- and outputs. subsection 2.4.1 and subsection 2.4.3 will go further into details over the inputs and outputs of the model.
Figure 2.2: Black Box approach
2.4.1.
I
NPUTSThe output of a model depends on the input specified by the user. The model of this research has two types of inputs; inputs that the user can specify in the graphical interface, see Figure 2.3, and initial values, which are specified by the program owner. The user can specify the following inputs:
• Number of products to be produced
• Number of stations
• Number of tasks
• Maximum learning rate of an operator
The user can indicate, through check boxes, if the following inputs are required: 2014.TEL.7893
2.4.IN- &OUTPUT OF THE MODEL 11
• A learning curve
• A fixed learning curve
• Interim reassigning of tasks after finishing the last product
By checking the ”Fixed learning curve?” check box, the user can create reproducible output data. It can also help to compare what the influence is of tuning certain input data at a certain maximum learning rate of the operators, like; the number of stations, number of tasks, number of products, etc..
Figure 2.3: The users graphical interface concerning inputs
The initial values specified in the model are:
• Iterative step size
• Minimum & maximum task time
2.4.2.
I
NPUT DATA SETIn order to run the model and create results and data for verification, the model requires simple test input data. Table 2.2 shows the test input data that are partly established after consultation with the supervisor. To compare and create an understanding of the models output, certain types of input data have multiple values. These multiple value inputs are the number of products, the maximum learning rate of the operator and if the learning curve of an operator is turned ”on”.
Table 2.2: Simple test input data for model verification
Variable Symbol Value Unit
Number of stations m 20
-Number of products DP 4, 8, 16 or 32
-Number of tasks n 50
-Maximum learning rate of an operator LRmax 70, 75, 80, 85, 90 or 95 %
Learning curve operator LRoperator Uniform distributed [LRmax- 100] %
Task time tj Uniform distributed [10 - 30] seconds
Iterative step size of cycle time cst ep 1 seconds
Learning curve - ON/ OFF
-Fixed learning curve - ON/ OFF
-Interim reassigning of tasks after finishing the last product
- ON/ OFF
-2.4.3.
O
UTPUTSFigure 2.4 presents the graphical interface with multiple outputs. The most important output variables of the model are listed below:
• (Decreased) Production time of the last product
• Average idle time per station of the last product
• Average station time after reassigning all tasks after finishing the last product
12 2.MODEL SET-UP
• The minimum and maximum workload at different process moments (start, at the last product, after the interim reassigning of all tasks)
• The line efficiency at certain production moments
• If interim reassigning all tasks is useful
Figure 2.4: The graphical interface when simulating
The graphical interface shows multiple outputs, which are enumerated. The enumerated outputs will be described below more in detail;
1. Input boxes: Described in subsection 2.4.1.
2. Stations: The situation and information of the stations (1,...,m) are presented here (a) Station name: The station name/ number that indicates which station is meant (b) Learning rate: The learning rate as percentage of the operator of the station (c) Task list: Presents which tasks are assigned to the station
(d) Tasks per station: The number of tasks assigned to the stations (e) Station time: The total time of the tasks assigned to the station
(f ) Product box: When this box is red, it shows that the station is occupied by the product ”Pj”
(g) Product box: When this box is green, it shows that the station is free 3. Station process: Every handling step of the stations process is defined here 4. Origin cycle time: The iterative determined cycle time at the start of the process 5. Total origin assembly time: The total time of all the tasks at the start
6. Tasks per station: Just like 2b, but needed for processing the output 7. Station times: Just like 2c, but needed for processing the output
8. End results: Gives the outputs; cycle times at different process moments, # iterative steps, iterative step size, average station times at different process moments, workload distribution at different process moments, product finish-, idle- and production times, the decreased assembly line time at the end of the process and if it is efficient to interim reassign the tasks
9. Learning rate operators: Just like 2a, but needed for processing the output
10. New task times influenced by the learning curve: Shows the current task time determined by the learn-ing curve of the operator
2.5.KEY PERFORMANCE INDICATORS 13
11. Stationtimes after last product: Presents the individual station times just before the reassigning of tasks 12. Line Efficiency: Shows the line efficiency at the start of the process, before and after the interim
reas-signing of tasks
2.5.
K
EY PERFORMANCE INDICATORS
A key performance indicator (KPI) is a type of performance measurement. According to Gutierrex-Miravete [5], the key objective in the operation of each assembly line is to minimization the idle time. The model can use KPI’s to evaluate the performance of the assembly line. The KPI’s for this simulation program have therefore been defined as:
• (Decreased) Process time
• Average idle time per station of the last product
• Average station time after interim reassigning of the tasks
• The line efficiency before and after the interim reassigning of tasks
The next chapter shows how the in- and output and key performance indicators are incorporated in the struc-ture of the model.
3
M
ODEL
The model’s structure is described in this chapter. The basic structure of the model, the element classes and attributes, are given in section 3.1. The code content and the procedures are described in section 3.2 and section 3.3.
3.1.
E
LEMENT CLASSES AND ATTRIBUTES
Before the models processes can be describe, it is important to know which classes and attributes are used. The classes and attributes, that are needed for the software program TOMAS, are listed and shortly explained in this section.
Assembly Line (SimElement)
The assembly line is the system boundary for the stations, tasks and products.
• AllStationQ (Queue)
The AllStationQ contains all stations of the assembly line.
• FinishedProductsQ (Queue)
The FinishedProductsQ contains all the products that are processed by all the stations.
• AlltasksQ (Queue)
The AlltasksQ contains all the tasks when the tasks are not assigned to the stations.
Station (SimElement)
The assembly line consists of several stations.
• StationQ (Queue)
The StationQ is a queue that contains the product that is inside the station.
• StationqQ (Queue)
The StationqQ contains all the products that are waiting to be processed by the station.
• Stationnumber (Value)
The Stationnumber is a number that indicates which station is meant.
• TasklistQ (Queue)
The TasklistQ is a queue that contains all the tasks that are assigned to the station.
• LRperoperator (Value)
The LRperoperator is a percentage that indicates what the learning rate is of the operator of the station.
• Origintasksperstation (Value)
The Origintasksperstation is a value that indicates the amount of tasks assigned to the station at the start of the process.
• Originstationtime (Value)
The Originstationtime is the total time of all the tasks assigned to the station at the start of the process.
• Process
16 3.MODEL
Product (SimElement)
The Product is the object that moves around in the system. From the first to the last station of the assembly line.
• Arrivaltime (Value)
The Arrivaltime is the time that all the products, that need to be processed by the assembly line, arrive at/ delivered to the assembly line.
• Starttime (Value)
The Starttime is a time value that is determined when the products leave the first StationqQ and by that enters the first stationQ. This is the start of the products process time.
• Finishtime (Value)
The Finishtime is the time at which the product is passed all the stations of the assembly line process.
• Productnumber (Value)
The Productnumber is a number that indicates which product is meant.
• Tasktime (Value)
The Tasktime is the time of a task, which is dependent on the series of products and the LRperoperator.
Task (SimElement)
The Task is the object that is (interim re)assigned from the AlltasksQ of the assembly line to the TasklistQ of the stations. A Task is a process step of the product.
• tj (Value)
The tj is the time that is required to process a task.
• Origintj (Value)
The Origintj is the original tj of a task at the start of the process.
• Originstation (Value)
The Originstation is the station where the task was to assigned at the start of the process.
• Tasknumber (Value)
The Tasknumber is a number that indicates which task is meant.
3.2.
M
ODEL CODE
A simplified version of the model code is presented in this section. Here the build up and procedures of the model are placed in order. The entire model code can be found in section A.6 of the appendix.
- unit AssemblyLineBalancingProblem; + interface
- implementation
{$R *.dfm}
+ constructor AssemblyLineclass.Create(Aname: string); + constructor Stationclass.Create(Bname: string);
//////////Initialize Process /////////////////////////////
+ procedure initialize;
//////////Station Process //////////////////////////////
+ procedure Stationclass.process;
//////////Buttons /////////////////////////////////////
+ procedure Start button; + procedure Interrupt button; + procedure Stop button; + procedure Resume button; end.
3.3.PROCEDURES 17
In the initialize procedure and station procedure a couple of processes are required to run the model. The following processes will be described in detail in section 3.3.
Initialize procedure: Station procedure:
- Creating tasks - Process products
- Creating stations with operators - Remove tasks form stations
- Create products - Reassign tasks to stations
- Assign tasks to stations
3.3.
P
ROCEDURES
In this section the different kind of processes are described in more detail that are used in the two procedures; Initialize procedure in subsection 3.3.1 and the station procedure in subsection 3.3.2.
3.3.1.
I
NITIALIZE PROCEDUREThe initializing procedure is activated when the start button is clicked. This procedure is needed to build the structure of the model and sets all conditions right to start the station procedure. After the assembly line is created, which is also the system boundaries, the following processes will follow in chronological order.
CREATING TASKS
One of the inputs that is determined by the user is the number of tasks (n) that need to be preformed on a product. These n tasks are created with the variables; tasknumber (1,...,n), tasktime and the origin tasktime. The tasktime is determined by a sample out of a uniform distribution between 10 and 30 seconds (the initial values; minimum and maximum task times). At this point, the tasktime and origin tasktime are the same. After all the tasks are created, the total time of all tasks is determined for calculations of the cycle time.
CREATING STATIONS WITH OPERATORS
The number of m stations are created next. The stations have the variable stationnumber (k = 1,....,m). The stations are created with an operator with the variable LRoper at or. LRoper at or is the learning rate of the
oper-ator and is determined by a sample out of a uniform distribution between the maximum learning rate (=70%, 75%, 80%, 85%, 90% and 95%) and no learning curve (=100%).
The learning curve of an operator is dependent on the production rate. Assumed is that with each twofold in product passing by, the stationtime is multiplied by the learning percentage of the operator. This twofold in production passing is called the geometric product progression and has the sequence 1, 2, 4, 8, 16, 32, etc.. In Table 3.1 an example is given for an operator with a learning percentage of 100% (= no learning curve), 90% and 80%. In conclusion; after the production of 32 products, the operator with a learning percentage of 90%, will decrease the stationtime with 41% and the operator with a learning percentage of 80%, will decrease the stationtime with 67%.
Table 3.1: Learning curve dependent on the production rate
# Products: 1 2 4 8 16 32
100% learning percentage: 100% 100% 100% 100 % 100% 100%
90% learning percentage: 100% 90% 81% 73 % 66% 59%
80% learning percentage: 100% 80% 64% 51 % 41% 33%
CREATE PRODUCTS
After the first station is created, the model begins to create products. The products are created with the variables; productnumber, location, tasktime and arrivaltime. All the products are placed in the queue (Sta-tionqQ) of station 1. This allows the station procedure to start after the initialize procedure is finished.
18 3.MODEL
ASSIGN TASKS TO STATIONS
When all the elements are created, the assigning of the tasks can begin. This is the main part of the model of this SALBP. There are several SALBP versions when varying the objectives as shown in Figure 3.1.
Figure 3.1: Versions of SALBP [3] [10]
When studying Figure 3.1, it can be concluded that the SALBP objective version of this research is the SALBP-2, with a given number of stations (m) and the goal to minimize the cycle time (c). According to Scholl and Becker SALBP-2 can be formulated as ”the problem of finding the smallest cycle time c for which the corre-sponding SALBP-F instance (m,c) has a feasible solu-tion”. Only a few exact solutions have been developed which directly solve SALBP-2; the iterated search meth-ods and direct solution approaches [10].
• The iterated search methods has two common methods [4] [6] [7]:
– Lower bound search: The lower bound LC is used as the start of the trial cycle time, which is successively increased by 1 until the respective SALBP-F instance (m,c) is feasible.
– Binary search: First the search interval [LC, UC] is determined, where the mean of the two subin-tervals determine c (= (LC+UC)/2). If SALBP-F is feasible for c, the UC is is set to the maximum station time in the corresponding solution. When that is not possible, the LC is set to c+1. The search for the optimal cycle time is finished when UC= LC .
• There are only two branch and bound (B&B) procedures which directly solve SALBP-2:
– Task-oriented B&B procedure TBB-2 [8]: This method is based on a successive reduction of the precedence graph to a station graph.
– SALOME-2 [7]: Utilizes the local lower bound method (LLBM), a bidirectional branching strategy, and several dominance and reduction rules which have to be modified to fit the conditions of SALBP-2 .
The lower bound search is used to find the optimal cycle time c in the model. The reasons of this choice is because the lower bound search is a very exact and simple method to use in the programming software Del-phi & TOMAS.
The lower bound (LC) is obtained by dividing the total time of all task over the number of stations (m), see Equation 3.1. The LC is corrected when the operators have a learning curve (Equation 3.2).
LC=tsum
m (3.1)
LCcor r ec t ed=LC×(∑
Operataors learning rates
m [%]) (3.2)
With the (corrected) LC the iterated search for the optimal cycle time (c) can start and will go on until all the tasks are out of the AlltaskQ of the assembly line. At first the model will begin to assign tasks to stations by using the following steps:
1. Check if the total station time is smaller than the cycle time (c)
2. Check if the task time of the to-be-assigned task is smaller than the (remaining) station time
(a) When this is the case, the task will be assigned to the TasklistQ of the station and the remaining station time is reduced by the task time
(b) When the task does not fit in the (remaining) station time, it will be assigned to the successor station.
3. After all the station times are filled by tasks, but not all tasks are assigned to stations, the cycle time will be increased by 1 second, all tasks are placed back from the station TasklistQ’s to the AlltaskQ of the assembly line.
4. Step 1 till 3 are continued until all n tasks are assigned to all m stations. 2014.TEL.7893
3.3.PROCEDURES 19
There is an exceptional case; When the to-be-assigned-task is n, it could only be assigned to station m. When that is not the case, the task-assigning process needs to be start over. The tasks will be placed back in the AlltaskQ of the assembly line, the cycle time is reduced by two times the iterated step size and the iterated step size is divided by 2.
When all tasks are assigned to stations, the following outputs at the start can be determined/ calculated;
• The total station time and number of assigned tasks of each station
• The average station time
• The line efficiency [E], which is calculated as followed:
E= tsum m×c where tsum= n ∑ j=1 tj[3] (3.3)
• The workload distribution [LC, UC], where
LC=Min(Stationtime) & UC=Max(Stationtime)=c (3.4)
3.3.2.
S
TATION PROCEDUREThe initialize procedure causes the station procedure to start by placing products in the stationqQ of station 1. When there are no products in the stationqQ of a station, the station will go in standby.
PROCESS PRODUCTS
When there are products in a stationqQ, the station of that stationqQ, will place the product in its stationQ. In the stationQ the following steps will take place:
1. Carry out the first task of the station on the product
2. If there is a next task also carry that one out and repeat this step until all tasks are performed.
Here the task time will decrease if the operator has a learning curve (described in subsection 3.3.1) and if the product has the productnumber of the geometric product progression. Hence the station time is decreasing.
3. When all tasks are carried out, the product will be placed in the stationqQ of the successor of the station. The last station does not have a successor, hence the product is placed in the FinishedProductsQ. The new task time, as a result of the operators learning curve, is dependent on the amount of products pro-cessed, the learning curve itself and the task times. The new task time can be calculated when combining the geometric progression (Equation 3.5) and the Wright’s Cumulative Average Model (Equation 3.6) [11]. In Figure 3.2 the gradient of the tasktime affected by the learning curve is presented, which can be described by Equation 3.7.
a, ar, ar 2, ar 3, ..., with a = 1 and r = 2 (3.5)
tj×LRoper at orb (3.6)
Where:
a = first term of the geometric progression r = common ratio
tj = time required to produce the first unit [s]
LRoper at or = Learning percentage of the operator [%]
b=1, 2, 3,...
j=Number of products, j=1, 2, 4, 8, 16, 32, ...(geometric sequence with common ratio 2) When combining the two formula’s it can calculate the new tasktime:
New tj=tj×LR l og(j) l og(2)
20 3.MODEL
Figure 3.2: Learning curve of the operator in the model
After finishing this sub-process, the following outputs are created/ calculated:
• New task times
• Production times of the products
• Idle time of the products
• Line efficiency after the last product with the new task times [E]
• Workload distribution after the last product with the new task times
REMOVE TASKS FORM STATIONS
If all the products are processed and the check box ”Interim reassigning of Tasks?” is checked, the model will determine if it is efficient to reassign the tasks with their new task times. First the new LC needs to be calculated by using Equation 3.8. Where col dis the cycle time determined at the start.
c=col d−Round(col d×( LRmax
100 −0.05)) (3.8)
Before the tasks can be reassigned to stations, the tasks need to be taken out of the TasklistQ’s of stations and be placed back in the AlltaskQ of the assembly line. Henceforth the model is ready to reassign the tasks to stations.
REASSIGN TASKS TO STATIONS
The reassigning of tasks to stations is the same process as described in ”Assign tasks to stations” in sub-section 3.3.1 with here and there a small adjustment. One of that adjustments is that if a task is placed to an other station, so not the origin station at the start, than the task time will be set back to the origin time at the start of the station process. This is because the operator of other station has no experience with that task. At the end of the whole process, the following last outputs are created/ calculated:
• The total station time and number of assigned tasks of each station
• The new optimal cycle time
• Workload distribution after the last product with the new task times [LC, UC]
• The new average station time
• The line efficiency after reassigning the tasks [E]
• The user is notified when the number of tasks per station differ with the number of tasks per station at the start of the station process
This chapter shows how the model works, where the next chapter will show the results of the produced data of the model.
4
R
ESULTS
This chapter shows the results from the data analysis from the model with the inputs defined in subsec-tion 2.4.2. The first secsubsec-tion describes the performance indicators, defined in secsubsec-tion 2.5. The second secsubsec-tion shows the additional results created by the model.
4.1.
K
EY PERFORMANCE INDICATORS RESULTS
The KPI’s where set up in chapter 2 to measure the performance of the model. The following subsections will show the results per indicator.
4.1.1.
(D
ECREASED) P
ROCESS TIMEAn important objective of an assembly line is to have a small process time. This can be achieved for example by creating more stations with less tasks or when operators have a steep learning curve. For this research, the model took different kind of learning curves for each station into the scope to see what the effect is. Figure 4.1 shows the production and idle times per product influenced by the different learning curves. The sum of both times is the process time per product, also presented in the figure.
A couple of conclusions can be made by looking at Figure 4.1. The process time decreases when the max-imum learning rate per operator increases. The process time of product 32 with a maxmax-imum learning rate of 70% decreased 17.2% in relation to the process time of product 32 with no learning curve. The production time is decreasing exponential with every learning process step by each doubling of the production (P = 2, 4, 8, 16, 32, ....). This is also clearly visible in Table 4.1. The Idle time goes from linear to exponential, which is because the production times decreases. The product (2, 4, 8, 16, ...) are faster produced than the predecessor products. This is also clearly visible in Table 4.2.
22 4.RESULTS
Table 4.1: Decreased production time per geometric progression product by different learning curves
# Products: 1 2 4 8 16 32 100% 0% 0% 0% 0% 0% 0% 95% 0% 3% 7% 10% 13% 15% 90% 0% 6% 12% 17% 22% 26% 85% 0% 9% 17% 24% 30% 35% 80% 0% 12% 22% 30% 38% 44% 75% 0% 14% 26% 36% 44% 50% 70% 0% 17% 31% 41% 50% 56%
Table 4.2: Increased idle time per geometric progression product by different learning curves
# Products: 1 2 4 8 16 32 100% 0% 0% 0% 0% 0% 0% 95% 0% 47% 28% 15% 6% -1% 90% 0% 88% 53% 29% 13% 2% 85% 0% 131% 76% 42% 19% 3% 80% 0% 178% 99% 54% 24% 4% 75% 0% 221% 120% 64% 28% 5% 70% 0% 266% 142% 74% 32% 5%
In the appendix, section A.1, extra data can be found regarding the build up of the process time per product and learning curve (Figure A.3), the idle time per product per station against the station times at the start (Figure A.2) and the decreased production time per geometric product progression (Figure A.1).
4.1.2.
A
VERAGE STATION IDLE TIME OF THE LAST PRODUCTAs shown in the previous subsection, the idle time is exponential increasing per geometric product progres-sion. In Figure 4.2 the average idle time of a station is shown before all tasks are reassigned. The average station idle time increases with 188% for product 32 from no learning curve to a 70% maximum learning rate. The average station idle time is calculated with Equation 4.1. The production time is subtracted of the pro-cess time, which is the total idle time of the product. This total idle time is divided by the number of stations, creating the average station idle time.
Iaver ag e k=DPpr ocess t i me−tsum
m =
Ipr od uc t DP
m where DP=4, 8, 16, 32 and k=1, ..., m (4.1)
Figure 4.2: Average station idle time of the last product
4.1.KEY PERFORMANCE INDICATORS RESULTS 23
In Figure 4.3 the idle times per station between products are presented for the first 5 products. It can be concluded that when the successor station has a smaller station time it creates idle times for the successor station. The learning curve amplified this, because when the learning curve increases steeply, like for example station 5, it creates extra idle time.
Figure 4.3: Idle times per station between products for the first 5 products and a maximum learning rate of 80%
4.1.3.
A
VERAGE STATION TIME AFTER REASSIGNING ALL TASKSWhen the production time per geometric product progression decreases though a steeper learning curve, it is logical that the average station time (t(Sk)) also decreases. The decreasing average station times per
geo-metric product progression after reassigning all tasks is presented in Figure 4.4. The average station time is 50.7 seconds at the start, but for example after reassigning all tasks with a maximum learning rate of 70% and a production volume of 32, this is decreased to 28.4 seconds. The average station time before the reassign-ing is smaller, because the reassigned tasks are always assigned differently, compared to the start situation. Therefore some tasks ended up at different stations and were set back to their original time at the start of the station process.
Figure 4.4: Average station time after reassigning all tasks
4.1.4.
T
HE LINE EFFICIENCY BEFORE AND AFTER THE INTERIM REASSIGNING OF TASKSOne of the major goals of the modelling research is to maximize the line efficiency (E), which can be calculated with Equation 3.3. In Figure 4.5 the line efficiencies can be found per geometric product progression per maximum learning rate. There are three different kind of line efficiencies situations, namely;
• Start: At the start of the process
• Before: At the end of the process, but before the reassigning of tasks
• After: At the end of the process and after the reassigning of tasks
The ”start”-situation is always the same for all combinations possible. The graph shows that interim reas-signing of tasks is effective, especially for larger production volumes and steeper learning curves. This is further confirmed in Figure 4.6. The line efficiency after reassigning the tasks, with a maximum learning rate of 70% and a production volume of 32, increased with 29.4%. In the appendix, section A.2, the specific line efficiencies can be found per learning curve.
24 4.RESULTS
Figure 4.5: Line efficiency
Figure 4.6: Increased line efficiency after reassigning all tasks compared to before the reassigning
4.2.
A
DDITIONAL RESULTS
In this section the additional results of the model are discussed. These results also show that reassigning of the tasks at the end have a positive effect on the entire process.
4.2.1.
D
ECREASED CYCLE TIME AFTER REASSIGNING ALL TASKSThe smaller the cycle time, the larger the production rate. This is achieved with the learning curves and the reassigning of tasks. Figure 4.7 shows the decrease of the cycle times for the different learning curves and production volume. With the fixed uniform distributed task times, defined in subsection 2.4.2, the start cycle time is always 58 seconds. After a certain production volume and a certain learning curve, this cycle time is already decreased. The cycle time is further decreased by the reassigning of the tasks, which is further described in subsection 4.2.2.
Figure 4.7: Cycle times after reassigning all tasks
4.2.ADDITIONAL RESULTS 25
4.2.2.
T
HE MINIMUM AND MAXIMUM WORKLOAD AT DIFFERENT PROCESS MOMENTSTo gain more knowledge on the stations workload differences, the model also produces the minimum and maximum station time as output (in terms of the total task times per station). In Figure 4.8 the difference between the minimum and maximum workload per station are presented for two situations per geometric product progression per learning curve, namely;
• Before: At the end of the process, but before the reassigning of tasks
• After: At the end of the process and after the reassigning of tasks
The figure further shows that after the reassigning of tasks all workload differences, except one, are smaller. These smaller workload differences will mainly express in less idle time of stations. The production volume and learning curve have also here an influence on the size of the workload difference. Furthermore, in the appendix, section A.3, the minimum and maximum station times per geometric product progression and per learning curve are presented before and after the reassigning of tasks.
The exception (LRmax: 90%, DP: 8 products) is the workload difference after the reassigning of tasks, which is
more specific displayed in the appendix. The minimum and maximum workload before is 30,1 seconds and 56,3 seconds, which gives a difference of 26,1 seconds. After reassigning the tasks, the minimum and maxi-mum workload is 24,1 seconds and 52,4 seconds, which gives a difference of 28,3 seconds. The reassigning is efficient, because the workload is more evenly, but the extremes are more apart.
Figure 4.8: Workload difference before and after reassigning tasks in combination with learning curves
4.2.3.
I
F INTERIM REASSIGNING ALL TASKS IS USEFULAt the very end of the models simulation, the model gives an advise if interim reassigning of all tasks is useful. There are three possible advises, namely;
• When the the original tsum< tsumnew
Total assembly line time is decreased with (original tsum- new tsum) to new tsumand interim
reassign-ing of tasks is [efficient/ not efficient, because the same tasks are assigned to the same stations]
• When the the original tsum=tsumnew
The total assembly line time is the same and interim reassigning of tasks is [efficient/ not efficient, because the same tasks are assigned to the same stations]
• When the the original tsum> tsumnew
The learning curves of the operators have a negative effect on the total assembly line time with (new tsum- original tsum)
Interim reassigning of all tasks is only effective if the original tsum< tsumnew and if there is a difference in
as-signing of tasks to stations compared to the original task asas-signing.
The results are discussed and can be used to make a verification and validation of the simulation model, which is done in the next chapter.
5
V
ERIFICATION
& V
ALIDATION
Verification is a procedure, performed in section 5.1, that is used to check if the system meets the require-ments and specifications and that it fulfils its intended purpose. It confirms that ’the model is right’, while validation will confirm that it is ’the right model’. Validation, performed in section 5.2, checks if the model corresponds to reality. Because a model is always a simplification of reality some discrepancies will almost always exist.
5.1.
M
ODEL VERIFICATION
By using tests and checks, the verification is been performed. The verification can also be used to correct and repair the model.
5.1.1.
C
HECKSTo make sure that the quantities in the model match, some balance check are performed. These checks con-cern comparisons of inputs and outputs, checking flows of elements and consider the allocation of elements. The simulation model has passed the following checks:
• The length of the AllTaskQ at the beginning of the task (re)assigning process is always the number of tasks generated.
• The tasks are always performed in the right order on a product.
• The total time of all tasks in a station never exceed the cycle time.
• After a task is reassigned to another station, the original task time is set back.
• A stationQ never works on more than one product.
• A station never contained more than one stationQ and one stationqQ.
• The model visualization of the stations is correct. When the stations is free it is green and when the station is busy processing a product it is red. This is clearly visible in Figure 2.4.
• The product order is always performed in the right order.
• All products are placed in the stationqQ of station 1 after they are generated.
• All tasks and products are never located in two queues.
• The production time decrease when the product numbers increase or the learning curve increase.
• The right outputs are created in the right output boxes.
• The number of tasks, stations and products always match the input variables.
• The learning rate of an operator is always between the maximum and no learning rate.
The simulation model used two uniform distribution functions. A different set of random values is taken for each of the two distributions by means of different seeds. The seeds are fixed for each simulation run to be able to compare runs with different kind of input values (like; # stations (m), maximum learning rate (LRmax)
and production volume (DP)). The two distribution functions are;
• Task times (Uniform distributed between the initial values, minimum and maximum task time)
28 5.VERIFICATION& VALIDATION
Figure 5.1 and 5.2 show the two uniform distributed seeds. The possible values are plotted against the number of times used. The figures show that the values are within the boundaries of the distribution function.
Figure 5.1: Amount of task times used Figure 5.2: Amount of learning rates used
To ensure the model works with integer numbers as input, the simulation program has also been tested for entering negative variables, numbers with decimals, and text input. The program crashed immediately and showed the messages ”is not a valid integer value.” or ”The number of [input] must be > 0. The simulation is stopped.” This let the user know that a positive integer should be entered.
5.1.2.
A
NALYTICAL RESULTS AND EVENT TRACINGThis section is used to check if the model is right by using the results of the analytical verification. By com-paring hand calculations with the model trace with the input data set, which is defined in subsection 2.4.2. The following data will be checked:
• Task times after de last product
• Task times set back to original times after been placed to another station
• Workload differences
• Production and idle times of the first 5 products
• Line efficiency before and after the reassigning of all tasks
In section A.4 all task times can be found that were calculated by hand. This has been done to check if the task times are correctly calculated with the learning curve and the geometric product progression. After com-paring the data of the hand calculation and the model simulation it can be concluded that the model is right concerning the calculations of the task times.
Another check that needs to be done is to see if the task times are set back to their original times after been placed to another station. These changes are made visible in Figure 5.3 and Figure 5.4. The tasks; 3, 8, 15, 21, 24, 27, 29, 31, 33, 35, 44 and 49 are reassigned to another station. Figure 5.5 shows the check if the times of tasks, that are placed elsewhere, are set back to their original times.
Figure 5.3: Original assigned tasks for a production process of 32 products with a maximum learning rate of 80%
Figure 5.4: After reassigning all tasks for a production process of 32 products with a maximum learning rate of 80%
5.2.MODEL VALIDATION 29
Figure 5.5: Set back of task times after been placed to another station
The minimum and maximum workload were calculated by using the table of section A.4 and the calculated station times. The given workloads as output, plotted in Figure 4.8 and Figure A.5, were compared with the hand calculated minimum and maximum station times. Concluded it can be said that the model gives the right output concerning the minimum and maximum workloads.
Figure A.7, which can be found in the appendix, is the result of an event trace of the first 5 products with a LRmax=80%. This table is used to check the production, idle and process times of the first 5 products. With
this event trace, the same times are found as the model gives as outputs.
Furthermore the line efficiency was checked by using the hand calculated task times (section A.4). The equa-tion 3.3 was used with tsumas the sum of the hand calculated task times, m as the number of stations (= 20)
and c as the maximum station time. Just as the line efficiency before as after the reassigning of all tasks was correct.
The analytical verification procedure has been a useful debugging tool and helped to discover and repair a few errors in the model code that did not become apparent at first sight. The results in chapter 4 are cor-rected for these errors. After all the verifications that have been done in this section it can be concluded that the model is right.
5.2.
M
ODEL VALIDATION
In this section a validation is conducted, but the model has no real counterpart. Because there is no exper-imental or historical data available, alternative method of validations have to be applied to see if this is the right model.
Due to the fact that the model is not based on a real case and by that no corresponding experimental or historical data exist/ is available, it is difficult to validate the model. The alternative validation for this model will consist of internal consistency. The model is checked by comparing the results of the assembly line with and without operators having a learning curve.
When the operators of the assembly line do not have a learning curve, the task times will not change. When the KPI’s are analysed for this situation, it is expected that;
• The process time will not decrease and will stay constant.
• The average idle time per station of the last product will be a linear line. This like will be lower than when the operators of the assembly line has a learning curve.
• The average station time after interim reassigning of tasks will be the same as the average station time at the start and before interim reassigning of tasks.
• The line efficiency will be the same for all moments in time and for all production volumes.
When the operators of the assembly line have a learning curve, the task times will change. The expectations are the opposite of when the operators do not have a learning curve;
• The process time will decrease when the production volume and/or maximum learning rate will in-crease.
• The average idle time per station of the last product will be a linear line with steps per geometric prod-uct progression. This like will be higher than when the operators of the assembly line do not have a learning curve. This is because the products need to wait for the products that have to endure longer task times.
• The average station time after interim reassigning of tasks will decrease when the production volume and/or maximum learning rate will increase.
• The line efficiency before and after interim reassigning will increase when the production volume and/or maximum learning rate will increase.
30 5.VERIFICATION& VALIDATION
When these expectations indeed appear in the results of the model, it indicates that the simulation model shows valid behaviour.
In the figures 4.1, 4.2, 4.4 and 4.6 in chapter 4 it quickly becomes clear that the expectations made above ap-pear in the results. Therefore the results form this internal consistency check match the priori expectations. A side node must be mentioned for when the model is used for a real case. A few adjustment are needed to create a more customized model. The following four most important adjustments are required to create a simulation model based on an existing assembly line;
• Every learning rate of an operator needs to be separately be defined as an input.
• Currently no time is reserved between the cycle times. Men can imagine that a product has a ”trans-port” time between stations.
• For each product = ar2with r = 1, 2, 3,..., the task time is reduced with the learning curve of the operator. In real live this is not the case, so a more realistic geometric progression is needed for the learning curve. For suggestion;√x, b×log(x+1) or a×ln(x+1), with x as the product number, see Figure 5.6
• Each task time needs to be separately be defined as an input.
Figure 5.6: Suggested more realistic learning curves
After a successful verification and validation, conclusions and recommendation can be made. This is done in the next chapter.
6
C
ONCLUSION
& R
ECOMMENDATIONS
The main goal of this research study is to create a simulation model that creates a SALBP that includes learn-ing curves of operators. In the conclusion (section 6.1) the main research goal is answered with the research performed in the previous chapters. Suggested valuable future follow-up research is listed in the recommen-dations (section 6.2).
6.1.
C
ONCLUSION
The goal was to create a model that included the learning curve of an operator in the simple assembly line balancing problem. A simulation model was created which yields plausible results.
The research goal raised in chapter 1 was:
” Develop a model that includes learning curves of operators in a simple assembly line balancing problem and is able to balance the workload ”
After researching, writing the code and analysing the model the following conclusions can be made:
• The research goal has been reached, because a simulation model is created, which simulates a simple assembly line that includes the operators learning curve and balance the work load. Products, tasks and stations with operators are created in a separate process and the number of these items can be determined by the user in the users graphical interface.
• Besides that the user can determine the number of items in the assembly line, the user can also choose if the operator has a learning curve and in which magnitude. Furthermore can be chosen for interim reassigning of tasks at the end of the process.
• The results from the data created by the model looks promising and after verification and validation the model have proven to be programmed in the right manner. There is of course always room for improvement.
• In chapter 2 the model KPI’s were formulated, namely;
– (Decreased) Process time
– Average idle time per station of the last product
– Average station time after interim reassigning of the tasks
– The line efficiency before and after the interim reassigning of tasks
Summarized it can be said that by including the learning curve of an operator and the interim reassign-ing of the tasks, the KPI’s are improved with reference to the start situation.
Concluding it can be stated that a successful start has been made to include the learning curve of an operator in the simple assembly line balancing problem.
32 6.CONCLUSION& RECOMMENDATIONS
6.2.
R
ECOMMENDATION
With the research study a start is been made to create a simulation model of an assembly line with operators having a learning curve. Throughout the project several improvements were discovered, but could not be implemented, which were not included in the scope of this research. The following suggestions per topics are proposed for future improvements;
A more realistic model;
• Every learning rate of an operator needs to be separately defined as an input.
• Currently no time is reserved between the cycle times. One can imagine that there is a ”transport” time between stations.
• For each product = ar2with r = 1, 2, 3,..., the task time is reduced with the learning curve of the operator. In real live this is not the case, so a more realistic geometric progression is needed for the learning curve. For suggestion;√x, b×log(x+1) or a×ln(x+1), with x as the product number (Figure 5.6).
• Each task time needs to be separately be defined as an input.
Compare the model;
• To create a better understanding regarding the results of the model it would be a great improvement if the production is resumed after reassigning the tasks. This allows the user to compare the data of the products before and after reassigning the tasks (e.g. idle time per station and product). This can be achieved by hanging the product to a task instead of the station.
• At the current moment the model concludes, with the simple test input data, that every reassigning of the tasks for a process with a learning curve is effective. The model concludes that a reassigning is effective if the cycle time is decreased and if tasks are shifted. But it is logical that not every interim reassigning of the tasks is effective in terms of costs, because pausing assembly lines cost money. It is better if the model analyses the data of the interim reassigning of the tasks and compare them to the interim reassigning cost to check if the improvement is significant enough. If the saving is greater than the interim reassigning cost, it suggest an interim reassigning. With this improvement, the model can calculate for every x products if interim reassigning is useful.
Improve performance;
• The calculation time of the model is at the moment between the 35 seconds (4 products with no learn-ing curve and no interim reassignlearn-ing of the tasks) and 2 minutes and 40 seconds (32 products with a maximum learning rate of 70% and interim reassigning of the tasks). The main calculation time exist of initializing the optimal cycle time. This time can be reduced when equations 3.1 and 3.8 for the lower bound of the start and interim reassigning cycle times (LC) are more accurate.
Process suggestions;
• Most of the idle time of stations is created if the successor station has a lower process time than the station itself (visible in Figure 4.2). To prevent stations being idle, the station times could be increased throughout the process. So the first station has a workload of 100%, the second station a workload of 95%, etc. This needs to be dependent on the learning curve of the operator. When the operator has a large learning curve, the workload should not be increase (a lot).
• It could be an idea to see what the effect is of work overload on the process times. Whenever the opera-tor of a station is not able to complete the assigned tasks before the product leaves the station (due to a restricted station length or due to the transport system), work overload occurs. Work overload may be compensated by the temporary employment of utility workers, stopping the line or another sanction. But work overload is inefficient and expensive and should be minimized [3].
• The simulation model currently works only with a series station system, which in practise it not always the case. Therefore another control process could be added for a parallel station system. Furthermore this parallel station system can also be used to compare its line efficiency against the series station system line efficiency.
R
EFERENCES
[1] P. Ament. Fascinating facts about the invention of the Assembly Line by Ransom E. Olds in 1901., 2007. [2] M. Baeten, E. Kyndt, K. Struyven, and F. Dochy. Using student-centred learning environments to
stimu-late deep approaches to learning: Factors encouraging or discouraging their effectiveness, 2010. [3] C. Becker and A. Scholl. A survey on problems and methods in generalized assembly line balancing. Eur.
J. Oper. Res., 168:694–715, 2006.
[4] E. M. Dar-El and Y. Rubinovitch. Must–A Multiple Solutions Technique for Balancing Single Model As-sembly Lines, 1979.
[5] E. Gutierrez-miravete. Session 5 Assembly Lines. 2003.
[6] S. T. Hackman, M. J. Magazine, and T. S. Wee. Fast, Effective Algorithms for Simple Assembly Line Bal-ancing Problems, 1989.
[7] R. Klein and A. Scholl. Maximizing the production rate in simple assembly line balancing - A branch and bound procedure. Eur. J. Oper. Res., 91:367–385, 1996.
[8] A. Scholl. Ein Branch&Bound-Verfahren zur Abstimmung von Fließbändern bei gegebener Stationsan-zahl. In Oper. Res. Proc., pages 175–181. Springer, Berlin, 01993 edition, 1994.
[9] A. Scholl and C. Becker. A note on "an exact method for cost-oriented assembly line balancing". Int. J.
Prod. Econ., 97:343–352, 2005.
[10] A. Scholl and C. Becker. State-of-the-art exact and heuristic solution procedures for simple assembly line balancing. Eur. J. Oper. Res., 168:666–693, 2006.
A
A
PPENDIX
A.1.
P
RODUCTION
&
IDLE TIMES PER PRODUCT AND PER LEARNING CURVE
Figure A.1: Decreased production times
36 A.APPENDIX
Figure A.3: Production & idle times per product and per different learning curves
A.2.LINE EFFICIENCIES PER DIFFERENT LEARNING CURVES 37
A.2.
L
INE EFFICIENCIES PER DIFFERENT LEARNING CURVES
Figure A.4: Line efficiency per different learning curves
A.3.
C
YCLE TIMES BEFORE AND AFTER REASSIGNING TASKS PER DIFFERENT
LEARNING CURVES
38 A.APPENDIX
A.4.
H
AND CALCULATED TASK TIMES
Figure A.6: Hand calculated task times
A.5.EVENT TRACE 39
A.5.
E
VENT TRACE
40 A.APPENDIX
A.6.
T
HE MODEL CODE USED IN
D
ELPHI AND
TOMAS
Page 1 of 9 ALB.pas 15-4-2015 15:49:54 1: unitALB; 2: 3: interface 4: 5: uses
6: Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants, System.Classes, Vcl.Graphics, 7: Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.StdCtrls, tomas, TomasSeeds, TomasRead,
8: Vcl.ComCtrls, Math, VCLTee.TeEngine, VCLTee.Series, Vcl.ExtCtrls, VCLTee.TeeProcs, 9: VCLTee.Chart;
10: 11: type
12: TForm1 =class(TForm) 13: Button1: TButton; 14: DaPr: TEdit; 15: Label1: TLabel; 16: Memo1: TMemo; 17: Memo2: TMemo; 18: Panel1: TPanel; 19: Memo3: TMemo; 20: Button3: TButton; 21: Panel2: TPanel; 22: Panel3: TPanel; 23: Panel4: TPanel; 24: Panel5: TPanel; 25: Panel6: TPanel; 26: Panel7: TPanel; 27: Panel8: TPanel; 28: Panel9: TPanel; 29: Panel10: TPanel; 30: Panel11: TPanel; 31: Panel12: TPanel; 32: Panel13: TPanel; 33: Panel14: TPanel; 34: Panel15: TPanel; 35: Panel16: TPanel; 36: Panel17: TPanel; 37: Panel18: TPanel; 38: Panel19: TPanel; 39: Panel20: TPanel; 40: Memo4: TMemo; 41: Memo5: TMemo; 42: Memo6: TMemo; 43: Memo7: TMemo; 44: Memo8: TMemo; 45: Memo9: TMemo; 46: Memo10: TMemo; 47: Memo11: TMemo; 48: Memo12: TMemo; 49: Memo13: TMemo; 50: Memo14: TMemo; 51: Memo15: TMemo; 52: Memo16: TMemo; 53: Memo17: TMemo; 54: Memo18: TMemo; 55: Memo19: TMemo; 56: Memo20: TMemo; 57: Memo21: TMemo; 58: Memo22: TMemo; 59: Button2: TButton; 60: Button4: TButton; 61: Panel22: TPanel; 62: Panel23: TPanel; 63: Panel24: TPanel; 64: Panel25: TPanel; 65: Panel26: TPanel; 66: Panel27: TPanel; 67: Panel28: TPanel; 68: Panel29: TPanel; 69: Panel30: TPanel; 70: Panel31: TPanel; 71: Panel32: TPanel; 72: Panel33: TPanel; 73: Panel34: TPanel; 74: Panel35: TPanel; 75: Panel36: TPanel; 76: Panel37: TPanel; 77: Panel38: TPanel; 78: Panel39: TPanel; 79: Panel40: TPanel; 80: Panel42: TPanel; 81: Panel43: TPanel; 82: Panel44: TPanel; 83: Panel45: TPanel; 84: Panel46: TPanel; 85: Panel47: TPanel; 86: Panel49: TPanel; 87: Panel50: TPanel; 88: Panel51: TPanel; 89: Panel52: TPanel; 2014.TEL.7893
A.6.THE MODEL CODE USED INDELPHI ANDTOMAS 41 Page 2 of 9 ALB.pas 15-4-2015 15:49:54 90: Panel53: TPanel; 91: Panel54: TPanel; 92: Panel55: TPanel; 93: Panel56: TPanel; 94: Panel57: TPanel; 95: Panel58: TPanel; 96: Panel59: TPanel; 97: Panel60: TPanel; 98: Memo23: TMemo; 99: Memo24: TMemo; 100: Memo28: TMemo; 101: Memo29: TMemo; 102: Memo30: TMemo; 103: Memo31: TMemo; 104: Memo32: TMemo; 105: Memo33: TMemo; 106: Memo34: TMemo; 107: Memo35: TMemo; 108: Memo36: TMemo; 109: Memo37: TMemo; 110: Memo38: TMemo; 111: Memo39: TMemo; 112: Memo40: TMemo; 113: Memo41: TMemo; 114: Memo42: TMemo; 115: Panel21: TPanel; 116: Panel41: TPanel; 117: Memo25: TMemo; 118: Memo26: TMemo; 119: Memo27: TMemo; 120: CheckBox1: TCheckBox; 121: Panel61: TPanel; 122: Panel48: TPanel; 123: Panel62: TPanel; 124: Panel63: TPanel; 125: Panel64: TPanel; 126: Panel65: TPanel; 127: Panel66: TPanel; 128: Panel67: TPanel; 129: Panel68: TPanel; 130: Panel69: TPanel; 131: Panel70: TPanel; 132: Panel71: TPanel; 133: Panel72: TPanel; 134: Panel73: TPanel; 135: Panel74: TPanel; 136: Panel75: TPanel; 137: Panel76: TPanel; 138: Panel77: TPanel; 139: Panel78: TPanel; 140: Panel79: TPanel; 141: Panel80: TPanel; 142: CheckBox2: TCheckBox; 143: Memo43: TMemo; 144: Memo44: TMemo; 145: CheckBox3: TCheckBox; 146: CycleTime: TLabel; 147: Memo45: TMemo; 148: Label2: TLabel; 149: Memo47: TMemo; 150: Memo46: TMemo; 151: Memo48: TMemo; 152: Label3: TLabel; 153: Label4: TLabel; 154: Label5: TLabel; 155: Label6: TLabel; 156: Label7: TLabel; 157: Label8: TLabel; 158: Label9: TLabel; 159: Label10: TLabel; 160: Label11: TLabel; 161: Label12: TLabel; 162: Edit1: TEdit; 163: Edit2: TEdit; 164: Edit3: TEdit; 165: Memo49: TMemo; 166: Label13: TLabel; 167: Memo50: TMemo; 168: Label15: TLabel;
169: procedureButton1Click(Sender: TObject); 170: procedureButton3Click(Sender: TObject); 171: procedureButton2Click(Sender: TObject); 172: procedureButton4Click(Sender: TObject); 173: private 174: { Private declarations } 175: public 176: { Public declarations } 177: end; 178:
