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 24 pages and 2 appendices. 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: Transport Engineering and Logistics
Report number: 2015.TEL.7952
Title:
Simulation study of dispatching
rules for a Dynamic Stochastic Job
Shop Scheduling Problem
Author:
R. Kapelle
Title (in Dutch) Simulatie van dispatching regels voor een dynamisch stochastisch Job Shop Scheduling probleem
Assignment: Research
Confidential: no
Initiator (university): Dr. ir. H.P.M. Veeke Initiator (company): TU Delft
Supervisor: Dr. ir. H.P.M. Veeke
C
ONTENTS
1 Introduction 1
1.1 Introduction . . . 1
1.2 Objective . . . 1
1.3 Structure . . . 1
2 Job Shop Scheduling Problem 3 2.1 Introduction . . . 3
2.2 Job Shop Scheduling Problem. . . 3
2.3 Dispatching rules . . . 4
3 Machine Shop Model 5 3.1 Introduction . . . 5
3.2 Schematic model . . . 5
3.3 PROPER model . . . 5
4 Machine Shop Simulation 7 4.1 Introduction . . . 7
4.2 Model overview . . . 7
4.3 Characteristics . . . 8
4.3.1 Input variables . . . 8
4.3.2 Performance indicators . . . 9
4.4 Elements and Processes. . . 9
4.4.1 Initialization . . . 9
4.4.2 Job generation . . . 10
4.4.3 Machining . . . 11
4.4.4 Planning . . . 12
4.4.5 Scheduling . . . 16
5 Experiments and Results 17 5.1 Introduction . . . 17 5.2 Experimental setups . . . 17 5.3 Results . . . 17 5.3.1 Workload. . . 17 5.3.2 Occupancy . . . 19 5.3.3 Capacity . . . 19 5.3.4 Overall . . . 21
6 Conclusions and Recommendations 23 6.1 Conclusions. . . 23
6.2 Recommendations . . . 24
Bibliography 25 A Appendix Experimental Results 27 A.1 Workload . . . 27
A.2 Occupancy . . . 28
A.3 Machine capacity . . . 28
A.4 Overall . . . 28
A.5 All data . . . 29
B Appendix Delphi code 31
1
I
NTRODUCTION
1.1.
I
NTRODUCTION
The planning and scheduling of multiple jobs with a limited set of resources over time is associated with a large amount of decision taking in order to guarantee the delivery of products with maximum quality, mini-mum cost and minimini-mum lead time. These decisions lead to a schedule, which is defined by Framinan et al. [2014] as a specific assignment of operations to the resources on a time-scale. The schedule shows ideally which and when each job should claim a resource over time for the upcoming production period. However, a schedule should be treated as an estimation because it is common in manufacturing processes that unfore-seen events like machine breakdowns, priority orders or cancellation of received orders require a reschedul-ing of the production plan.
1.2.
O
BJECTIVE
This report describes a simulation study of a job shop scheduling problem (jssp) regarding a machine shop with random job arrivals and stochastic processing times. In this study the machine shop is a factory where parts are produced according to a sequence of machining processes. Each process is carried out on a spe-cific machine group, which is a portion of the factory where machines are aggregated by the nature of their machining method. The machine shop runs five days a week, eight hours a day and is fed by the front office which collects jobs from customers during the entire week. Each job consists of a specific set of one or mul-tiple tasks which have to be processed according to a given production sequence. At the end of each week, the collected jobs are sent to the planning department which acts between the front office and the machining department. The planning department is ought to generate a feasible planning in order to make efficient use of the available production resources. The planning and scheduling of jobs and their corresponding tasks is the most important and difficult aspect of the entire machine shop, because it has such a significant impact on the performance of the shop.
The simulation study is executed with Delphi/TOMAS to compare and gain insight in the importance and effects of various dispatching rules which could be applied by the planning department in order to gener-ate a schedule that minimizes lead times and maximizes customer satisfaction.
1.3.
S
TRUCTURE
First, Chapter 2 will describe the different types of job shop scheduling problems and the assumptions made for simulation. Also various dispatching rules will be outlined which will be used later on in the simulation model. Next, the machine shop model will be fully outlined with help of a PROPER model in Chapter 3. Ther-after, Chapter 4 will show all machine shop simulation elements and processes, including PDL. Subsequently the experiments and results will be described in Chapter 5. Finally the conclusions and recommendations for future research will be discussed in Chapter 6.
2
J
OB
S
HOP
S
CHEDULING
P
ROBLEM
2.1.
I
NTRODUCTION
This Chapter will briefly describe the different types of job shop problems, and the assumptions made for this specific study. Also various dispatching rules will be outlined which will be used later on in the simulation model. The job shop scheduling problem is roughly described as the situation when a number of jobs need to be executed with a number of machines. Each job consists of a given collection of tasks which need to be processed in the order given by the sequence. Each task requires the demand for a machine for a given time and only one task can be executed per machine at a time.
2.2.
J
OB
S
HOP
S
CHEDULING
P
ROBLEM
Although the structure of each job shop scheduling problem is quite similar, for instance a factory with multi-ple machines inside, a distinction can be made between some types of job shop scheduling problems. At first, a static jssp considers that all jobs are known from the beginning and are available to be scheduled at the same time (Haupt [1989]). With a dynamic jssp however, jobs may arrive at different times and can still be included in the planning and scheduling process to allow a continuous stream of orders. Subsequently, a jssp can be deterministic when all elements of the problem such as the arrival rate of jobs, the processing times of tasks and the availability of machines are known beforehand. On the other hand, a jssp can be stochastic, which means that the inter-arrival time of jobs and the processing times of tasks are considered random. Hence a combination of static/deterministic and dynamic/stochastic job shop scheduling problems can be made, where a dynamic and stochastic problem resembles the most with the real world manufacturing environ-ment. Although the stochastic dynamic scheduling problem has been studied recent years (Terekhov et al. [2014]), the solving of it stays challenging due to the stochastic character. Therefore, this simulation study will try to gain some insight in the effect of various dispatching rules (Section 2.3) at a dynamic stochastic job shop problems. In order to do this, a list of typical scheduling problem assumptions(Baker and Trietsch [2009], Barbosa et al. [2014], Framinan et al. [2014], Haupt [1989]) had to be made:
• Jobs arrive dynamically with an inter-arrival time according to a Poison distribution.
• Processing times of tasks are determined according to an exponential distribution, thus considered stochastic.
• The tasks that form a job are sequence dependent.
• The amount of machine groups and machines is completely specified after initialization.
• Each machine can perform only one task at a time.
• Once a task is started on a machine, it must go on until completion.
• No maintenance or breakdowns occur during the simulation.
• Transport and setup times are assumed to be negligible.
• There is no penalty for completing a job earlier than the due date.
• There is no possibility to reject job orders. 3
4 2.JOBSHOPSCHEDULINGPROBLEM
2.3.
D
ISPATCHING RULES
Dispatching rules are a kind of priority rules that utilize information of jobs and resources to decide which job is to be assigned to which resource. Haupt [1989] has made a classification of priority rules based on four characteristics:
Time-independent rules are based on individual job information and ignore the status of the shop floor due
to interaction with other job information.
Time-dependent rules are time dependent and priority changes over time according to the status of the
shop floor due to last minute decisions.
Local rules are concerned with the local available information and only requires information about the jobs
that are currently waiting in a local queue.
Global rules are used to dispatch jobs using all information available on the shop floor, thus including all
other queues.
Due to the dynamic and stochastic characteristics of the problem, the dispatching rules that are most ap-propriate are local time-independent rules (Conway et al. [1967], Jackson [1957], Panwalkar and Iskander [1977]). A list of the most basic local time-independent dispatching rules has been made from which several simulation experiments can be conducted:
FCFS (First Come First Served) Select the job which arrives first at the shop. This rule is mostly used as a
benchmark to compare more advanced rules with.
LWKR (Least Work Remaining) Select the task associated with the job having the least work remaining to be
completed. This rule tends to reduce the number of jobs in the shop.
FOPNR (Fewest Number of Operations Remaning) Job priority equals the number of tasks remaining to
com-plete the job. This rule also tends to reduce the number of jobs in the shop.
SPT (Shortest Processing Time) Select the task with the shortest processing time. This rule is the most
known and tends to reduce the work-progress and average job lateness. It requires the least in-formation, because only the task data is required instead of the parent job data.
3
M
ACHINE
S
HOP
M
ODEL
3.1.
I
NTRODUCTION
This Chapter will describe the structure of the schematic model of the machine shop. Looking at the machine shop, a number of functions can be identified. These functions will be shown in a black box model after which a PROPER model can be made.
3.2.
S
CHEMATIC MODEL
When a black box approach is applied on the machine shop, three flows can be distinguished. When a cus-tomer places an order, a job is created while it enters the machine shop. At the same time raw material is required to execute the tasks, listed in the job tasklist, on. In order to execute the tasks, specific machines are required. After all the machining is completed, the job is finished, the raw material is transformed into a product and the machines are used. A schematic of this black box approach is shown in Figure 3.1.
• The machine shop is running five days a week from 9h to 17h.
• Jobs are collected every day and scheduled between Friday 17h and Monday 9h.
• Raw material flow is not actually simulated but complements the picture of the real situation.
Figure 3.1: The machine shop as a black box
3.3.
PROPER
MODEL
The following section will describe the machine shop in terms of order flow, material flow and resource flow with help of a PROPER model (Veeke et al. [2008]). The PROPER model of the machine shop is shown in Fig-ure 3.2. The horizontal arrows represent the earlier mentioned order, material and resource flows while the vertical arrows represent the data flows. The horizontal flows contain mostly technical data whereas the ver-tical flows contain control data. The three parallel transformations within the black box can be distinguished by:
• The order flow starts as a customer order, known as job, and transforms by the "Plan and Schedule" function into a finished job.
6 3.MACHINESHOPMODEL
• The material flow consists of the transformation of raw material into a product by the "Machining" function.
• The resource flow shows the transformation of machines into used machines by the "Use" function. The control function coordinates these transformations by translating requirements from the environment into standards. The environment in this case are customers which desire punctuality in the form of a service level. The service level could for instance be a percentage of customer orders completed before due date. In order to be able to meet this service level a certain reliability of processes and occupancy of machinery is required. The results of these standards are analysed after a certain period and reported back to the envi-ronment. The interaction between the order flow, material flow and resource flow and their corresponding functions are simulated and described in Chapter 4.
4
M
ACHINE
S
HOP
S
IMUL ATION
4.1.
I
NTRODUCTION
The simulation of the machine shop will be done with help of Delphi/TOMAS. This Chapter will describe the structure of the simulation model, the required input variables (Section 4.3.1) as well as the performance indicators (Section 4.3.2). Also the Program Design Language of each simulation element will be outlined. The purpose of the simulation model is to give insight into the effects that a dispatching rule can have on the performance of a machine shop over a long period of time.
4.2.
M
ODEL OVERVIEW
The simulation will start with the initialization phase in which the major elements such as the job generator, machine groups, machines, planner and scheduler are created on the basis of the given input variables. After initialization is done, the job generator will generate jobs over time according to a specific distribution. Each job will enter a queue where it waits until the end of the week. At the end of the week, the collected jobs will be decomposed by the planner into tasks and the tasks are planned according to a dispatching rule and the available machine group capacities for the coming weeks. When a task has a release date assigned, it is placed into a collection queue where it waits until the planner actually releases the task. When a task is planned for the upcoming week, it is released from the collection queue into a release queue where the scheduler picks from. The scheduler assigns the released task to the designated machine group when a machine comes available. When the task being processed by the machine is the last task of the parent job, the job is finished after completion. Else, the task is finished and the next task of the parent job is required for scheduling. A simple schematic of this process is shown in Figure 4.1. A more detailed schematic of each element and its process will be described in Section 4.4.
Figure 4.1: Schematic of job flow between elements
8 4.MACHINESHOPSIMULATION
4.3.
C
HARACTERISTICS
This section will describe the input variables required to run the model as well as the performance indicators to measure how efficient the selected dispatching rule perform.
4.3.1.
I
NPUT VARIABLESTable 4.1 provides an overview of the input variables that are required to run the simulation model of the machine shop. The number of groups, group name, number of machines per group and the fraction of ma-chine group hours need to be entered in the Jobshop input.txt file, shown in Figure 4.2. The remaining input variables should be entered in the simulation control panel shown in Figure 4.3. The job selection method input variable determines which dispatching rule will be used. A collection of five dispatching rules is built in, which were mentioned in Section 2.3.
Table 4.1: Input variables
Input variable Default value
Number of machine groups 5
Machine group name "Mill, Weld, Drill, Fit, Transport" Number of machines per machine group 1, 1, 1, 1, 1
Fraction of machine group hours 0.2, 0.2, 0.2, 0.2, 0.2
Total number of jobs 5000
Job selection method "FCFS, LWKR, FOPNR, SPT, CR"
Machine capacity [hrs] 40
Max task list length 9
Average task processing time [hrs] 5
Figure 4.2: Input variables in Jobshop input.txt
4.4.ELEMENTS ANDPROCESSES 9
4.3.2.
P
ERFORMANCE INDICATORSAs mentioned in Section 3.3 and shown in Figure 3.2, the customers desire that their job is completed at the agreed due date. Based on the machine group capacity and the selected dispatching rule, a due date for each new job is determined by the planner at the end of the week after all work in progress has been identified. To translate the customer’s desire into a measurable indicator, a service level is determined. The service level could for instance be a percentage of customer orders completed at the due date. In order to be able to meet this service level, a certain reliability of processes and occupancy of machinery is required. The occupancy of machinery is an important performance indicator, because it shows how much of the time a machine is idle. An idle machine could for example mean that the process is not yet optimized. While a occupancy rate of nearly 100 percent might suggest that a machine is always running and that jobs have a probability of greater lead times due to waiting. The performance indicators to give an insight in the efficiency of the selected dispatching rule are :
• Average and maximum time of a job in the machine shop from the moment of collection until comple-tion.
• Average and maximum time of a job in the machine shop from the moment of release until completion.
• Percentage of jobs that are completed in time, thus before or at the due date.
• Occupancy rate of the machinery.
4.4.
E
LEMENTS AND
P
ROCESSES
The simulation elements and corresponding processes will be fully outlined in this section. Every simulation element has its own attributes which are shown in the related Table. Also the PDL of each process will be mentioned after which a detailed schematic of processes will be shown.
4.4.1.
I
NITIALIZATIONIn the initialization phase, the input variables are obtained from which the number of machine groups and the number of machines are created. Also several queues are created to eventually contain jobs which are just generated and jobs that are just being processed. Moreover, all simulation elements like the machines, planner, scheduler and job generator are created and started.
Table 4.2: Global attributes
Global Type Description
MachGroupQ TomasQueue Contains all machine groups
ThroughputTimeQ TomasQueue Contains jobs from generation until completion ProcessingTimeQ TomasQueue Contains jobs that are being processed by the shop
NJobsInTime Integer Number of jobs completed before the due date
NJobsDelayed Integer Number of jobs completed after the due date
NrOfGroups Integer Number of machine groups
NrOfMachines Integer Number of total amount of machines in the shop
Week Integer Reference to the actual week number
JobSelectionMethod Integer Reference to the selected dispatching rule
PDL
Create ThroughputTimeQ, ProcessingQ and machGroupQ Read inputfile to obtain the machine group details Read the input variables from the simulation panel For i = 1 to NrOfGroups do begin
Create machine group Enter the machGroupQ
Determine required amount of machines, NrOfMachines Create a calendar item for the first week and put in CalendarQ Create animation panel for machine group
For j = 1 to NrOfMachines do begin Create and activate machine
10 4.MACHINESHOPSIMULATION
Create a tasklist for the machine End
End
Create and start the Planner Create and start the Scheduler Create and start the JobGenerator Assign an outputfile
End
4.4.2.
J
OB GENERATIONThe job generator creates jobs with an inter-arrival time according to a Poisson distribution with aµ of 8 hours (working day). Each job has a tasklist which contains all tasks required to complete the job. The number of tasks per job is generated according to a uniform distribution between 1 and 9 tasks. Each task is assigned to a specific machine group according to a Table distribution from a specified Seed. The processing time of a task is determined by an Exponential distribution with aµ of 5 hours. After all tasks are added to the tasklist, the total amount of processing time to complete the job is recorded in the MachineHoursToGo attribute of the corresponding job. The job number is added, the status is set to non-active and the due date is temporary set to 0. At last the job is placed in the ThroughputTimeQ and the JobCollectQ of the Planner. Each task contains information about the required processing time, the assigned machine group, the parent job and the (plan)week that the task should be released in. However, the planweek is determined later on at the Planner.
Table 4.3: Job Generator attributes
Job Generator
InterArrivalTimeDist TExponentialDistribution Job inter-arrival time NrTasksDistribution TUniformDistribution Number of tasks per job
GroupDistribution TTableDistribution Assigns tasks to machine groups
TaskHoursDistribution TExponentialDistribution Determines task workload
Table 4.4: Job attributes
Job
Tasklist TomasQueue Contains all tasks of this job
MachineHoursToGo Double Machine hours still to go for completion of the job
DueDate Double The time that the job should be completed
Active Integer Status for being processed: 0 is no, 1 is yes
Number Integer Job creation number
Table 4.5: Task attributes
Task
CalendarQ TomasQueue Contains all determined planweeks of this task
MachineHours Double Machine hours of this task
OnGroup MachineGroup Reference to assigned machine group
OnMachine Machine Reference to assigned machine
OnJob Job Reference to assigned job
OnWeek Integer Reference to assigned planweek number
PDL
While TRUE do Begin
4.4.ELEMENTS ANDPROCESSES 11
Assign job number and job status to job NrTasks = Trunc(NrTaskDistribution) For i = 1 to NrTasks do begin
Assign a machine group to the task Assign taskhours to the task
Update the machinehourstogo of the parent job Put the task in the parent job tasklist
End
Put job in ThroughputTimeQ and Planner.JobCollectQ End
4.4.3.
M
ACHININGA machine group is physically a portion of the factory where machines are aggregated by the nature of their machining method. The number of machine groups in the factory is determined by an input variable, as well as the number of machines per machine group. Each machine group has its own CalendarQ which contains calendar items.
A calendar item represents a planweek and is located in the CalendarQ of a task or machine group. The calen-dar item of a task only uses the Planweek and Taskhours attributes, whereas the calencalen-dar item of a machine group only uses the Planweek and MGHours attributes. Every planweek has an attribute called MGHours to record how much processing time the machine group has left in that particular week.
Every machine has its own tasklist which contains the task that is being processed on the machine until completion. When a machine has no task assigned, it is located in the IdleQ of the corresponding machine group. Likewise, when a machine is processing a task, it is located in the BusyQ of the corresponding machine group.
Table 4.6: Machine group attributes
Machine Group
JobQ TomasQueue Contains the job to do
IdleQ TomasQueue Contains the idle machine(s)
BusyQ TomasQueue Contains the active machine(s)
CalendarQ TomasQueue Contains the planweek items
NrMachines Integer Number of machines in this group
FracMchHours Double Relative work load of this group
Table 4.7: Calendar attributes
Calendar
Planweek Integer Reference to the corresponding planweek MGHours Double Machine group capacity remaining
Taskhours Double Reference to the taskhours of a task planned in this planweek
Table 4.8: Machine attributes
Machine
Tasklist TomasQueue Contains the task being processed
12 4.MACHINESHOPSIMULATION
4.4.4.
P
LANNINGAs shown in Figure 4.1, the planner is located between the job generator and the scheduler. It is the most important element of the entire model because it decides when each job/task needs to be performed. In order to systematically do this, the planner consists of the following procedures which run in this sequence:
1. Update queue 2. Collect tasks 3. Update calendar 4. Plan tasks 5. Set due date 6. Release tasks
In order to successfully plan each task, several queues are required to organize the complexity (Table 4.9).
Table 4.9: Planner attributes
Planner
JobCollectQ TomasQueue Contains all collected jobs of the past week
ReleaseQ TomasQueue Contains all tasks that are released for the upcoming week CollectQ TomasQueue Contains all tasks that are decomposed from jobs
TempQ TomasQueue Temporary buffer for tasks
2. COLLECT TASKS
During a week new jobs are created and stored into the JobCollectQ. At the end of the week, the planner runs the "Collect tasks" procedure which decomposes each newly received job from the JobCollectQ into under-lying tasks and stores them in the CollectQ (Figure 4.4). The way the tasks are stored in the CollectQ is de-pendent on the selected dispatching rule that sequences the tasks according to the corresponding attribute.
Figure 4.4: Schematic of the Collect tasks procedure
PDL
While JobCollectQ.Length > 0 do begin For i = 0 to Job.Tasklist.Length do begin If Jobselectmethod = FCFS then
Add task sorted on jobnumber into CollectQ If Jobselectmethod = LWKR then
Add task sorted on the job’s MachineHoursToGo into CollectQ If Jobselectmethod = FOPNR then
Add task sorted on the job’s tasklist.length into CollectQ If Jobselectmethod = SPT then
Add task sorted on the task’s processing time into CollectQ If Jobselectmethod = CR then
4.4.ELEMENTS ANDPROCESSES 13
End
After the last task of the job has been added to the CollectQ Enter Job in the ProcessingTimeQ and leave JobCollectQ End
3. UPDATE CALENDAR
Before the tasks can be planned into future weeks, it is necessary that a calendar item is created in the Calen-darQ of each machine group, representing the upcoming planweek. This is crucial because when the "Plan tasks" procedure requires capacity information of a machine group in a future week which does not exist yet, the simulation comes to a halt.
PDL
For i = 0 to Number of machine groups do begin Select machine group i
Create a calendar item named Planweek+weeknr for the next week if that does not exist yet Put the calendar item in the CalendarQ of the machine group
End
4. PLAN TASKS
Now that all tasks are waiting to be planned in a planweek and a calendar item for the next planweek is created for every machine group, the planning of the tasks can start. The first task of the CollectQ is selected and checked whether the task hours could be added to the machine group such that the machine group capacity is not violated.
• If the task hours fit within the machine group capacity, the machine group capacity is updated and the task has a release date assigned which is recorded at the task Onweek attribute.
• If the task hours do not entirely fit within the machine group capacity for the upcoming week, it is checked if a portion of the task hours could be planned at the machine group such that the capacity is not violated. The remaining task hours are planned the week after the upcoming week, while there is enough machine group capacity available. This process is repeated until the task hours are all planned in a week and the release date of the task is recorder as the first week that the task is being processed.
• If none of the task hours can be planned in the upcoming week, the week after the upcoming week is checked and the process described before is repeated.
After the task has a release date assigned, the next task in the CollectQ is selected. If that task is part of the same job as the previous task, the first available week to be planned in must be the week that the previous task ended and not before. For example, if the first task of a job requires the upcoming two weeks to be completed, the second task of the job cannot be planned into the upcoming week due to sequence violation.
PDL
Planweek = Week
For i = 0 to CollectQ.Length -1 do begin Select the task i
Obtain the assigned machine group
Obtain the corresponding calendar item for the planweek If calendar item does not exist yet, create one
If task hours + already planned machine group capacity < maximum machine group capacity then
Assign this planweek to the task and add the task hours to the machine group planning for this week
If task hours + already planned machine group capacity > maximum machine group capacity then
Check how much task hours you can plan in the planweek and plan if possible Repeat until all task hours are planned
If task hours have to be planned in a planweek that does not exist yet then Create calendar item for this planweek for all machine groups
14 4.MACHINESHOPSIMULATION
5. SET DUE DATE
After all tasks have been assigned a release date and corresponding planweek(s), the due date of the parent job needs to be determined in order to inform the customer who placed the order. To be able to set a due date to a job, the last task of the job’s tasklist needs to be searched in the CollectQ and checked to see in which planweek that task is planned, such that the job’s due date can be determined at the last planweek that the last task is processed in. A due date is always set to the last day of a planweek, even if the last task of a job is completed in the begin of the wee.
PDL
For i = 0 to CollectQ.Length-1 do begin Select the ith task
Obtain the parent job
Check if the selected task is the last task of the job’s tasklist Check if the job does not have a due date set yet
If both conditions are true, then set job due date to planweek of last task
Add 40 hours to the due date, because of the 40 hours idle time at the start of simulation End
6. RELEASE TASKS
Finally, the tasks in the CollectQ that are planned for the upcoming week need to be moved to the ReleaseQ so that the Scheduler can pick those tasks at the beginning of the planweek. To do this, every task in the CollectQ is checked if the first calendar item of the task has a planweek that is equal to the upcoming week. If that is the case, the task is moved to the ReleaseQ. Else the next task is selected until the entire CollectQ is checked. At the end, some tasks have been moved to the ReleaseQ and the remaining tasks stay in the CollectQ the entire week.
Figure 4.5: Schematic of the Release tasks procedure
PDL
For j = 0 to CollectQ.Length -1 do begin Task = CollectQ.Element(j-k)
Calendar = Task.CalendarQ.FirstElement
If Calendar.Planweek = equal to actual Planweek then Task.LeaveQueue(CollectQ)
Task.EnterQueue(ReleaseQ) Inc(k)
End
1. UPDATE QUEUE
The very first procedure of the planner is to update the CollectQ and the ReleaseQ. Every task in the CollectQ is removed from the CollectQ and moved to a TempQ. Also the release date, Onweek attribute, of each task is deleted together with the planned task hours in all the machine group planweeks. Hereafter, the content of the ReleaseQ is checked. If the ReleaseQ is empty it means that every task that was planned for the past
4.4.ELEMENTS ANDPROCESSES 15
and store them in the CollectQ. Also the task hours which were planned for all machine group planweeks are deleted. After the tasks of the ReleaseQ are added to the CollectQ, the tasks in the TempQ are added to the tail of the CollectQ. This procedure makes sure that the tasks which had to be finished already are selected first again in the upcoming procedures. The tasks that were planned for the week after are placed just after the former released tasks.
PDL
While CollectQ.Length > 0 do begin Select first task
Obtain the assigned machine group
Subtract the task hours from the machine group hours of that planweek Move the task from the CollectQ to the TempQ
End
While ReleaseQ.Length > 0 do begin Select first task
Obtain the assigned machine group
Subtract the task hours from the machine group hours of that planweek Move the task from the ReleaseQ to the CollectQ
End
While TempQ.Length > 0 do begin Select first task
Move the task from the TempQ to the tail of CollectQ End
As an example, Table 4.10 gives a clear visualization of the effect of planner procedures on the queue contents. In the example, 5 jobs were collected until the end of week 0. When the planner gets active at the end of the week, the UpdateQ procedure starts but there are no tasks in the CollectQ and ReleaseQ so the procedure is skipped. Thereafter the CollectTasks procedure starts to decompose the 5 jobs in the JobCollectQ into 25 tasks in the CollectQ with help of the selected dispatching rule. After the CollectTasks procedure, the planner will start the UpdateCalendar procedure in which a planweek is made for the upcoming week. Thereafter, the planner will plan all the tasks in the CollectQ and give each task a release week. In this example, 10 tasks are planned for the upcoming week while the other 15 tasks are planned for future weeks. Then the due dates are assigned to the parent jobs and the planner starts the ReleaseTasks procedure. This procedure moves the 10 tasks which are planned for the upcoming week into the ReleaseQ and leaves 15 tasks behind in the CollectQ. The next 40 hours, the scheduler will pick tasks from the ReleaseQ and assign them to their designated machine group. During this week, 8 new jobs were collected and stored in the JobCollectQ. At the end of the week, the planner gets active again and starts the UpdateQ procedure. First the 15 tasks in the CollectQ are temporary placed into the TempQ. Then the planner notifies that the ReleaseQ is not empty, so the 2 remaining tasks in the ReleaseQ are moved to the CollectQ. Hereafter, the planner moves the tasks in the TempQ back to the tail of the CollectQ. Hereafter the planner starts the CollectTasks procedure and the 8 new jobs are decomposed into the CollectQ according to the selected dispatching rule.
Table 4.10: Example: Time lapse of queue contents over time (CT=CollectTasks, RT=ReleaseTasks, EoW=EndofWeek)
EoW 0 CT RT EoW 1 UpdateQ UpdateQ UpdateQ
Time [hr] 40 40 40 80 80 80 80 JobCollectQ 5 0 0 8 8 8 8 CollectQ 0 25 15 15 0 2 17 ReleaseQ 0 0 10 2 2 0 0 TempQ 0 0 0 0 15 15 0 R. Kapelle 2015.TEL.7952
16 4.MACHINESHOPSIMULATION
4.4.5.
S
CHEDULINGThe scheduler is located between the planner and the machinery. After the planner releases the tasks for the upcoming week into the ReleaseQ, the scheduler picks the first available task in the ReleaseQ to check whether multiple conditions are met before it can be passed to a Machine of the assigned machine group. When the assigned Machine Group has an idle machine and when the task is the first task of the job tasklist and when the job’s status is non-active, a machine is selected and the task is assigned to this machine. The machine leaves the IdleQ of the machine group and enters the BusyQ. The job’s status is set to active while the task is being processed and the task leaves the ReleaseQ of the Planner such that the scheduler can pick the next task.
PDL
While TRUE do Begin
MyTask = First element of Planner.ReleaseQ While MyTask <> nil do begin
NextTask = Successor of MyTask MyJob = MyTask.OnJob
MyGroup = MyTask.OnGroup
If MyGroup.IdleQ.Length>0 and MyTask=First element of MyJob.Tasklist and MyJob is not active then
begin
Put MyJob into MyGroup.JobQ
Select an idle machine from MyGroup.IdleQ Assign the machine to the task
Move machine from IdleQ to BusyQ Color the machine panel red
Move task from ReleaseQ to Machine tasklist Set Job status to active(=1)
5
E
XPERIMENTS AND
R
ESULTS
5.1.
I
NTRODUCTION
Four experiments will be executed with the simulation model to try to gain some insight in the effects of the various dispatching rules on the performance of the machine shop. Also other variables are varied to give the simulation study a broader perspective.
5.2.
E
XPERIMENTAL SETUPS
The first experiment will investigate what the influence of the task size, with equal workload, is on the punctu-ality and flow of the jobs with the five dispatching rules. The second experiment will investigate the influence of the job inter-arrival time on the occupancy of the machinery for the five dispatching rules with equal work-load and a machine capacity of 30 hours per week. The job inter-arrival time is varied between 6 and 8 hours. The third experiment will investigate the influence of the machine capacity per week on the punctuality and flow of jobs for the FCFS rule while keeping the workload at 15 hours per job. The last experiment will inves-tigate the overall performance of the five dispatching rules while varying the machine capacity per week and keeping the workload at 15 hours per job.
5.3.
R
ESULTS
This Section will show the results of the four experiments which were conducted with the simulation model according to the experimental setups previously described. From each experiment a Table with full data is available at the Appendix A. The experimental results are explained and visualized with some Figures which include a legend that names the dispatching rules DR 1, DR 2, DR 3, DR 4 and DR 5. These stand respectively for FCFS, LWKR, FOPNR, SPT and CR.
5.3.1.
W
ORKLOADThe influence of the average hours per task for the five dispatching rules, while keeping the workload at 15 hours per job, can be seen in Figure 5.1 and Figure 5.2. The entire Table with data from this experiment can be seen in Appendix A.1. As Figure 5.1 shows, the percentage of jobs completed in time increases if the average hours per task increases while keeping the workload equal. This suggests that planning larger but fewer tasks leads to an increased punctuality with a single machine available per machine group. Figure 5.2 shows that the average processing time per job decreases significantly if the average hours per task increases while keeping the workload equal. This suggests that the waiting time for jobs decrease when larger but fewer tasks are planned. This experiment also suggests that under these circumstances, the dispatching rules LWKR and CR perform best. Finally it can be seen that DR 4, SPT, does not perform well. The dispatching rule tends to get stuck in a loop because it is, unlike the other dispatching rules, solely task oriented. That means that the planner is able to plan tasks of a job in the upcoming week without consideration whether the first task of the job is also in the upcoming week. Therefore the scheduler cannot pick any of the released tasks by the planner, because not all three conditions, mentioned in Section 4.4.5, are met.
18 5.EXPERIMENTS ANDRESULTS
Figure 5.1: 5 Dispatching rules @ Workload 15hr/job: average hours per task VS percentage of jobs completed in time
5.3.RESULTS 19
5.3.2.
O
CCUPANCYThe influence of the job inter-arrival time on the punctuality and job flow for the five dispatching rules is only shown in Table A.2. The data suggests that while keeping the machine capacity and workload the same, the job inter-arrival time influences the percentage of jobs completed in time in such a way that when the job inter-arrival time increases, the punctuality also increases. This makes sense, because less jobs are collected during the week. The average processing time of the jobs decreased significantly with an increase of job inter-arrival time, again because there are less jobs to be performed during the week which leaves more margin for the remaining jobs. The reason for the overall low occupancy rate despite a single machine per machine is partly due to the low value of job inter-arrival time and the relative high variety of machine groups. When less machine groups are created, the tasks are divided amongst less machine groups which should increase the occupancy rate of the machinery.
5.3.3.
C
APACITYThe influence of the machine capacity per week for the FCFS dispatching rule, while keeping the workload at 15 hours per job, can be seen in Figure 5.3 and Figure 5.4. The entire Table with data from this experiment can be seen in Appendix A.3. As Figure 5.3 shows, the percentage of jobs completed in time decreases if the machine capacity per week is increased. Although the machine capacity per week cannot physically be higher than 40 hours per week, it was interesting to see what the percentage would be if the planner thought it could plan every task for the upcoming week. On the other hand, when the planner only had 20 machine hours available per week, the percentage of jobs completed in time nearly reached 100 percent. This makes sense because the planner saved 20 hours of spare time on purpose which offered some extra margin. But from Figure ?? it can be seen that when the planner only had 20 machine hours available per week, the average processing time per job increased significantly. This is due to the fact that the planner plans a job in way more weeks than normal and thus sets the duedate at the planweek of the last task of the job. This way, the job is completed in time because the due date was set miles away. This suggests that one cannot look at one performance indicator solely and that there is a break-even-point between the jobs completed in time and the average processing time per job.
Figure 5.3: FCFS @ Workload 15hr/job: machine capacity per week VS percentage of jobs completed in time
20 5.EXPERIMENTS ANDRESULTS
5.3.RESULTS 21
5.3.4.
O
VERALLThe influence of the machine capacity per week for all dispatching rules, while keeping the workload at 15 hours per job, can be seen in Figure 5.5 and Figure 5.6. The entire Table with data from this experiment can be seen in Appendix A.4. As Figure 5.6 shows, the percentage of jobs completed in time decreases if the machine capacity per week is increased. This was also partly visualized in Figure 5.3 for the FCFS dispatching rule. The same explanation of the experiment of Section 5.3.3 applies here, but now all five dispatching rules are showed. Together with Figure 5.5, it can be seen once again that dispatching rules LWKR and CR perform best at percentage of jobs completed in time as well as average processing time per job.
Figure 5.5: 5 Dispatching rules @ Workload 15hr/job: machine capacity per week VS percentage of jobs completed in time
Figure 5.6: 5 Dispatching rules @ Workload 15hr/job: machine capacity per week VS average processing time per job
6
C
ONCLUSIONS AND
R
ECOMMENDATIONS
6.1.
C
ONCLUSIONS
The main goal of this simulation study was to gain insight in the importance and effects of various dispatch-ing rules which could be applied by the planndispatch-ing department in order to generate a schedule that minimizes lead times and maximizes customer satisfaction in terms of punctuality. The simulation model was built with Delphi/TOMAS and is a representation of a machine shop where parts are produced according to a sequence of machining processes. Each process is carried out on a specific machine group, which is a portion of the fac-tory where machines are aggregated by the nature of their machining method. The planning and scheduling of jobs and their corresponding tasks is the most important and difficult aspect of the entire machine shop, because it has such a significant impact on the performance of the shop. Four experiments were executed while not only the dispatching rules were observed. Other variables such as the machine capacity per week, job inter-arrival time and and task hours per task were varied to give the study a broader perspective. The first experiment investigated the influence of the task size, with equal workload, on the punctuality and flow of the jobs with the five dispatching rules. The results of this experiment suggest that planning larger but fewer tasks lead to an increased punctuality, thus customer satisfaction. It also suggests that the average processing time per job decrease with larger but fewer tasks which leads to shorter waiting times for jobs. In this experiment, the dispatching rules LWKR and CR performed best.
The second experiment investigated the influence of the job inter-arrival time on the occupancy of the ma-chinery for the five dispatching rules with equal workload and a machine capacity of 30 hours per week. The results of this experiment suggest that the job inter-arrival time influences the punctuality of jobs such that when the inter-arrival time is increased, the punctuality also increases. The explanation is that less jobs are collected during the week so that there is more margin to complete jobs in time.
The third experiment investigated the influence of the machine capacity per week on the punctuality and flow of jobs for the FCFS rule while keeping the workload at 15 hours per job. The results showed that when the machine capacity per week decreased, the punctuality of jobs increased. The main reason for this result is that the due date for the job was set a lot of weeks ahead, because due to the limited machine capacity the job must be planned in more weeks than normal. This suggests that one cannot look at one performance indicator solely and that there is a break-even-point between the jobs completed in time and the average processing time per job.
The last experiment investigated the overall performance of the five dispatching rules while varying the ma-chine capacity per week and keeping the workload at 15 hours per job. As the third experiment already demonstrated, the punctuality of jobs decreased with an increase in machine capacity. The same explanation applies here, but now all five dispatching rules were considered. Again, the dispatching rules LWKR and CR performed best at percentage of jobs completed in time as well as average processing time per job.
24 6.CONCLUSIONS ANDRECOMMENDATIONS
Finally, it is concluded from the simulation that when jobs contain larger but fewer tasks, the punctuality and average job processing time improve. Also, when the machine capacity per week increases, the punc-tuality gets worse while the average processing time per job improves. The dispatching rules LWKR and CR proved to perform best in the experiments, while the best expected dispatching rule SPT performed worse. The reason for the SPT dispatching rule to perform bad in this simulation is because it tends to create a sit-uation where the planner dispatches and releases the collected tasks in such a way that the scheduler is not allowed to pick any task to assign to a machine.
6.2.
R
ECOMMENDATIONS
The simulation model is based on the job shop model created by J.A. Ottjes and H.P.M. Veeke, Veeke [2010]. The main structure of the model, like the job generation principle is kept the same but a planner and sched-uler are inserted between the job generator and machines. The model is set up in such a way that it tries to represent a real world example where a person, the planner, should make on-floor decisions on its own with-out help of any cost functions for earliness and tardiness for example. However, some researchers (Laslo et al. [2008], Soroush [1999]) obtained reasonable results with similar functions. Therefore it is recommendable to construct a simulation model in such way that cost functions for earliness and tardiness for example can be implemented to obtain results, which are more based on mathematics than real world solutions.
Although the planning procedures of the simulation model are complex, the performance of the model has room for improvement regarding simulation time. For example, a procedure searches for one specific task based on an attribute but needs to check the entire queue to get its position. Many procedures are based on for-loops which require a lot of time, thus it might be useful to try to re-organise some procedures.
Finally, while the SPT dispatching rule normally performs good in planning and scheduling problems, it is not the case in this simulation study. This model decomposes the jobs in such a way that each task has a par-ent job attribute assigned in order to keep the link with the job, but the package of tasks of a job is jumbled when a dispatching rule determines that some tasks of the same job may not be performed the same week as the others. Eventually, no job is able to be completed because the tasks are completely spread over the weeks. It might be useful to come up with another approach to decompose tasks from jobs, or leave jobs as they are and give them task attributes instead of a tasklist queue.
B
IBLIOGRAPHY
Kenneth R. Baker and Dan Trietsch. Principles of Sequencing and Scheduling. John Wiley & Sons, Inc., Hobo-ken, NJ, USA, March 2009. ISBN 9780470451793.
Edna Barbosa, Michele Goncalves Costa, and F Marilda. Simulation study of dispatching rules in stochastic job shop dynamic. 10(3):231–240, 2014.
RW Conway, WL Maxwell, and LW Miller. Theory of Scheduling. Addison-Wesley, 1967.
Jose M. Framinan, Rainer Leisten, and Rubén Ruiz García. Manufacturing Scheduling Systems. Springer London, London, 2014. ISBN 978-1-4471-6271-1. doi: 10.1007/978-1-4471-6272-8. URLhttp://link. springer.com/10.1007/978-1-4471-6272-8.
R. Haupt. A survey of priority rule-based scheduling. OR Spektrum, 11(1):3–16, March 1989. ISSN 0171-6468. doi: 10.1007/BF01721162. URLhttp://link.springer.com/10.1007/BF01721162.
James R Jackson. Simulation research on job shop production. 233(02):287–295, 1957.
Zohar Laslo, Dimitri Golenko-Ginzburg, and Baruch Keren. Optimal booking of machines in a virtual job-shop with stochastic processing times to minimize total machine rental and job tardiness costs.
Interna-tional Journal of Production Economics, 111(2):812–821, February 2008. ISSN 09255273. doi: 10.1016/j.ijpe.
2007.03.018. URLhttp://linkinghub.elsevier.com/retrieve/pii/S0925527307001715. S S Panwalkar and Wafik Iskander. A Survey of Scheduling Rules. (June 2015), 1977.
H M Soroush. Sequencing and due-date determination in the stochastic single machine problem with ear-liness and tardiness costs. European Journal of Operational Research, 113(2):450–468, March 1999. ISSN 03772217. doi: 10.1016/S0377-2217(98)00003-4. URLhttp://linkinghub.elsevier.com/retrieve/ pii/S0377221798000034.
Daria Terekhov, Tony T Tran, Douglas G Down, and J Christopher Beck. Integrating Queueing Theory and Scheduling for Dynamic Scheduling Problems. 50:535–572, 2014.
H P M Veeke. TomasWeb Examples, 2010. URLhttp://www.tomasweb.com/examples.html.
H P M Veeke, Ottjes J A, and Lodewijks G. The Delft Systems Approach. Springer London, Delft, 2008. ISBN 978-1-84800-176-3. doi: 10.1007/978-1-84800-177-0. URLhttp://link.springer.com/10.1007/ 978-1-84800-177-0.
A
E
XPERIMENTAL
R
ESULTS
The abbreviations in the Tables are defined as Dispatching Rule, Number of Machines, Machine Capacity per week, Job IAT, Average Time per Job, Average Task Hours, Jobs Passed Total, Job percentage In Time, Average Job Time In System, Maximum Job Time In System, Average Job Processing Time, Maximum Job Processing Time and Occupancy rate of the machinery.
A.1.
W
ORKLOAD
Table A.1: 5 Dispatching rules, workload 15hr/job, capacity 30 hr, varying average task hours
DR M CAP JIAT AT/J ATH WL JP JIT AJTIS MJTIS AJPT MJPT OCC
1 1 30 8 10 1,5 15 2000 0,920 47,200 127,520 27,390 111,510 0,400 2 1 30 8 10 1,5 15 2000 0,915 45,180 145,190 25,370 119,660 0,400 3 1 30 8 10 1,5 15 2000 0,910 46,060 136,420 26,250 110,150 0,400 4 1 30 8 10 1,5 15 2000 0,732 58,840 222,740 39,030 195,260 0,400 5 1 30 8 10 1,5 15 2000 0,917 45,290 130,370 25,480 109,410 0,400 1 1 30 8 5 3 15 2000 0,943 46,640 155,710 26,820 135,720 0,300 2 1 30 8 5 3 15 2000 0,949 44,530 149,560 24,730 122,080 0,300 3 1 30 8 5 3 15 2000 0,946 45,760 161,040 25,960 133,560 0,300 4 1 30 8 5 3 15 2000 0,000 0,000 0,000 0,000 0,000 0,000 5 1 30 8 5 3 15 2000 0,950 44,400 130,190 24,580 11,910 0,300 1 1 30 8 3 5 15 2000 0,974 43,740 133,600 23,930 104,960 0,300 2 1 30 8 3 5 15 2000 0,975 40,940 141,110 21,130 107,190 0,300 3 1 30 8 3 5 15 2000 0,975 42,790 134,710 22,980 114,770 0,300 4 1 30 8 3 5 15 2000 0,000 0,000 0,000 0,000 0,000 0,000 5 1 30 8 3 5 15 2000 0,975 40,870 137,590 21,050 104,960 0,300 1 1 30 8 2 7,5 15 2000 0,995 39,450 116,080 19,620 98,230 0,300 2 1 30 8 2 7,5 15 2000 0,989 37,040 137,050 17,240 103,390 0,300 3 1 30 8 2 7,5 15 2000 0,994 39,100 137,050 19,290 102,020 0,300 4 1 30 8 2 7,5 15 2000 0,960 38,110 133,250 18,290 107,200 0,300 5 1 30 8 2 7,5 15 2000 0,989 37,090 137,050 17,270 102,020 0,300 27
28 A.EXPERIMENTALRESULTS
A.2.
O
CCUPANCY
Table A.2: 5 Dispatching rules, workload 15hr/job, capacity 30 hr, varying job inter-arrival time
DR M CAP JIAT AT/J ATH WL JP JIT AJTIS MJTIS AJPT MJPT OCC
1 1 30 8 10 1,5 15 2000 0,920 47,200 127,520 27,390 111,510 0,400 1 1 30 6 10 1,5 15 2000 0,886 60,710 163,960 40,710 159,950 0,500 2 1 30 8 10 1,5 15 2000 0,915 45,180 145,190 25,370 119,660 0,400 2 1 30 6 10 1,5 15 2000 0,893 56,740 187,680 36,770 160,680 0,500 3 1 30 8 10 1,5 15 2000 0,910 46,060 136,420 26,250 110,150 0,400 3 1 30 6 10 1,5 15 2000 0,895 59,000 182,820 39,010 164,840 0,500 4 1 30 8 10 1,5 15 2000 0,732 58,840 222,740 39,030 195,260 0,400 4 1 30 6 10 1,5 15 2000 0,000 0,000 0,000 0,000 0,000 0,000 5 1 30 8 10 1,5 15 2000 0,917 45,290 130,370 25,480 109,410 0,400 5 1 30 6 10 1,5 15 2000 0,893 58,020 178,800 38,030 154,370 0,500
A.3.
M
ACHINE CAPACITY
Table A.3: FCFS rule, workload 15hr/job, varying machine capacity per week
DR M CAP JIAT AT/J ATH WL JP JIT AJTIS MJTIS AJPT MJPT OCC
1 1 20 8 10 1,5 15 2000 0,988 77,260 238,700 57,470 233,350 0,400 1 1 30 8 10 1,5 15 2000 0,920 47,200 127,520 27,390 111,510 0,400 1 1 40 8 10 1,5 15 2000 0,868 44,860 127,560 25,040 92,730 0,400 1 1 50 8 10 1,5 15 2000 0,838 43,610 119,910 23,800 94,920 0,400 1 1 80 8 10 1,5 15 2000 0,848 44,500 108,500 24,690 92,660 0,400
A.4.
O
VERALL
Table A.4: 5 Dispatching rules, workload 15hr/job, varying machine capacity per week
DR M CAP JIAT AT/J ATH WL JP JIT AJTIS MJTIS AJPT MJPT OCC
1 1 20 8 10 1,5 15 2000 0,988 77,260 238,700 57,470 233,350 0,400 1 1 30 8 10 1,5 15 2000 0,920 47,200 127,520 27,390 111,510 0,400 1 1 40 8 10 1,5 15 2000 0,868 44,860 127,560 25,040 92,730 0,400 2 1 20 8 10 1,5 15 2000 0,988 74,44 265,6 54,66 233,02 0,4 2 1 30 8 10 1,5 15 2000 0,915 45,180 145,190 25,370 119,660 0,400 2 1 40 8 10 1,5 15 2000 0,855 43,670 123,960 23,850 98,430 0,400 3 1 20 8 10 1,5 15 2000 0,988 77,44 250,23 57,66 234,82 0,4 3 1 30 8 10 1,5 15 2000 0,910 46,060 136,420 26,250 110,150 0,400 3 1 40 8 10 1,5 15 2000 0,845 44,180 121,450 24,360 89,310 0,400 4 1 20 8 10 1,5 15 2000 0 0 0 0 0 0 4 1 30 8 10 1,5 15 2000 0,732 58,840 222,740 39,030 195,260 0,400 4 1 40 8 10 1,5 15 2000 0,880 43,410 120,430 23,590 95,560 0,400 5 1 20 8 10 1,5 15 2000 0,981 75,32 263,71 55,54 231,13 0,4 5 1 30 8 10 1,5 15 2000 0,917 45,290 130,370 25,480 109,410 0,400 5 1 40 8 10 1,5 15 2000 0,874 43,790 114,440 23,970 95,670 0,400
A.5.ALL DATA 29
A.5.
A
LL DATA
Table A.5: All data 1/2
DR M CAP JIAT AT/J ATH WL JP JIT AJTIS MJTIS AJPT MJPT OCC
1 1 20 8 10 1,5 15 2000 0,988 77,260 238,700 57,470 233,350 0,400 1 1 30 8 5 2 10 2000 0,993 34,650 82,010 14,830 65,390 0,200 1 1 30 8 10 1 10 2000 0,990 35,540 80,170 15,730 63,470 0,200 1 1 30 8 10 1,5 15 2000 0,920 47,200 127,520 27,390 111,510 0,400 1 1 30 8 5 3 15 2000 0,943 46,640 155,710 26,820 135,720 0,300 1 1 30 6 10 1,5 15 2000 0,886 60,710 163,960 40,710 159,950 0,500 1 1 30 8 3 5 15 2000 0,974 43,740 133,600 23,930 104,960 0,300 1 1 30 8 2 7,5 15 2000 0,995 39,450 116,080 19,620 98,230 0,300 1 1 30 8 5 4 20 2000 0,888 74,160 274,750 54,350 256,150 0,500 1 1 30 8 10 2 20 2000 0,786 78,420 249,450 58,630 244,090 0,500 1 1 40 8 5 2 10 2000 0,986 34,390 75,070 14,570 58,640 0,200 1 1 40 8 10 1 10 2000 0,986 35,370 76,950 15,560 61,200 0,200 1 1 40 8 5 3 15 2000 0,895 43,740 127,050 23,930 107,060 0,300 1 1 40 8 10 1,5 15 2000 0,868 44,860 127,560 25,040 92,730 0,400 1 1 40 8 5 4 20 2000 0,766 59,660 216,240 39,840 196,250 0,500 1 1 40 8 10 2 20 2000 0,676 62,300 172,510 42,490 150,840 0,500 1 1 50 8 5 3 15 2000 0,864 43,310 123,480 23,490 103,490 0,300 1 1 50 8 10 1,5 15 2000 0,838 43,610 119,910 23,800 94,920 0,400 1 1 80 8 5 3 15 2000 0,852 43,210 123,480 23,400 103,490 0,300 1 1 80 8 10 1,5 15 2000 0,848 44,500 108,500 24,690 92,660 0,400 2 1 20 8 10 1,5 15 2000 0,988 74,440 265,600 54,660 233,020 0,400 2 1 30 8 5 2 10 2000 0,990 33,660 87,500 13,850 66,780 0,200 2 1 30 8 10 1 10 2000 0,990 34,620 95,260 14,800 68,250 0,200 2 1 30 8 10 1,5 15 2000 0,915 45,180 145,190 25,370 119,660 0,400 2 1 30 8 5 3 15 2000 0,949 44,530 149,560 24,730 122,080 0,300 2 1 30 6 10 1,5 15 2000 0,893 56,740 187,680 36,770 160,680 0,500 2 1 30 8 3 5 15 2000 0,975 40,940 141,110 21,130 107,190 0,300 2 1 30 8 2 7,5 15 2000 0,989 37,040 137,050 17,240 103,390 0,300 2 1 30 8 5 4 20 2000 0,891 70,680 298,390 50,900 279,790 0,500 2 1 30 8 10 2 20 2000 0,796 73,790 236,150 53,990 218,620 0,500 2 1 40 8 5 2 10 2000 0,983 33,450 86,680 13,640 57,910 0,200 2 1 40 8 10 1 10 2000 0,985 34,510 85,040 14,700 59,250 0,200 2 1 40 8 5 3 15 2000 0,896 42,030 126,060 22,210 98,580 0,300 2 1 40 8 10 1,5 15 2000 0,855 43,670 123,960 23,850 98,430 0,400 2 1 40 8 5 4 20 2000 0,770 57,210 193,920 37,410 168,400 0,500 2 1 40 8 10 2 20 2000 0,680 60,170 183,770 40,360 161,100 0,500 3 1 20 8 10 1,5 15 2000 0,988 77,440 250,230 57,660 234,820 0,400 3 1 30 8 5 2 10 2000 0,991 34,260 89,870 14,440 67,580 0,200 3 1 30 8 10 1 10 2000 0,990 34,870 89,880 15,060 62,740 0,200 3 1 30 8 10 1,5 15 2000 0,910 46,060 136,420 26,250 110,150 0,400 3 1 30 8 5 3 15 2000 0,946 45,760 161,040 25,960 133,560 0,300 3 1 30 6 10 1,5 15 2000 0,895 59,000 182,820 39,010 164,840 0,500 R. Kapelle 2015.TEL.7952
30 A.EXPERIMENTALRESULTS
Table A.6: All data 2/2
DR M CAP JIAT AT/J ATH WL JP JIT AJTIS MJTIS AJPT MJPT OCC
3 1 30 8 3 5 15 2000 0,975 42,790 134,710 22,980 114,770 0,300 3 1 30 8 2 7,5 15 2000 0,994 39,100 137,050 19,290 102,020 0,300 3 1 30 8 10 2 20 2000 0,796 75,140 224,870 55,350 219,510 0,500 3 1 40 8 5 2 10 2000 0,980 34,020 85,490 14,200 63,240 0,200 3 1 40 8 10 1 10 2000 0,983 34,800 85,060 14,990 58,970 0,200 3 1 40 8 5 3 15 2000 0,892 43,040 131,500 23,220 102,590 0,300 3 1 40 8 10 1,5 15 2000 0,845 44,180 121,450 24,360 89,310 0,400 3 1 40 8 5 4 20 2000 0,763 58,190 212,170 38,380 199,130 0,500 4 1 20 8 10 1,5 15 2000 0,000 0,000 0,000 0,000 0,000 0,000 4 1 30 8 5 2 10 2000 0,985 33,610 106,360 13,800 73,850 0,200 4 1 30 8 10 1 10 2000 0,990 34,420 95,780 14,610 68,480 0,200 4 1 30 8 10 1,5 15 2000 0,732 58,840 222,740 39,030 195,260 0,400 4 1 30 8 5 3 15 2000 0,000 0,000 0,000 0,000 0,000 0,000 4 1 30 6 10 1,5 15 2000 0,000 0,000 0,000 0,000 0,000 0,000 4 1 30 8 2 7,5 15 2000 0,960 38,110 133,250 18,290 107,200 0,300 4 1 40 8 5 2 10 2000 0,990 33,130 91,990 13,320 59,140 0,200 4 1 40 8 10 1 10 2000 0,994 34,190 84,990 14,370 53,580 0,200 4 1 40 8 5 3 15 2000 0,886 42,420 128,920 22,600 101,430 0,300 4 1 40 8 10 1,5 15 2000 0,880 43,410 120,430 23,590 95,560 0,400 4 1 40 8 5 4 20 2000 0,000 0,000 0,000 0,000 0,000 0,000 5 1 20 8 10 1,5 15 2000 0,981 75,320 263,710 55,540 231,130 0,400 5 1 30 8 5 2 10 2000 0,993 33,690 90,580 13,880 64,370 0,200 5 1 30 8 10 1 10 2000 0,994 34,730 88,880 14,910 70,110 0,200 5 1 30 8 10 1,5 15 2000 0,917 45,290 130,370 25,480 109,410 0,400 5 1 30 8 5 3 15 2000 0,950 44,400 130,190 24,580 11,910 0,300 5 1 30 6 10 1,5 15 2000 0,893 58,020 178,800 38,030 154,370 0,500 5 1 30 8 3 5 15 2000 0,975 40,870 137,590 21,050 104,960 0,300 5 1 30 8 2 7,5 15 2000 0,989 37,090 137,050 17,270 102,020 0,300 5 1 40 8 5 2 10 2000 0,985 33,520 84,020 13,710 56,010 0,200 5 1 40 8 10 1 10 2000 0,989 34,640 84,260 14,830 56,430 0,200 5 1 40 8 5 3 15 2000 0,908 42,100 140,260 22,280 112,780 0,300 5 1 40 8 10 1,5 15 2000 0,874 43,790 114,440 23,970 95,670 0,400 5 1 40 8 5 4 20 2000 0,765 56,730 220,880 36,920 202,270 0,500
