Weight: 30% course mark
Purpose
The purpose of this assessment is to create a fully functional simulation of a more complex system. Building simulations is one of the key objectives of this course. You will need to be able to do this in an industry or government job working in decision sciences. Building a simulation is also the best way to absorb and gain a deep understanding of the ideas and topics that are discussed in this course. Even if you are just managing simulations projects, you should have some experience in creating the simulation itself.
This is quite a large and di cult task, but the assessment will provide considerable structure.
Outcomes
This Task addresses the following Course Learning Outcomes:
• communicate how randomness and controlled variation can be used to model complex systems in a range of application domains such as industry, health, and transportation;
• create a model of a real-world problem specified in words and implement it as a discrete-event simulation;Assignment Project Exam Help
• validate results from a discrete-event simulation.
You will be simulating a factory production line that constructs lawnmowers to order.
The bottleneck in this process is that, in this factory, there is only one machine that can properly fasten the blades to the motor as they have to be attached securely to make them safe.
Unfortunately, the blade-fitting machine is old and breaks down sometimes. If this happens, it is out of service while it is being repaired, and any orders will have to wait.
Assumptions
You should assume the following:
• Orders for new lawnmowers are processed in a FIFO manner and there can be an unlimited number waiting.
• Times: all times are independent and
– the inter-arrival times between orders are independent and exponential with a mean of one hour.
– the time to construct a lawnmower from parts is deterministic with a time of 45 minutes.
– the time between breakdowns of the blade-fitting machine is exponential with a mean of two days as measured from the last time it was repaired.
– the time to fix the machine when it breaks is exponential with a meantime of three hours.
• There is an unlimited number of parts available to construct new lawnmowers.
• If the blade-fitting machine breaks down while constructing a lawnmower, the work already completed on that lawnmower is interrupted but ‘saved’. That is, the total time to complete the lawnmower is the construction time, plus any repair times that interrupt construction (it is technically possible that more than one breakdown could occur during the same lawnmower build).
Questions
The factory owner wants to know how to improve their factory, the most obvious change would be to buy a replacement machine to attach the blades. The new machine would break down less often, so the mean time between breakdowns will be longer. They would like to assess the business case for such a purchase, i.e., what would the reduction in waiting time for orders be, and what percentage of orders would be interrupted with the new machine. Therefore, the questions they would like to answer are:
• How much production time is lost to repairs?
• How long do orders wait in this system before being completed, and how much would this be improved if the time between breakdowns was extended?
Your Task
This assessment is sca olded into three parts:
• Part 1: Modelling (Module 2)Assignment Project Exam Help
• Part 2: Programming (Module 3)
• Part 3: Verification and testing (Module 4)
Requirements
You will be assessed on three components of this work:
• a PDF document showing your schematic, state diagram, flow chart and any other documentation you created.
• two .jl files with your code for implementing the discrete-event simulation.
• a pair of data files (an entities and a state file) produced from your simulation with seed=1 and where the simulation was stopped at time T=20000.0.
Consult the assessment rubric when preparing your submission.
You are welcome to ask questions of course sta at any time.
Grading Criteria
This assessment is worth 30% of your overall grade. Refer to the attached rubric for detailed information on the grading criteria for this assessment.
Appendix 1 – Part 1: Modelling
In this part, you will consider the system model that you will be implementing.
The system
You will be simulating a factory production line that constructs lawnmowers to order.
The construction process involves a small number of main steps. Each is a series of tasks, but you will only model the main bottleneck task. You can presume that the mower is built from a series of prefabricated parts (the engine, the blades, the frame and so on).
The bottleneck in this process is that, in this factory, there is only one machine that can properly fasten the blades to the motor as they have to be attached securely to make them safe, so only one lawnmower can be made at once. Unfortunately, the blade-fitting machine is old and breaks down sometimes. If this happens, it is out of service while it is being repaired, and any orders have to wait.
Assumptions
You should assume the following:
• Orders for new lawnmowers are processed in a FIFO manner and there can be an unlimited number waiting.
• Times: all times are independent andAssignment Project Exam Help
– the inter-arrival times between orders are independent and exponential with a mean of one hour
– the time to construct a lawnmower from parts is deterministic with a time of 45 minutes
– the time to fix the machine when it breaks is exponential with a mean of time three hours.
• If the blade-fitting machine breaks down while constructing a lawnmower, the work already completed on that lawnmower is interrupted but ‘saved’. That is, the total time to complete the lawnmower is the construction time, plus any repair times that interrupt construction (it is technically possible that more than one breakdown could occur during the same lawnmower build).
Questions
The factory owner wants to know how to improve their factory, the most obvious change would be to buy a replacement machine to attach the blades. The new machine would break down less often, so the mean time between breakdowns will be longer. They would like to assess the business case for such a purchase, i.e., what would the reduction in waiting time for orders be, and what percentage of orders would be interrupted with the new machine. Therefore, the questions they would like to answer are:
• How much production time is lost to repairs?
• How long do orders wait in this system before being completed, and how much would this be improved if the time between breakdowns was extended?
Tasks for Part 1
Your assessment will require you to write code to simulate the system. However, writing the code can wait until next week when you will have seen more examples and been taught more of the tools required.
Hint: What state details are needed to answer factory owner’s questions? 3. Determine the entities in the system in relation to the state. (1 mark)
4. List the types of events in your model (1 mark):
• describe how each event changes the state of the system.
As part of your assessment, you will be required to submit a PDF document showing your schematic, flow chart and responses to these tasks.
Hint: You can create flow charts with the free diagram drawing tool Inkscape, but there are many other tools available for drawing connected series of boxes. Find a tool you like. Also, your boxes and links don’t have to look exactly like those in the course materials, but they have to be: (i) clear and readable, and (ii) consistent.
Appendix 2 – Part 2: Programming
In this part, you will start to program the model.
Reminder
The system to be modelled is described in Part 1.
Tasks for Part 2
1. Refine your schematic of the system. (see Part 1)
2. Draw a state-diagram of the system. (see Part 1) [1 mark] 3. Write code to implement a discrete-event simulation of the system.
As part of your assessment, you will be required to submit a PDF document showing your schematic and stateAssignment Project Exam Help
diagram, along with the flow chart from Part 1 and responses to these tasks. You will also be required to submit two .jl files with your code for implementing the discrete-event simulation from Task 3 above.
This week you will start coding your simulation. A good deal of the structure of the code is provided.
• It ensure that everyone has a common starting point.
• It makes it easier to review and assess your progress by ensuring that everyone adopts the same basic structure for their implementation.
Here are the required specification details:
1. Your code must be included in a two stand-alone .jl files. These should be named:
• factory_simulation.jl
• factory_simulation_run.jl
The first file should contain all of your data structures and functions. The second file should initialise all variables to values you choose and run the main event loop.
Note that the second file is a temporary file. The second is for your own benefit, for the moment, to test your code. It will be replaced in Part 3 of this assessment with a simulation harness. [1 mark]
2. You should use the standard packages that you have been using in this course. These include:
• DataStructures
• Distributions
• StableRNGs
Do not use any packages other than these or those that have been discussed in the course. [1 mark]
3. Your code must specify three data structures:
abstract type Event end mutable struct Entity … mutable struct State …
Each will contain fields as required. The state structure should contain any queues or lists required, for instance, the event list.
• The Event is an abstract type, which will have more sub-types for each event in your simulation, for instance: Arrival and Breakdown events.
• The Entity should contain fields to record important event times in the lifetime of the entity.
• The State will, as in car park simulations contain a time, event list (queue) and queues for all resources in the system. It will contain other details as needed, such as the state of repair of the machine and the number of events so far.Assignment Project Exam Help
You should create convenience constructor functions for each of these types, that allow you to create an object when not all of its fields are known. For instance, a function State(), that returns an initial and system State variable with any required queues or lists created (but empty) and the clock time set to 0.0.
using DataStructures pq = PriorityQueue()
pq[“a”] = 10; pq[“b”] = 5; pq
Output:
PriorityQueue{Any, Any, Base.Order.ForwardOrdering} with 2 entries:
“b” => 5
“a” => 10
To change the priority of an object: pq[“a”] = 0 # change the priority of “a” pq Output:
PriorityQueue{Any, Any, Base.Order.ForwardOrdering} with 2 entries:
“a” => 0 “b” => 5
Note that the order of the two items in the queue has swapped. However, be careful if you also store the time of an event in the Event structure because that would not be updated in the above code. [1 mark]
5. Your factory_simulation.jl code must have a set of ‘update! functions with signatures:
function update!( S::State, R::RandomNGs, E::SomeEvent )
Each update function should process one of your event types so you will need one function per event type.
Each update function should modify the state S appropriately, including
• adding any new events created from this one
• moving any entities from queues to servers and so on.
6. Your code should have a data structure for passing parameters:
struct Parameters seed::Int
mean_interarrival::Float64 mean_construction_time::Float64 mean_interbreakdown_time::Float64 mean_repair_time::Float64
end
[1 markAssignment Project Exam Help]
interarrival_time::Function construction_time::Function interbreakdown_time::Function repair_time::Function
end
• Your initialise function should create a set of random number generators to populate the above structure. Create and initialisation constructor function for RandomNGs using code similar to that below (the parameters used here to create these should come from variable P::Parameters).
rng = StableRNG(P.seed)
interarrival_time() = rand(rng, Exponential(P.mean_interarrival)) construction_time() = P.mean_construction_time
interbreakdown_time() = rand(rng, Exponential(P.mean_interbreakdown_time)) repair_time() = rand(rng, Exponential(P.mean_repair_time))
Note that, although construction times are deterministic, you can use the same functional form to be consistent.
• The initialisation function should also create a new system state and inject an initial arrival at time 0.0 and initial breakdown at time 150.0 minutes. The function should return the system state and the random number structure.
Therefore, your initialisation function should look like:
function initialise( P::Parameters ) R = RandomNGs( P ) # create the RNGs
system = State() # create the initial state structure
# add an arrival at time 0.0 t0 = 0.0
system.n_events += 1 # your system state should keep track of events enqueue!( system.event_queue, Arrival(0,t0), t0)
# add a breakdown at time 150.0 t1 = 150.0 system.n_events += 1
enqueue!( system.event_queue, Breakdown(system.n_events, t1), t1 )
return (system, R)
end
This code presumes you have created appropriate constructors for the random number generators and system state as described above.
8. Your code should include a run!(state::State, R::RandomNGs, T::Float64, fid_state::IO, fid_entities) function. The inputs are:
• state: a structure containing the system state;
• R:Assignment Project Exam Helpa structure of type RandomNGs that contains your random variable generators;
• T: a floating-point number stating how long to run the simulation;
9. Your code must output two CSV files. The files should both commence with metadata (you can include comments preceded with a #).
• The first file should contain a time-ordered list of all events that are processed in the simulation. This should be written from the point of view before the event, for instance, you should report the system that an arriving customer sees immediately prior to their arrival. The CSV file should have columns titled:
time,event_id,event_type,length_event_list,length_queue,in_service,machine_status
• The second file should contain a list of all entities that have completed service. The CSV file should have columns titled:
id,arrival_time,start_service_time,completion_time,interrupted
You will need to write and construct these CSV files line by line, but you can do this using either the CSV or the Printf package, or using raw print statements.
10. Your code must be written with good style. See Julia’s style guidelines for information, but in particular:
• avoid global variables wherever possible (1 mark)
• choose good variable names (1 mark)
• use white space well (1 mark)
• avoid very ine cient approaches (1 mark).
You should use your factory_simulation_run.jl to run this code and construct some tests. More detail of running the code and testing it will follow in Part 3.
Appendix 3 – Part 3: Verification and testing
In this part, you will test your implementation and make sure it can output results.
Reminder
The system to be modelled is described in Part 1 and builds on the code written in Part 2.
As part of your assessment, you will be required to submit:
• a PDF document showing your schematic, state diagram, flow chart and responses to tasks in Part 1 and Part 2
• two .jl files with your code for implementing the discrete-event simulation
• a pair of data files (an entities and a state file) that you have produced from your simulation with seed=1 and where the simulation was stopped at time T=20000.0. Part of the marking process involves, checking that these files came from your simulation.
When marking your assessment, the output of your code will be checked by running the code that you submit. This is the code you created in Part 2 and which you will now refine by completing the tasks outlined here.
Tasks for Part 3
Here are some sample outputs when the code is run with with seed=1 for T=5000.0 minutes (note the output you will submit must use T=20000.0):
# file created by code in factory_simulation.jl
# parameter: seed = 1
# parameter: mean_interarrival = 60.0
# parameter: mean_construction_time = 45.0
# parameter: mean_interbreakdown_time = 2880.0
# parameter: mean_repair_time = 180.0
# T = 5000.0
# units = minutes
time,event_id,event_type,length_event_list,length_queue,in_service,machine_status
0.000, 1, Arrival, 1, 0, 0, 0
40.499, 3, Arrival, 2, 0, 1, 0 45.000, 4,Departure, 2, 1, 1, 0
51.694, 5, Arrival, 2, 0, 1, 0 90.000, 6,Departure, 2, 1, 1, 0
117.235, 7, Arrival, 2, 0, 1, 0 135.000, 8,Departure, 2, 1, 1, 0 150.000, 2,Breakdown, 2, 0, 1, 0
182.987, 9, Arrival, 2, 0, 1, 1
• The start of the entity file showing a list of entities with information output on departure is as follows:
# file created by code in factory_simulation.jl
# parameter: seed = 1
# parameter: mean_interarrival = 60.0
# parameter: mean_construction_time = 45.0
# parameter: mean_interbreakdown_time = 2880.0
# parameter: mean_repair_time = 180.0
# T = 5000.0
# units = minutes
id,arrival_time,start_service_time,completion_time,interrupted
1,0.0,0.0,45.0,0
2,40.49940643026974,45.0,90.0,0
3,51.69359364153775,90.0,135.0,0
4,117.2350182717608,135.0,760.5865405812849,1
2. Create a test harness that will:
• run your code for 100 di erent seed values ranging from 1–100
• run your code for a set of parameters specified in the following CSV file:
# parameters mean_interarrival,mean_construction_time,mean_interbreakdown_tim e,mean_repair_time
60.0,45.0,2880.0,180.0Assignment Project Exam Help
Test Data
• state.csv
• entities.csv
1. If you have implemented your code exactly as specified, and used the same seed and random number generation, your output should look very, very similar (the only di erences should be in details such as numbers of decimal points, white-spacing, ID numbers or units such as hours or minutes).
Note that you can see the metadata in the files, and from that determine any parameters used.
Detailed rubric
You will be assessed on three components of your work:
Note in the below rubric, the final mark for Component 3 (for “Ine cient approaches”) should read: “Code implements the model e ciently, e.g., there are no unneeded steps, and the underlying algorithm is appropriate.” Additionally, the final mark in Component 2 should be for “Output entity file: Entity IDs”, not a duplicate of a previous criterion for the event IDs.
Component 1: Conceptual Model
Criteria Ratings Points
Task 1
Draw a schematic of the system Points: 2.0
Name: Full points
Points: 1.0
Name: Partial points
Points: 0.0
Name: No points
2 pts
Your schematic correctly shows the standard queue components and the breakdown-repair cycle in some way. You have correctly shown either the standard queue components or the breakdown-repair cycle. Assessment requirements for this step have not been met.
Task 2
Describe the state(s) of the system Points: 2.0 Assignm
Name: Full points
ent Project Exam Points: 1.0
Name: Partial points
HelpPoints: 0.0
Name: No points
2 pts
You have correctly described the state(s) of the
Task 3
Determine the entities in the system in relation to the state Points: 1.0
Points: 0.0 powcoderName: No points
1 pt
You have correctly determined the entities in the system. Assessment requirements for this step have not been met.
Task 4
List the types of events in your model
• describe how each event changes the
state of the system
Name: Full points
Points: 0.0
Name: No points
1 pt
You have correctly listed the types of events in your model.
Assignment Projec Assessment requirements for this step have not been met.
t Exam Help
Task 5
Draw a flow chart illustrating your simulation structure Points: 3.0
Name: Full points
Points: 2.0 https://powcoName: Partial points
Points: 1.0 der.comName: Partial points
Points: 0.0
Name: No points
3 pts
(except for the termination step); and (iii) included vacation (machine breakdowns). You have successfully completed one of the following: (i) correctly
powcoderdrawn a valid flow chart, (ii) there are no dead ends (except for the termination step); and (iii) included vacation (machine breakdowns). Assessment requirements for this step have not been met.
Section total: 9 pts
Component 2: Functionality
Criteria Ratings Points
Task 1
Task 2
Draw a state-diagram of the system Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your state diagram shows the correct state transitions. Assessment requirements for this step have not been met.
Task 3
Write code to implement a discrete-event simulation of the system.
Output state file: Initialisation Points: 2.0
Name: Full points
Points: 1.0
Name: Partial points
Points: 0.0
Name: No points
2 pts
Your initialisation creates a valid starting state with an arrival at time 0.0 and a breakdown at Assignm time 150.0. You have done one of the following: (i) created
ent Projeca valid starting state wit Exam Hth an arrival at time 0.0, and (ii) created a valid starting state with a breakdown at time 150.0. Assessment requirements for this step have elpnot been met.
Output state file: run! Initialisation Points: 1.0 https://powco
Name: Full points
der.comPoints: 0.0
Name: No points
1 pt
Your run! function can be called with the prescribed inputs and does
Output state file:
Random number generators Points: 4.0
Name: Full points
Points: 3.0
Name: Partial points
Points: 2.0
Name: Partial points Points: 1.0
Name: Partial points
Points: 0.0
Name: No points
4 pts
Your random number generators create suitable random numbers for: (i) inter-arrival times, (ii) construction times, (iii) breakdown times, and (iv) repair times. Your random number generators have created suitable random numbers for three of the following: (i) inter-arrival times, (ii) construction times, (iii) breakdown times, and (iv) repair times. Your random number generators have created
suitable random numbers for two of the following: (i) inter-arrival times, (ii) construction times, (iii) breakdown times, and (iv) repair times. Your random number generators have created suitable
random numbers for
one of the following: (i) inter-arrival times, (ii) construction times, (iii) breakdown times, and
(iv) repair times. Assessment requirements for this step have not been met.
Output state file: CSV format and metadata
Points: 2.0
Name: Full points
Points: 1.0
Name: Partial points
Points: 0.0
Name: No points
2 pts
Your output state file conforms to the correct CSV format and contains satisfactory metadata. You have done one of the following: (i) created an output state file that conforms to the correct CSV format, (ii) created an output state file that contains satisfactory metadata. Assessment requirements for this step have not been met.
Output state file: States Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your output state file contains states that are sequentially ordered in
increasing time. Assignment Projec Assessment requirements for this step have not been met.
t Exam Help
Output state file: Event IDs Points: 1.0
Name: Full points
https://powco Points: 0.0
Name: No points
der.com 1 pt
Your output state file contains unique event IDs. Assessment requirements for this step have not been met.
Output state file:
Arrival and
breakdown Points: 2.0 Name: Full points Add
Points: 1.0
Points: 0.0
Name: No points
2 pts
Your output state file contains an arrival at time 0.0 and breakdown time at 0.0. You have done one of the following: (i) created an output state file that contains an arrival time at 0.0, and (ii) created an output state file that contains a breakdown time at 0.0. Assessment requirements for this step have not been met.
Output state file:
Queue Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your output state file shows that the queue grows during the breakdown. Assessment requirements for this step have not been met.
Output state file: Events Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your output state file shows that the event list always has 1 or 2 events in it. Assessment requirements for this step have not been met.
Output state file: Machine status Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your output state file shows that the machine status is 0 normally and 1 after the start of a breakdown up until a repair. Assessment requirements for this step have not been met.
Output entity file: CSV format and metadata
Points: 2.0 Assignm
Name: Full points
ent ProjecPoints: 1.0 t Exam H
Name: Partial points
elpPoints: 0.0
Name: No points
2 pts
Your output entity file conforms to the correct CSV format and contains satisfactory https metadata. You have done one of the following: (i) created
//powcoan output entity file thader.comt conforms to the
correct CSV format, and (ii) created an output entity file that contains satisfactory metadata. Assessment requirements for this step have not been met.
Name: Full points
powcoderPoints: 0.0
Name: No points
1 pt
Your output entity file contains arrival times, start service times and completion times that are in increasing order. Assessment requirements for this step have not been met.
Output state file: Event IDs Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your output entity file contains entities with unique IDs. Assessment requirements for this step have not been met.
Section total: 21 pts
Component 3: Programming Style
Criteria Ratings Points
Specification 1 File names, functions and data structures Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your file names are correct, and the correct code is in the correct place (functions and data structures in particular). Assessment requirements for this step have not been met.
Specification 2 Packages Points: 1.0
Name: Full points Assignment Projec
Points: 0.0
t Exam HelpName: No points
1 pt
Your file names are correct, and the correct code is in the correct place (functions and data structures in particular). Assessment requirements for this step have not been met.
Specification 3 Data structures Points: 3.0
Name: Full points
https://powco
Points: 2.0
Name: Partial points
der.com
Points: 1.0
Name: Partial points
Points: 0.0
Name: No points
3 pts
structures declared in a valid manner with appropriate constructors. powcoderYou have one of the three data
structures declared in a valid manner with appropriate constructors. Assessment requirements for this step have not been met.
Specification 3 Event types Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
You have included concrete event types. Assessment requirements for this step have not been met.
Specification 4
Machine breakdowns Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
You have included extra delays for machine breakdowns in the update function for breakdowns. Assessment requirements for this step have not been met.
Specification 5 Update functions Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
You have included update functions for four types of events. Assessment requirements for this step have not been met.
Specification 6 Parameters Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your code has a data structure for passing parameters. Assessment requirements for this step have not been met.
Specification 7 Constructor Points: 1.0 Name: Full points
Assignment Projec Points: 0.0
Name: No points
t Exam Help 1 pt
You have included a random number generator constructor. Assessment requirements for this step have not been met.
Specification 7 Specification Points: 1.0
Name: Full points https://powco
Points: 0.0 der.comName: No points
1 pt
You have included an initialise function matching specification. Assessment requirements for this step have not been met.
Name: Full points
powcoderPoints: 0.0
Name: No points
1 pt
You have included a run! function that runs the simulation. Assessment requirements for this step have not been met.
Specification 9
Entities file Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your program writes an entities file. Assessment requirements for this step have not been met.
Specification 9
State file Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
Your program writes a state file. Assessment requirements for this step have not been met.
Specification 10 Variables Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
You have not included any global variables. Assessment requirements for this step have not been met.
Specification 10 Variable names Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
You have used meaningful variable names, with the exception of local variables with small scope. Assessment requirements for this step have not been met.
Specification 10 Comments Points: 2.0 Name: Full points Assignm
Points: 1.0
ent ProjecName: Partial points t Exam H
Points: 0.0 elpName: No points
2 pts
You have used comments efficiently and effectively.
https You have partially used comments efficiently and effectively.
Specification 10 White space Points: 1.0 Name: Full points
Name: No points
You have used correctly and consistently used indentation and space to separate important components and expressions. Assessment requirements for this step have not been met.
Specification 10
Inefficient
approaches Points: 1.0
Name: Full points
Points: 0.0
Name: No points
1 pt
You have used correctly and consistently used indentation and space to separate important components and expressions. Assessment requirements for this step have not been met.
Section total: 20 pts
Assessment total: 50 pts
