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程序代写案例-IB2110
时间：2022-05-18
IB2110
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Student Number______________________________
Desk Number______________________________
UNIVERSITY OF WARWICK
Summer 2019
Simulation
Closed Book Examination
For those students taking the 12CAT option you must answer all questions in SECTION
A only. Time Allowed: 90 minutes
For those students taking the 15CAT option you must answer all questions in SECTION
A and SECTION B. Time Allowed: 120 minutes
Answers should be entered on the examination paper in the spaces provided. If you run
out of space continue on the back of the page but make sure that you number the answers
clearly. Where graph paper is used, make sure that you write your student number on the paper
and attach it securely to the examination paper.
Silent pocket calculators that are not capable of text storage or retrieval are permitted, but full
working should be shown. PDAs, mobile phones or any other hand-held devices that facilitate
wireless communication are NOT permitted.
Add your student number and desk number to the top of this examination paper and make sure
that you hand the paper to an invigilator (together with any answer book if required) at the end
of the examination.
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SECTION A
Question 1
Complete the following statements (- each may require one or more words to complete):
a) In DES the system is represented by a series of …………….. .
b) VIS stands for ……………………. .
c) Discrete Event Simulations are good for modelling systems that are …………..………….. .
[Write your answers in the box provided below] (3 marks)
a) Events
b) Visual Interactive Simulation
c) complex, change over time (dynamic), have variability (randomness) in them, are
queuing systems.
Question 2 over the page….\
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Question 2 (18 marks in total)
Please read the following ‘story’ and then answer Questions 2a), b), c), d) and e) which are
based on this text:
SimULink Consultancy is a consultancy firm that specialise in conducting DES projects using
the Simul8 software. They have recently been hired by Portland Police Department (PPD)
Crime Laboratory.
Faced with tighter funding and increased demand, many forensic laboratories are examining
their processes to do more with their resources. DNA Units in particular have experienced a
sharp rise in demand in recent years as a result of the growing use of DNA testing as an
investigative tool. Between 2001 and 2011, the DNA Unit of the PPD Crime Laboratory saw
a 225% increase in its caseload. Despite expanding the laboratory to improve capacity, and
running the lab 24 hours a days, 7 days a week, using a staff shift system, the volume of
cases submitted for DNA testing continues to lead to longer turnaround times. Turnaround
times are the time taken from when a lab request is received until the results are reported.
The DNA Unit has target turnaround times of seven days for rush cases and 45 days for all
other case types.
With a growing backlog of work, identifying potential improvements is a challenge with
limited flexibility to assess operational changes that could help to further increase capacity.
The PPD Crime Laboratory is challenged by the fact that it only has a subjective view of its
processes, as well as limited data to assess solutions to improve efficiency. They do not
know, for instance, whether the existing laboratory equipment is being utilized at full
capacity, or whether there are areas that are ‘resource starved’, i.e. equipment waiting for
an analyst to become available to complete the task. So it is completely unclear to them
whether it is a lack of equipment or staff or both that is causing the backlog and long
turnaround times.
To overcome this challenge, Discrete Event Simulation has been chosen as a solution to
provide a more objective, evidence-based approach. The PPD Crime Laboratory turned to
SimULink Consultancy to thoroughly evaluate two potential investment options for
improving efficiency: purchasing additional equipment and hiring more staff. The PPD
Crime Laboratory wants to use the simulation to identify whether additional equipment
and/or staff could help alleviate the case backlog and achieve turnaround times.
The SimULink consultants have been hired to develop a simulation model that captures the
entire flow of the DNA laboratory processes that could then be turned over to the PPD
Crime Laboratory Improvement Project Manager within one month of the project start date.
It is important that the PPD Crime Laboratory Improvement Project Manager, who has no
previous simulation or computing experience, can use the simulation model easily to make
changes to the existing laboratory processes and hence evaluate the impact of adding
additional equipment and staffing on overall efficiency and turnaround times.
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The lab currently has 10 pieces of equipment. The PPD Crime Lab are confident that they
could accommodate twice this number in the existing building, if this was found to be
necessary to achieve their targets. They are also prepared to increase the current staff
numbers of 7 analysts, 1 lab technician and 2 supervisors to as many as necessary to reach
their targets.
The DES model is to be created in conjunction with the personnel working in the DNA unit to
help ensure that all steps in the laboratory processes are captured within the simulation. To
further validate the simulation, one year of real casework data will be provided to be
entered and ran through the simulation to compare the results and verify its accuracy. It is
important to the PPD that the final model should mimic the running of the lab for three
years, so that it will help them understand the long-term impact and the return on
investment of any additional resources as well as showing how long it will take to eliminate
the existing backlog.
It is therefore a priority to SimULink to produce a computer simulation that can complete a
model run in less than 4 minutes, to allow for efficient running of a large number of possible
scenarios by the PPD Crime Laboratory Improvement Project Manager. The PPD are also
intending to use the model to create buy-in from stakeholders, such as staff and funding
sources, for the proposed changes. They are also interested in re-using the model in the
longer term as a management and planning tool.
a) State the proposed clock time of the PPD Crime Laboratory Simulation.
[Write your answer in the box provided below] (1 mark)
Real time being modelled = 3 years
Question 2 continued over page....\
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Question 2 continued…\
b) State the proposed model duration of the PPD Crime Laboratory Simulation.
[Write your answer in the box provided below] (1 mark)
How long the model takes to run = less than 4 minutes
c) Write down in detail the modelling objectives of the PPD Crime Lab project as
described (including the proposed experimental factors).
[Write your answer in the box provided below and carry on over the page as
needed] (5 marks)
Question 2c) answer box continued over page....\
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Question 2c) answer box continued…\
Achievement:
To understand the long-term impact
and the return on investment of any additional resources
as well as showing how long it would take to eliminate the existing backlog
current utilization of resources,
(or otherwise explain the PPD overall aim)
Performance: so that target turnaround times are achieved of seven days for rush cases
and 45 days for all other case types.
Changes: by increasing staffing from current levels of 7 analysts, 1 lab technician and 2
supervisors to as many as necessary to reach their targets
and by increasing equipment numbers from 10 pieces of equipment to 20 (Constraint).
(marks are given for the correct information in logical format)
Question 2 continued over page....\
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Question 2 continued…\
d) Write down in detail what model outputs should be monitored from the PPD Crime
Lab simulation model.
[Write your answer in the box provided below] (5 marks)
To determine achievement of objective
• Turn around times of rush cases
• Turn around times of other types of cases
• % utilisation of resources.
• Time to elimination of back-log
To identify reasons for failure to meet objective
• Bar chart of turn around times for each case
• Min, max, mean, variance of turn around times
• Time series of mean turn around time
• Number of cases waiting at each equipment – bottle necks
• Utilisation of staff
• Utilisation of equipment.
Question 2 continued over page....\
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Question 2 continued…\
e) Write in detail, with explanations and justifications, the General Project Objectives of
the described PPD Crime Lab simulation project.
[Write your answer in the box provided below] (6 marks)
• Time Scale for project – produce validated, working computer simulation within
one month.
• Nature of model use:
– Flexibility: Model shouldn’t need to be changed beyond varying the 2
stated experimental factors: equipment and staff numbers.
– Run speed: Number of possible scenarios quite large, so need model to run
reasonably fast, at least 4 minutes/run
– Visual display: 2D or 3D model adequate (should be justified). Clients will
see and use model to create buy-in from stakeholders, so should be
recognisable as lab.
– Ease of use: Clients need to interact directly with model so consider
creating user interface, as Project manager is not simulation or computer
savvy.
– Foreseen reuse of model or components as a planning/management tool
Question 3 over page....\
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Question 3
Explain clearly the differences between making simplifications and assumptions in DES
conceptual modelling and hence explain clearly when and why each would be made.
Clearly describe one example of each (one simplification and one assumption) that was (or
could have been) made in modelling the system in your group assignment. Justify why each
is an assumption or a simplification. State the system you modelled in your group work as
part of your answer.
[Write your answers in the box provided below and continue over the page as necessary]
(6 marks)
Simplifications are modelling decisions made in order to reduce complexity.
Whereas,
Assumptions are modelling decisions made because of uncertainties or beliefs about the
real system.
Looking for a clear appropriate example of one simplification and one assumption clearly
related to the group assignment project with clear and correct justifications of which they
are and why.
Marks can not be given if examples are incorrectly labelled as simplifications when they
are justifed as assumption and visa versa.
Question 3) answer box continued over page....\
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Question 3) answer box continued…\
Question 4 over page....\
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Question 4
Explain what the method MSER-5 is used for in DES and why you would use it.
Hence, clearly explain and justify in detail why you would or would not have used MSER-5 or
an equivalent method with your group assignment model. State the system you modelled
in your group work as part of your answer.
[Write your answer in the box provided below] (4 marks)
MSER-5 is a warm-up method
for finding the trunction point/end of transient phase/ warm-up period length)
to illiminate the effect of the initial transient on the resulting output
for steady-state output.
Looking for clear correct argument as to whether the group work system model output
would have an initial transient and be steady state and therefore whether a warm-up
period is appropriate, or otherwise clear full arguments as to why MSER-5 is not
appropriate.
Question 5 over page....\
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Question 5 (14 marks in total)
A DES model was constructed to investigate the functioning of a canteen. It currently has
one cold food counter which is self-service, followed by a checkout counter for cold food
only, manned by one dedicated assistant. It also has one hot food counter with one server,
followed by a checkout counter for hot food only, manned by one dedicated assistant. Both
cold and hot foods can be eat-in or take-away. Once the customer has paid they continue
into the seating area where they can either sit and eat or exit the canteen with their ‘take-
away’ food.
The canteen has been receiving rising numbers of customer complaints regarding the time
spent queuing to get food and pay for food. The manager wants to achieve 98% of
customers wating less than 2 minutes in a queue to choose food (hot or cold) and 98% of
customers waiting less than 1 minute in a queue to pay for the food (hot or cold) once
chosen.
The manager is willing to increase the number of servers at the hot food counter to a
maximum of three. He is also willing to put in one more (identical) cold food self service
counter.
The manager is also willing to increase the number of cold food checkouts (each with
dedicated assistant) up to a total of three. Likewise, he is willing to increase the number of
hot food checkouts (each with dedicated assistant) up to a total of three.
Alternatively he is willing to consider doing away with the dedicated hot and cold checkouts
and have one to five general checkouts instead that can serve anyone, with just one queue
for the multiple checkouts.
A floor plan of the current system is shown in Figure 5.1
Figure 5.1: Canteen current floor plan – not drawn to scale.
Question 5 continued over page....\
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Question 5 continued…\
Answer the following questions:
a) Draw two separate Activity Flow Diagrams, one for the current canteen system and
one for the altered canteen under the proposed change of creating four general
checkouts but keeping the cold and hot food counters unchanged. Clearly state and
justify any assumptions or simplifications you make (if any) and title the diagrams to
clearly indicate which system is being depicted.
[Write your answers in the box provided below] (10 marks)
Question 5a answer box continued over page....\
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Question 5a answer box continued…\
No marks were given if a logic flow diagram was drawn instead.
Valid differences are allowed if justifiable and explained clearly.
Question 5 continued over page....\
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Question 5 continued…\
b) List all the bound events in a DES of the current canteen system.
[Write your answers in the box provided below] (5 marks)
Customer arrives
End choosing cold food
End choosing hot food
End paying for cold food
End paying for hot food
End eating
Question 6 over page....\
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Question 6 (11 marks total)
Carry out a manual simulation of a part of the current canteen system as described in
Question 5 using the following information.
a) Assume that an exponential distribution is suitable for modelling the inter-arrival
times of groups of customers at this canteen in the first hour after opening. Assume
that the mean inter-arrival time was estimated to be 4.2 minutes. Use the inverse-
transform formula method to sample three inter-arrival times (in minutes) from this
distribution, using the following three random numbers in the order given: 0.562,
0.781, 0.245. Show your workings and round your answers to the nearest whole
minute. Hence complete Table 6.1 over the page, to simulate the arrival times of the
first three groups entering the canteen. Assume the simulation clock starts at time
8am (i.e. 08:00 where the format is Hour:Minutes).
[NB. The CDF for the Exponential distribution is () = 1 − ିఒ௫, where will
represent the sampled inter-arrival time and ଵ
ఒ
is the mean inter-arrival time.]
[Write your working in the box provided below and your answers in Table 6.1]
(6 marks)
() = 1 − ିఒ௫
= 1 − ିఒ௫
1 − = ିఒ௫
ln (1 − ) = −
[1 mark for working can be given if does not reach answer]
୪୬ (ଵି௨)
ିఒ
= [either this or] = ି୪୬ (௨)
ఒ
Either ୪୬ (ଵି௨)
ିఒ
=
ଵ = − ln(1 − 0.562) × 4.2 = 3.467 = 3
ଶ = − ln(1 − 0.781) × 4.2 = 6.378 = 6
ଷ = − ln(1 − 0.245) × 4.2 = 1.180 = 1
Or = ି୪୬ (௨)
ఒ
ଵ = − ln(0.562) × 4.2 = 2.420 = 2
ଶ = − ln(0.781) × 4.2 = 1.038 = 1
ଶ = − ln(0.245) × 4.2 = 5.907 = 6
(Follow through marks allowed)
Question 6a answer box continued over page....\
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Question 6a answer box continued…\
Group of
customers
Random
number
Time between arrivals
(in whole minutes)
Arrival Time
(HH:MM)
08:00
1
0.562
3 08:03
2 08:02
2
0.781
6 08:09
1 08:03
3
0.245
1 08:10
6 08:09
Table 6.1: Arrival time simulation for the first three groups of customers
Question 6 continued over page....\
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Question 6 continued…\
b) Data has been collected regarding the number of people in each group as shown in
Table 6.2 below. Complete Table 6.2 by correctly allocating the random number
integers 0-99 to the observed group sizes. Then carry on to simulate the group sizes
of your three arriving groups using the following random numbers in the order given:
2, 25, 84. [Write your answers and any workings in the box provided below]
(5 marks)
Table 6.2: Frequency table for number of customers within an arriving group.
Group
size Frequency
Percentage
frequency
Cumulative %
frequency Random Numbers
1 5 5% 5 0-4
2 20 20% 25 5-24
3 25 25% 50 25-49
4 35 35% 85 50-84
5 10 10% 95 85-94
6 5 5% 100 95-99
2 -> group size of one
25 -> group size of three
84 -> group size of four
(Follow through marks allowed)
Question 7 over page....\
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Question 7 (18 marks total)
A DES model was constructed to investigate the functioning of the canteen as described in
Question 5. After preliminary experimentation and consultation with the canteen manager
there were six potentially useful scenarios that it was decided to explore in more detail. It
was decided to formally compare the results of these six scenarios by constructing
confidence intervals around the difference between the means of the results, using an
overall significance level of 10%.
The results for two key performance indicators (KPI) were compared:
KPI1: Percentage of customers waiting less than 1 minute in a queue to be served at check-
out to pay.
KPI2: Percentage of customers waiting less than 2 minutes in a queue to choose food (hot or
cold).
The six chosen scenarios were:
S1. 2 cold food counters, 1 hot food server, 2 dedicated cold food checkouts, 2
dedicated hot food checkouts.
S2. 2 cold food counters, 2 hot food servers, 2 dedicated cold food checkouts, 2
dedicated hot food checkouts.
S3. 2 cold food counters, 2 hot food servers, 3 dedicated cold food checkouts, 3
dedicated hot food checkouts.
S4. 2 cold food counters, 1 hot food servers, 3 general checkouts.
S5. 2 cold food counters, 2 hot food servers, 3 general checkouts.
S6. 2 cold food counters, 2 hot food servers, 4 general checkouts.
Figures 7.1 to 7.4 show a selection of the output from the MSExcel file used to compare the
output results for KPI1: Percentage of customers waiting less than 1 minute in a queue to be
served at check-out to pay.
Question 7 continued over page....\
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Question 7 continued…\
Figure 7.1: Variance Reduction Check for KPI1 – output from MSExcel.
Figure 7.2: Paired-t Confidence Interval comparisons for KPI1 – output from MSExcel.
Question 7 continued over page....\
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Question 7 continued…\
Figure 7.3: Standard t Confidence Interval comparisons for KPI1 – output from MSExcel.
Figure 7.4: Confidence Interval comparisons for KPI1 – output from MSExcel.
a) Using the results shown in Figures 7.1 to 7.4, write down the appropriate Confidence
Interval for the mean difference between scenarios 1 and 2 (where the order of
calculation was: S1 – S2). Fully explain in detail why your chosen CI is appropriate.
Fully interpret this confidence interval in context and hence complete the
significance conclusions shown in Figure 7.4.
[Write your answers in the box provided over the page] (6 marks)
Question 7a) answer box over page....\
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Question 7a) answer box continued....\
(7.98, 15.74)
Since Variance of differences (59.72) > Sum of variances (58.99)
the variance is not reduced
and the results from each scenario are not connected via the CRNs or CRNs are not
working.
Therefore need to use standard CI approach to compare the differences between
S1 and S2
---------------------------------------------------------------------------------------------------------------
A higher percentage of customers were served within 1 minute in S1 than S2.
S1>S2
Question 7 continued over page....\
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Question 7 continued…\
Figure 7.5 displays the Significance Conclusions from the full pairwise comparison of the six
scenarios, where the results now being analysed are for KPI2: percentage of customers
waiting less than 2 minutes in a queue to choose food (hot or cold).
SCENARIOS 2 3 4 5 6
1 S1< S2 S1< S3 S1< S4 S1< S5 S1< S6
2 S2< S3 No difference S2< S5 S2< S6
3 S3> S4 S3> S5 No difference
4 S4< S5 S4< S6
5 S5< S6
Figure 7.5: Significance Conclusions from a full pairwise comparison of the 6 scenarios S1 to S6. The
KPI being compared is percentage of customers waiting less than 2 minutes in a queue to choose
food (hot or cold).
b) Using the results in Figure 7.5, clearly state the order of the scenarios from smallest
average KPI to largest.
Based solely on the comparison results shown in Figures 7.4 and 7.5 and the
definition given of the scenarios S1 to S6, what would your recommendation be to
the client? Fully explain and justify your answer.
What other results / data / information might you wish to view in order to make a
better informed recommendation to the client? Explain your reasoning.
[Write your answers in the box provided below and continue over the page as
needed] (12 marks)
S1 < S4 = S2 < S5 < S6 = S3
The KPIs are % of customers being served, so we are interested in maximising the
KPIs.
S3 and S6 are both significantly greater (more) than the other 4 scenarios for both
KPIs
but they are not significantly different from each other
Therefore either S3 or S6 are the best performing scenarios for both KPIs
But since S3 has six pay counters and S6 has only four and otherwise they are
identical
S6 probably takes less resources and cost,
So recommend S6 [must follow from argument above]
Question 7b) answer box continued over page....\
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Question 7b) answer box continued....\
Mean Percentage of customers waiting less than 2mins for food for each scenario
to see if its at least 98%
CI around the Mean Percentage of customers waiting less than 2mins for each
scenario to see if bottom limit is at least 98%
Mean Percentage of customers waiting less than 1min to pay in each scenario to
see if its at least 98%
CI around the Mean Percentage of customers waiting less than 1min for each
scenario to see if bottom limit is at least 98%
Utilisation of resources to see how well or poorly utilised the staff are to help in
selecting the ‘best’ scenarios….
[Other logical full justified statements can gain marks]
END OF SECTION A
SECTION B over page....\
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SECTION B
Question 8
The number of vehicles arriving at a petrol station were counted within many different 10
minute periods. This count data was found to follow a Poisson distribution where the mean
number arriving within a 10 min period was 25. State the probability distribution that
describes the length of time between these arrivals (inter-arrival times) and specify its mean
value in minutes.
[Write your answer in the box provided] (2 marks)
Exponential
Mean = 10 / 25
= 0.4 mins
Question 9 over page....\
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Question 9
Describe in detail the three phase simulation approach.
[Write your answer in the box provided] (8 marks)
• Time phase: Move simulation clock to time of next B-event
• B-phase: Execute all B-events due at this time:
Arrival: End Service:
• Create new entity and put in queue
• Schedule next arrival
• Dispose of entity
• Make resource free
• C-phase: Test conditions of all C-events and execute any which are satisfied:
Start Service:
• IF there is an entity in the queue
AND the resource is free THEN
Take entity off queue
Make resource busy
Schedule End Service event
Return to time phase (iterate around) till reach end of run.
Question 10 over page....\
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Question 10
A petrol station is to be remodelled in order to satisfy increasing demand in the area. The
company has employed you to construct a simulation model of the proposed station in
order to decide on the best configuration of different components in order to satisfy
demand. They want 98% of vehicles to wait less than 1.5 minutes for a free fuel pump.
The company is prepared to install between 8 to 12 petrol pumps. These petrol pumps can
either be all standard pumps or all new pumps with pay at pump facilities. They could also
decide to not offer LPG (liquid petroleum gas) at the station at all, or provide up to two
special pumps to dispense this fuel. Within the shop on the forecourt the company is
prepared to create from one to four separate cashier desks as necessary.
Create a 2 factorial design that would allow you to develop an understanding of the
solution space for this system problem. Clearly define and explain your design.
[Write your answer in the box provided and continue over the page as needed]
(8 marks)
Scenario Factor 1 Factor 2 Factor 3 Factor 4 Response CI
1 - - - - R1 (L,U)
2 + - - - R2 (L,U)
3 - + - - R3 (L,U)
4 + + - - R4 (L,U)
5 - - + - R5 (L,U)
6 + - + - R6 (L,U)
7 - + + - R7 (L,U)
8 + + + - R8 (L,U)
9 - - - + R9 (L,U)
10 + - - + R10 (L,U)
11 - + - + R11 (L,U)
12 + + - + R12 (L,U)
13 - - + + R13 (L,U)
14 + - + + R14 (L,U)
15 - + + + R15 (L,U)
16 + + + + R16 (L,U)
[marks for correct pattern and clear format]
R = % of vehicles waiting less than 1.5 minutes for a free pump.
Factors:
1. Number of pumps (- 8, + 12)
2. Whether to have pay at pump machines or not (- no, + yes)
3. Number of LPG machines (- 0, + 2)
4. Number of cashiers (- 1, + 4)
Question 10 answer box continued over page....\
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Question 10 answer box continued…\
(NOTE: - and + can be allocated to qualitative factors any way round. CI column is not necessary
for full marks)
Question 11 over page....\
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Question 11
Within the conceptual modelling phase of a DES simulation project we consider what level
of detail is required for each component included in the model. State three details of a
queue that could be included if required.
[Write your answer in the box provided] (3 marks)
Single or multiple server queue
Capacity
Queue discipline
Dwell time
Routing
Reneging/baulking
(marks for valid full statements up to max of three)
Question 12 over page....\
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Question 12
Describe what replications are in DES. Explain why replications are used in DES.
[Write your answer in the box provided] (4 marks)
Replications are multiple runs of the model
each using a different random number stream.
To collect enough output to make robust and accurate estimates of the KPIs
Because one run may lead to an atypical result due to the random number used.
Because it is easier to create statistically valid CIs around the mean output using
replications.
Because it may not be possible to run one long run if it’s a terminating system.
Because it may not be possible to create CIs around mean output from one long
run in the software used.
THE END
1
Student Number______________________________
Desk Number______________________________
UNIVERSITY OF WARWICK
Summer 2019
Simulation
Closed Book Examination
For those students taking the 12CAT option you must answer all questions in SECTION
A only. Time Allowed: 90 minutes
For those students taking the 15CAT option you must answer all questions in SECTION
A and SECTION B. Time Allowed: 120 minutes
Answers should be entered on the examination paper in the spaces provided. If you run
out of space continue on the back of the page but make sure that you number the answers
clearly. Where graph paper is used, make sure that you write your student number on the paper
and attach it securely to the examination paper.
Silent pocket calculators that are not capable of text storage or retrieval are permitted, but full
working should be shown. PDAs, mobile phones or any other hand-held devices that facilitate
wireless communication are NOT permitted.
Add your student number and desk number to the top of this examination paper and make sure
that you hand the paper to an invigilator (together with any answer book if required) at the end
of the examination.
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SECTION A
Question 1
Complete the following statements (- each may require one or more words to complete):
a) In DES the system is represented by a series of …………….. .
b) VIS stands for ……………………. .
c) Discrete Event Simulations are good for modelling systems that are …………..………….. .
[Write your answers in the box provided below] (3 marks)
a) Events
b) Visual Interactive Simulation
c) complex, change over time (dynamic), have variability (randomness) in them, are
queuing systems.
Question 2 over the page….\
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Question 2 (18 marks in total)
Please read the following ‘story’ and then answer Questions 2a), b), c), d) and e) which are
based on this text:
SimULink Consultancy is a consultancy firm that specialise in conducting DES projects using
the Simul8 software. They have recently been hired by Portland Police Department (PPD)
Crime Laboratory.
Faced with tighter funding and increased demand, many forensic laboratories are examining
their processes to do more with their resources. DNA Units in particular have experienced a
sharp rise in demand in recent years as a result of the growing use of DNA testing as an
investigative tool. Between 2001 and 2011, the DNA Unit of the PPD Crime Laboratory saw
a 225% increase in its caseload. Despite expanding the laboratory to improve capacity, and
running the lab 24 hours a days, 7 days a week, using a staff shift system, the volume of
cases submitted for DNA testing continues to lead to longer turnaround times. Turnaround
times are the time taken from when a lab request is received until the results are reported.
The DNA Unit has target turnaround times of seven days for rush cases and 45 days for all
other case types.
With a growing backlog of work, identifying potential improvements is a challenge with
limited flexibility to assess operational changes that could help to further increase capacity.
The PPD Crime Laboratory is challenged by the fact that it only has a subjective view of its
processes, as well as limited data to assess solutions to improve efficiency. They do not
know, for instance, whether the existing laboratory equipment is being utilized at full
capacity, or whether there are areas that are ‘resource starved’, i.e. equipment waiting for
an analyst to become available to complete the task. So it is completely unclear to them
whether it is a lack of equipment or staff or both that is causing the backlog and long
turnaround times.
To overcome this challenge, Discrete Event Simulation has been chosen as a solution to
provide a more objective, evidence-based approach. The PPD Crime Laboratory turned to
SimULink Consultancy to thoroughly evaluate two potential investment options for
improving efficiency: purchasing additional equipment and hiring more staff. The PPD
Crime Laboratory wants to use the simulation to identify whether additional equipment
and/or staff could help alleviate the case backlog and achieve turnaround times.
The SimULink consultants have been hired to develop a simulation model that captures the
entire flow of the DNA laboratory processes that could then be turned over to the PPD
Crime Laboratory Improvement Project Manager within one month of the project start date.
It is important that the PPD Crime Laboratory Improvement Project Manager, who has no
previous simulation or computing experience, can use the simulation model easily to make
changes to the existing laboratory processes and hence evaluate the impact of adding
additional equipment and staffing on overall efficiency and turnaround times.
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The lab currently has 10 pieces of equipment. The PPD Crime Lab are confident that they
could accommodate twice this number in the existing building, if this was found to be
necessary to achieve their targets. They are also prepared to increase the current staff
numbers of 7 analysts, 1 lab technician and 2 supervisors to as many as necessary to reach
their targets.
The DES model is to be created in conjunction with the personnel working in the DNA unit to
help ensure that all steps in the laboratory processes are captured within the simulation. To
further validate the simulation, one year of real casework data will be provided to be
entered and ran through the simulation to compare the results and verify its accuracy. It is
important to the PPD that the final model should mimic the running of the lab for three
years, so that it will help them understand the long-term impact and the return on
investment of any additional resources as well as showing how long it will take to eliminate
the existing backlog.
It is therefore a priority to SimULink to produce a computer simulation that can complete a
model run in less than 4 minutes, to allow for efficient running of a large number of possible
scenarios by the PPD Crime Laboratory Improvement Project Manager. The PPD are also
intending to use the model to create buy-in from stakeholders, such as staff and funding
sources, for the proposed changes. They are also interested in re-using the model in the
longer term as a management and planning tool.
a) State the proposed clock time of the PPD Crime Laboratory Simulation.
[Write your answer in the box provided below] (1 mark)
Real time being modelled = 3 years
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Question 2 continued…\
b) State the proposed model duration of the PPD Crime Laboratory Simulation.
[Write your answer in the box provided below] (1 mark)
How long the model takes to run = less than 4 minutes
c) Write down in detail the modelling objectives of the PPD Crime Lab project as
described (including the proposed experimental factors).
[Write your answer in the box provided below and carry on over the page as
needed] (5 marks)
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Question 2c) answer box continued…\
Achievement:
To understand the long-term impact
and the return on investment of any additional resources
as well as showing how long it would take to eliminate the existing backlog
current utilization of resources,
(or otherwise explain the PPD overall aim)
Performance: so that target turnaround times are achieved of seven days for rush cases
and 45 days for all other case types.
Changes: by increasing staffing from current levels of 7 analysts, 1 lab technician and 2
supervisors to as many as necessary to reach their targets
and by increasing equipment numbers from 10 pieces of equipment to 20 (Constraint).
(marks are given for the correct information in logical format)
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Question 2 continued…\
d) Write down in detail what model outputs should be monitored from the PPD Crime
Lab simulation model.
[Write your answer in the box provided below] (5 marks)
To determine achievement of objective
• Turn around times of rush cases
• Turn around times of other types of cases
• % utilisation of resources.
• Time to elimination of back-log
To identify reasons for failure to meet objective
• Bar chart of turn around times for each case
• Min, max, mean, variance of turn around times
• Time series of mean turn around time
• Number of cases waiting at each equipment – bottle necks
• Utilisation of staff
• Utilisation of equipment.
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Question 2 continued…\
e) Write in detail, with explanations and justifications, the General Project Objectives of
the described PPD Crime Lab simulation project.
[Write your answer in the box provided below] (6 marks)
• Time Scale for project – produce validated, working computer simulation within
one month.
• Nature of model use:
– Flexibility: Model shouldn’t need to be changed beyond varying the 2
stated experimental factors: equipment and staff numbers.
– Run speed: Number of possible scenarios quite large, so need model to run
reasonably fast, at least 4 minutes/run
– Visual display: 2D or 3D model adequate (should be justified). Clients will
see and use model to create buy-in from stakeholders, so should be
recognisable as lab.
– Ease of use: Clients need to interact directly with model so consider
creating user interface, as Project manager is not simulation or computer
savvy.
– Foreseen reuse of model or components as a planning/management tool
Question 3 over page....\
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Question 3
Explain clearly the differences between making simplifications and assumptions in DES
conceptual modelling and hence explain clearly when and why each would be made.
Clearly describe one example of each (one simplification and one assumption) that was (or
could have been) made in modelling the system in your group assignment. Justify why each
is an assumption or a simplification. State the system you modelled in your group work as
part of your answer.
[Write your answers in the box provided below and continue over the page as necessary]
(6 marks)
Simplifications are modelling decisions made in order to reduce complexity.
Whereas,
Assumptions are modelling decisions made because of uncertainties or beliefs about the
real system.
Looking for a clear appropriate example of one simplification and one assumption clearly
related to the group assignment project with clear and correct justifications of which they
are and why.
Marks can not be given if examples are incorrectly labelled as simplifications when they
are justifed as assumption and visa versa.
Question 3) answer box continued over page....\
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Question 3) answer box continued…\
Question 4 over page....\
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Question 4
Explain what the method MSER-5 is used for in DES and why you would use it.
Hence, clearly explain and justify in detail why you would or would not have used MSER-5 or
an equivalent method with your group assignment model. State the system you modelled
in your group work as part of your answer.
[Write your answer in the box provided below] (4 marks)
MSER-5 is a warm-up method
for finding the trunction point/end of transient phase/ warm-up period length)
to illiminate the effect of the initial transient on the resulting output
for steady-state output.
Looking for clear correct argument as to whether the group work system model output
would have an initial transient and be steady state and therefore whether a warm-up
period is appropriate, or otherwise clear full arguments as to why MSER-5 is not
appropriate.
Question 5 over page....\
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Question 5 (14 marks in total)
A DES model was constructed to investigate the functioning of a canteen. It currently has
one cold food counter which is self-service, followed by a checkout counter for cold food
only, manned by one dedicated assistant. It also has one hot food counter with one server,
followed by a checkout counter for hot food only, manned by one dedicated assistant. Both
cold and hot foods can be eat-in or take-away. Once the customer has paid they continue
into the seating area where they can either sit and eat or exit the canteen with their ‘take-
away’ food.
The canteen has been receiving rising numbers of customer complaints regarding the time
spent queuing to get food and pay for food. The manager wants to achieve 98% of
customers wating less than 2 minutes in a queue to choose food (hot or cold) and 98% of
customers waiting less than 1 minute in a queue to pay for the food (hot or cold) once
chosen.
The manager is willing to increase the number of servers at the hot food counter to a
maximum of three. He is also willing to put in one more (identical) cold food self service
counter.
The manager is also willing to increase the number of cold food checkouts (each with
dedicated assistant) up to a total of three. Likewise, he is willing to increase the number of
hot food checkouts (each with dedicated assistant) up to a total of three.
Alternatively he is willing to consider doing away with the dedicated hot and cold checkouts
and have one to five general checkouts instead that can serve anyone, with just one queue
for the multiple checkouts.
A floor plan of the current system is shown in Figure 5.1
Figure 5.1: Canteen current floor plan – not drawn to scale.
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Question 5 continued…\
Answer the following questions:
a) Draw two separate Activity Flow Diagrams, one for the current canteen system and
one for the altered canteen under the proposed change of creating four general
checkouts but keeping the cold and hot food counters unchanged. Clearly state and
justify any assumptions or simplifications you make (if any) and title the diagrams to
clearly indicate which system is being depicted.
[Write your answers in the box provided below] (10 marks)
Question 5a answer box continued over page....\
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Question 5a answer box continued…\
No marks were given if a logic flow diagram was drawn instead.
Valid differences are allowed if justifiable and explained clearly.
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Question 5 continued…\
b) List all the bound events in a DES of the current canteen system.
[Write your answers in the box provided below] (5 marks)
Customer arrives
End choosing cold food
End choosing hot food
End paying for cold food
End paying for hot food
End eating
Question 6 over page....\
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Question 6 (11 marks total)
Carry out a manual simulation of a part of the current canteen system as described in
Question 5 using the following information.
a) Assume that an exponential distribution is suitable for modelling the inter-arrival
times of groups of customers at this canteen in the first hour after opening. Assume
that the mean inter-arrival time was estimated to be 4.2 minutes. Use the inverse-
transform formula method to sample three inter-arrival times (in minutes) from this
distribution, using the following three random numbers in the order given: 0.562,
0.781, 0.245. Show your workings and round your answers to the nearest whole
minute. Hence complete Table 6.1 over the page, to simulate the arrival times of the
first three groups entering the canteen. Assume the simulation clock starts at time
8am (i.e. 08:00 where the format is Hour:Minutes).
[NB. The CDF for the Exponential distribution is () = 1 − ିఒ௫, where will
represent the sampled inter-arrival time and ଵ
ఒ
is the mean inter-arrival time.]
[Write your working in the box provided below and your answers in Table 6.1]
(6 marks)
() = 1 − ିఒ௫
= 1 − ିఒ௫
1 − = ିఒ௫
ln (1 − ) = −
[1 mark for working can be given if does not reach answer]
୪୬ (ଵି௨)
ିఒ
= [either this or] = ି୪୬ (௨)
ఒ
Either ୪୬ (ଵି௨)
ିఒ
=
ଵ = − ln(1 − 0.562) × 4.2 = 3.467 = 3
ଶ = − ln(1 − 0.781) × 4.2 = 6.378 = 6
ଷ = − ln(1 − 0.245) × 4.2 = 1.180 = 1
Or = ି୪୬ (௨)
ఒ
ଵ = − ln(0.562) × 4.2 = 2.420 = 2
ଶ = − ln(0.781) × 4.2 = 1.038 = 1
ଶ = − ln(0.245) × 4.2 = 5.907 = 6
(Follow through marks allowed)
Question 6a answer box continued over page....\
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Question 6a answer box continued…\
Group of
customers
Random
number
Time between arrivals
(in whole minutes)
Arrival Time
(HH:MM)
08:00
1
0.562
3 08:03
2 08:02
2
0.781
6 08:09
1 08:03
3
0.245
1 08:10
6 08:09
Table 6.1: Arrival time simulation for the first three groups of customers
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Question 6 continued…\
b) Data has been collected regarding the number of people in each group as shown in
Table 6.2 below. Complete Table 6.2 by correctly allocating the random number
integers 0-99 to the observed group sizes. Then carry on to simulate the group sizes
of your three arriving groups using the following random numbers in the order given:
2, 25, 84. [Write your answers and any workings in the box provided below]
(5 marks)
Table 6.2: Frequency table for number of customers within an arriving group.
Group
size Frequency
Percentage
frequency
Cumulative %
frequency Random Numbers
1 5 5% 5 0-4
2 20 20% 25 5-24
3 25 25% 50 25-49
4 35 35% 85 50-84
5 10 10% 95 85-94
6 5 5% 100 95-99
2 -> group size of one
25 -> group size of three
84 -> group size of four
(Follow through marks allowed)
Question 7 over page....\
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Question 7 (18 marks total)
A DES model was constructed to investigate the functioning of the canteen as described in
Question 5. After preliminary experimentation and consultation with the canteen manager
there were six potentially useful scenarios that it was decided to explore in more detail. It
was decided to formally compare the results of these six scenarios by constructing
confidence intervals around the difference between the means of the results, using an
overall significance level of 10%.
The results for two key performance indicators (KPI) were compared:
KPI1: Percentage of customers waiting less than 1 minute in a queue to be served at check-
out to pay.
KPI2: Percentage of customers waiting less than 2 minutes in a queue to choose food (hot or
cold).
The six chosen scenarios were:
S1. 2 cold food counters, 1 hot food server, 2 dedicated cold food checkouts, 2
dedicated hot food checkouts.
S2. 2 cold food counters, 2 hot food servers, 2 dedicated cold food checkouts, 2
dedicated hot food checkouts.
S3. 2 cold food counters, 2 hot food servers, 3 dedicated cold food checkouts, 3
dedicated hot food checkouts.
S4. 2 cold food counters, 1 hot food servers, 3 general checkouts.
S5. 2 cold food counters, 2 hot food servers, 3 general checkouts.
S6. 2 cold food counters, 2 hot food servers, 4 general checkouts.
Figures 7.1 to 7.4 show a selection of the output from the MSExcel file used to compare the
output results for KPI1: Percentage of customers waiting less than 1 minute in a queue to be
served at check-out to pay.
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Question 7 continued…\
Figure 7.1: Variance Reduction Check for KPI1 – output from MSExcel.
Figure 7.2: Paired-t Confidence Interval comparisons for KPI1 – output from MSExcel.
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Question 7 continued…\
Figure 7.3: Standard t Confidence Interval comparisons for KPI1 – output from MSExcel.
Figure 7.4: Confidence Interval comparisons for KPI1 – output from MSExcel.
a) Using the results shown in Figures 7.1 to 7.4, write down the appropriate Confidence
Interval for the mean difference between scenarios 1 and 2 (where the order of
calculation was: S1 – S2). Fully explain in detail why your chosen CI is appropriate.
Fully interpret this confidence interval in context and hence complete the
significance conclusions shown in Figure 7.4.
[Write your answers in the box provided over the page] (6 marks)
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Question 7a) answer box continued....\
(7.98, 15.74)
Since Variance of differences (59.72) > Sum of variances (58.99)
the variance is not reduced
and the results from each scenario are not connected via the CRNs or CRNs are not
working.
Therefore need to use standard CI approach to compare the differences between
S1 and S2
---------------------------------------------------------------------------------------------------------------
A higher percentage of customers were served within 1 minute in S1 than S2.
S1>S2
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Question 7 continued…\
Figure 7.5 displays the Significance Conclusions from the full pairwise comparison of the six
scenarios, where the results now being analysed are for KPI2: percentage of customers
waiting less than 2 minutes in a queue to choose food (hot or cold).
SCENARIOS 2 3 4 5 6
1 S1< S2 S1< S3 S1< S4 S1< S5 S1< S6
2 S2< S3 No difference S2< S5 S2< S6
3 S3> S4 S3> S5 No difference
4 S4< S5 S4< S6
5 S5< S6
Figure 7.5: Significance Conclusions from a full pairwise comparison of the 6 scenarios S1 to S6. The
KPI being compared is percentage of customers waiting less than 2 minutes in a queue to choose
food (hot or cold).
b) Using the results in Figure 7.5, clearly state the order of the scenarios from smallest
average KPI to largest.
Based solely on the comparison results shown in Figures 7.4 and 7.5 and the
definition given of the scenarios S1 to S6, what would your recommendation be to
the client? Fully explain and justify your answer.
What other results / data / information might you wish to view in order to make a
better informed recommendation to the client? Explain your reasoning.
[Write your answers in the box provided below and continue over the page as
needed] (12 marks)
S1 < S4 = S2 < S5 < S6 = S3
The KPIs are % of customers being served, so we are interested in maximising the
KPIs.
S3 and S6 are both significantly greater (more) than the other 4 scenarios for both
KPIs
but they are not significantly different from each other
Therefore either S3 or S6 are the best performing scenarios for both KPIs
But since S3 has six pay counters and S6 has only four and otherwise they are
identical
S6 probably takes less resources and cost,
So recommend S6 [must follow from argument above]
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Question 7b) answer box continued....\
Mean Percentage of customers waiting less than 2mins for food for each scenario
to see if its at least 98%
CI around the Mean Percentage of customers waiting less than 2mins for each
scenario to see if bottom limit is at least 98%
Mean Percentage of customers waiting less than 1min to pay in each scenario to
see if its at least 98%
CI around the Mean Percentage of customers waiting less than 1min for each
scenario to see if bottom limit is at least 98%
Utilisation of resources to see how well or poorly utilised the staff are to help in
selecting the ‘best’ scenarios….
[Other logical full justified statements can gain marks]
END OF SECTION A
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SECTION B
Question 8
The number of vehicles arriving at a petrol station were counted within many different 10
minute periods. This count data was found to follow a Poisson distribution where the mean
number arriving within a 10 min period was 25. State the probability distribution that
describes the length of time between these arrivals (inter-arrival times) and specify its mean
value in minutes.
[Write your answer in the box provided] (2 marks)
Exponential
Mean = 10 / 25
= 0.4 mins
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Question 9
Describe in detail the three phase simulation approach.
[Write your answer in the box provided] (8 marks)
• Time phase: Move simulation clock to time of next B-event
• B-phase: Execute all B-events due at this time:
Arrival: End Service:
• Create new entity and put in queue
• Schedule next arrival
• Dispose of entity
• Make resource free
• C-phase: Test conditions of all C-events and execute any which are satisfied:
Start Service:
• IF there is an entity in the queue
AND the resource is free THEN
Take entity off queue
Make resource busy
Schedule End Service event
Return to time phase (iterate around) till reach end of run.
Question 10 over page....\
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Question 10
A petrol station is to be remodelled in order to satisfy increasing demand in the area. The
company has employed you to construct a simulation model of the proposed station in
order to decide on the best configuration of different components in order to satisfy
demand. They want 98% of vehicles to wait less than 1.5 minutes for a free fuel pump.
The company is prepared to install between 8 to 12 petrol pumps. These petrol pumps can
either be all standard pumps or all new pumps with pay at pump facilities. They could also
decide to not offer LPG (liquid petroleum gas) at the station at all, or provide up to two
special pumps to dispense this fuel. Within the shop on the forecourt the company is
prepared to create from one to four separate cashier desks as necessary.
Create a 2 factorial design that would allow you to develop an understanding of the
solution space for this system problem. Clearly define and explain your design.
[Write your answer in the box provided and continue over the page as needed]
(8 marks)
Scenario Factor 1 Factor 2 Factor 3 Factor 4 Response CI
1 - - - - R1 (L,U)
2 + - - - R2 (L,U)
3 - + - - R3 (L,U)
4 + + - - R4 (L,U)
5 - - + - R5 (L,U)
6 + - + - R6 (L,U)
7 - + + - R7 (L,U)
8 + + + - R8 (L,U)
9 - - - + R9 (L,U)
10 + - - + R10 (L,U)
11 - + - + R11 (L,U)
12 + + - + R12 (L,U)
13 - - + + R13 (L,U)
14 + - + + R14 (L,U)
15 - + + + R15 (L,U)
16 + + + + R16 (L,U)
[marks for correct pattern and clear format]
R = % of vehicles waiting less than 1.5 minutes for a free pump.
Factors:
1. Number of pumps (- 8, + 12)
2. Whether to have pay at pump machines or not (- no, + yes)
3. Number of LPG machines (- 0, + 2)
4. Number of cashiers (- 1, + 4)
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Question 10 answer box continued…\
(NOTE: - and + can be allocated to qualitative factors any way round. CI column is not necessary
for full marks)
Question 11 over page....\
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Question 11
Within the conceptual modelling phase of a DES simulation project we consider what level
of detail is required for each component included in the model. State three details of a
queue that could be included if required.
[Write your answer in the box provided] (3 marks)
Single or multiple server queue
Capacity
Queue discipline
Dwell time
Routing
Reneging/baulking
(marks for valid full statements up to max of three)
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Question 12
Describe what replications are in DES. Explain why replications are used in DES.
[Write your answer in the box provided] (4 marks)
Replications are multiple runs of the model
each using a different random number stream.
To collect enough output to make robust and accurate estimates of the KPIs
Because one run may lead to an atypical result due to the random number used.
Because it is easier to create statistically valid CIs around the mean output using
replications.
Because it may not be possible to run one long run if it’s a terminating system.
Because it may not be possible to create CIs around mean output from one long
run in the software used.
THE END
