IB2110 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. IB2110 2 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…. IB2110 3 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. IB2110 4 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…. IB2110 5 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…. IB2110 6 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…. IB2110 7 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…. IB2110 8 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…. IB2110 9 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…. IB2110 10 Question 3) answer box continued… Question 4 over page…. IB2110 11 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…. IB2110 12 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…. IB2110 13 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…. IB2110 14 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…. IB2110 15 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…. IB2110 16 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 , where will represent the sampled inter-arrival time and is the mean inter-arrival time.] [Write your working in the box provided below and your answers in Table 6.1] (6 marks) () = 1 = 1 1 = ln (1 ) = [1 mark for working can be given if does not reach answer] ( ) = [either this or] = ( ) Either ( ) = = ln(1 0.562) × 4.2 = 3.467 = 3 = ln(1 0.781) × 4.2 = 6.378 = 6 = ln(1 0.245) × 4.2 = 1.180 = 1 Or = ( ) = ln(0.562) × 4.2 = 2.420 = 2 = ln(0.781) × 4.2 = 1.038 = 1 = ln(0.245) × 4.2 = 5.907 = 6 (Follow through marks allowed) Question 6a answer box continued over page…. IB2110 17 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…. IB2110 18 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…. IB2110 19 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…. IB2110 20 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…. IB2110 21 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…. IB2110 22 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…. IB2110 23 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.... IB2110 24 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.... IB2110 25 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.... IB2110 26 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.... IB2110 27 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.... IB2110 28 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.... IB2110 29 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.... IB2110 30 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