Police Car Maintenance Garage

Police Car Maintenance Garage

Hobbiton city council owns and operates a garage in which maintenance and repair work is performed on the city’s police car fleet. The garage has one repair bay and one mechanic; therefore service can be performed on only one car at a time.  There are two types of service required:

  • Scheduled (police cars booked in for routine maintenance and repairs)
  • Unscheduled (urgent repairs that must be given priority over scheduled vehicles)

Having visited the garage and spoken with various staff, you have gathered the following information:

  • Police cars are in use 24 hours a day, 7 days a week.
  • A workday for the garage (and mechanic) is 8 hours per day, 7 days a week.
  • Any cars scheduled to come in on a given day are left at the garage at the start of that day.
  • Scheduled maintenance jobs are interrupted for unscheduled police car arrivals.
  • Unscheduled police cars, however, cannot interrupt another unscheduled police car’s service.
  • Interrupted jobs will be serviced after all unscheduled jobs leave, for the remainder of their service time.
  • Unscheduled police cars arriving while the garage is closed wait until the garage is next open.

The garage has made available four datasets:

  • The number of scheduled cars that arrived for service each day (ArrivalScheduled.csv)
  • The time required to service scheduled vehicles (ServiceScheduled.csv)
  • The date and time that each unscheduled service police care arrived (ArrivalUnscheduled.csv)
  • The time required to service unscheduled vehicles (ServiceUnscheduled.csv)

Hobbiton city council has asked for your assistance to simulate the garage and its functionality using Simul8 to:

Question 1: Obtain a 95% confidence interval for the utilisation of the mechanic.

Question 2: Complete the following table:

 MinimumAverageMaximum
Number of scheduled cars waiting for service   
Waiting time of scheduled cars for service (hours)   
Number of unscheduled cars waiting for service   
Time schedule cars spent with the mechanic (hours)   
Time scheduled cars spent in garage, including interrupted time (hours)   

Question 3: Use the model to investigate some “What if?” type queries e.g. what influence do unscheduled police cars have on the overall service time of the scheduled cars? What if the arrival rates change? etc.

Your report should be word-processed, no more than four A4-pages in length, and consist of: a summary of your analysis and findings from the data sets provided; a brief description of the key features of your Simul8 model and how they capture the desired functionality; any assumptions made in your model; model run-time/warm-up considerations; model validation; results (questions 1 – 3) and summary of any recommendations.

Marking scheme

  • Data analysis: correct analysis of the datasets, parameter estimation, and clear and succinct summary and presentation of findings.                                                 [20]
  • Simul8 model: correct use of parameters, work centres, vehicle flows/rules etc; general presentation of model (use of graphics etc); assumptions, run-time/warm-up considerations, and model validation.                                                  [40]
  • Results: correct results for questions 1 and 2; the range of scenarios examined (question 3); clarity of presentation of results and recommendations.                  [40]           

    [Total 100 marks]

Simul8 tutorials and assistance

In Leaning Central there are several resources for help with Simul8, plus many others are available directly on the Simul8 website. 

Teaching assistants, Shauna Ford (fords6@cardiff.ac.uk) and Abigail Peters (petersa5@cardiff.ac.uk) will provide help with any queries you may have on Simul8 and for any assistance with this coursework. 

Virtual drop-in help sessions (15 minutes each) are available should you need them. 

Please book a time at:

https://outlook.office365.com/owa/calendar/CardiffUniversityMScMaths@cf.onmicrosoft.com/bookings/

Should there be no availability, please contact Shauna and Abigail directly.

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