- A brief non-technical report in plain English containing your recommendations. This should be written for the Library manager, who you can assume has no background in maths or statistics. The total word count of this section (excluding the covering letter) should not exceed 500 words.
- A technical appendix (for me) containing a description of how you validated your model, explaining how confident you are in your predictions, and stating any assumptions you have made. The total word count of this section should not exceed 500 words.
You must also upload the Simul8 file (showing your BEST solution). Please name the Simul8 file with your student number, e.g. “12345678.s8”. Please ensure you have RESET the simulation to time zero before you try to upload it. If you do not do this, the model will contain all your results and the file will be massive: you may even have problems uploading it to Blackboard as you are likely to exceed the maximum allowable filesize. I can easily run the model again to obtain the results when I am marking.
Burgess Road Public Library
The system for borrowing books from Burgess Road Public Library is as follows. There are two desks, an In desk and an Out desk, each of which is large enough for several librarians to work at the same time. Borrowers with books to return must first queue at the In desk until a librarian is free to attend to them. The librarian checks that the books are not overdue, crosses out the date stamp in the book, takes payment for any fines which are due, and puts the returned books on a trolley. This is essentially a single process called Return. Some people leave the library at this point if they do not wish to take out any new books or renew old ones. It is not possible to renew books at the In desk.
People wishing to Choose new books then go to the shelves. Borrowers who arrive at the library with no books to return go straight to the shelves and start choosing. Books on the trolley are not available to borrowers.
When people have made their selection, they join the queue at the Out desk to have their books stamped by a librarian. People who wish to renew old books without choosing any new ones go straight to this queue. At the Out desk, a librarian will Stamp the books, after which the borrowers leave the library.
Burgess Road Public Library currently employs three librarians, any of whom can work at either the In desk or the Out desk. If a librarian is not currently occupied at a desk, and if there is no queue at the other desk, he or she will start to Tidy the library by taking returned books off the trolley and putting them back on their correct shelves. The trolley for returned books has a capacity of 60 books. If this is exceeded, the extra books are piled up on the floor. This is regarded as a highly undesirable situation.
Recent housing development in the area has greatly increased usage of the library, and the librarians are working under great pressure. The local council need to know how many librarians they should employ. A study has been carried out at the library over a period of one month and the following data collected and fitted to probability distributions. All the times are in minutes.
|Arrival rate of borrowers with books to return||Exponential, one every 2 minutes|
|Number of books each person returns||1 book : 15%
2 books: 25%,
3 books : 60%
|% of borrowers who return books and then..||Leave straight away : 20%
Renew old books: 30%
Choose new books: 50%
|Time taken to Return books (any number)||Triangular; min = 2, mean = 4, max = 6|
|Arrival rate of customers without books to return||Exponential, one every 5 minutes|
|Time taken to Choose books||Uniform, min = 5, max = 15|
|Time taken by librarian to Stamp books||Fixed, 2 minutes|
|Time taken to Tidy one book||Uniform, min = 2, max = 4|
If people queuing for the Stamp activity find there are more than 8 people ahead of them in the queue, they will dump the books on the floor (for the librarians to tidy) and leave. Assume each person leaves 2 books and the Drop books activity takes a fixed time of 1 minute. It is obviously undesirable if people do this.
Construct a Simul8 model for this system to find the optimal number of librarians in order to keep the library tidy and the customers satisfied. You should run the model for a single day (09.00 to 20.00). It is acceptable for there to be up to 10 people inside the library at closing time, since you can assume that they will be served after the library has closed – you do not need to model this. It is not acceptable for there to be any books on the floor, although books left on the trolley are allowed.
Marks will be allocated (roughly) as follows:
|Simul8 model correct||30|
|Presentation of results in the report||15|
|Professional covering letter||5|
|Report – clarity of explanation, no jargon||10|
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