# what is the best way to structure this problem

 0 Am an undergraduate O.R student from Nigeria. we just bought 15 O.R textbooks for our library.the number of students the have a right to borrow the textbooks are 150.so i am trying to see how we can maximize the use of the textbooks at least among the number of students that will be interested in borrowing a textbook.In other words i am trying to decide how many hours (lead time) to allow if a book is borrowed so as to maximize the use of the textbooks among interested students.The total number of hours available for each textbook to be borrowed is 48 hours per week. I tried to applying LP but find it difficult to formulate the objective function and constraint parameters. I also think maybe it would be possible to use poisson distribution to calculate likelihood of a certain number of interested students that will appear to borrow a book AND use exponential distribution to calculate the probability of the minimum inter-arrival time, which will finally be used as the lead time.Please help me i am confused. asked 23 Aug '13, 07:16 ismahii 21●1 accept rate: 0%

 1 I'm going to assume that this is 15 copies of the same book (add opposed to one each of 15 different books). Common practice in university libraries is to loan a book for a somewhat extended period, but with the ability to recall it after some minimum time has elapsed if supreme else reserves it. Questions you should address at the outset include: What is a reasonable minimum length for a book loan? (A student will not derive much value from a short loan.) What is a reasonable amount of time to allow for the return of a book that has been called back due to competing demand for it? How frequently, on average, will a student attempt to check out (or reserve) a book? How would you measure your satisfaction with a system? I presume you would want to balance the number of requests satisfied within some reasonable time span, some cost measure for waiting time, and some value measure for the borrower (a homebrewing function of the duration of the loan). If you can answer those questions, you can treat the problem as a finite population (students) multiple server (books) queuing problem with preemption (book recall). Personally, I would write a simulation model and use trial-and-error to determine a good loan length. answered 23 Aug '13, 15:28 Paul Rubin ♦♦ 14.6k●5●13 accept rate: 19% Practically the 15 book are of different subjects.what do i do in this case. (24 Aug '13, 08:28) ismahii I think the single queue, multiserver model becomes 15 separate single queue, single server models. My third bullet, the arrival rate of demand, now becomes 15 separate arrival rates. You also now have to decide whether to allow a single student to check out more than one book at a time. One additional complication: if any of the books are "prerequisites" for other books (for instance, a book on linear programming might be a prerequisite for a book on integer programming), then the demands are not independent. :-( (24 Aug '13, 10:38) Paul Rubin ♦♦
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