Operations Research and Reliability (ISS Statistics Paper IV): Questions 1  3 of 3
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Question number: 1
» Operations Research and Reliability » Queuing Models » M/M/1 Model
Appeared in Year: 2015
Describe in Detail
(d) Show that for M/M/1/∞ queue model
where λ_{n} and µ_{n} are the means of Poisson and exponential distributions respectively where there are n people in the system.
Explanation
Suppose the system is in state j at time t. There are j people in the system. In the next time interval of a very small duration Δt, the system can move to state j1or j + 1with the following probabilities:
… (646 more words) …
Question number: 2
» Operations Research and Reliability » Finding Solutions in 22, 2xm and Mxn Games
Appeared in Year: 2015
Describe in Detail
Prove that the number of basic variables is a balanced transportation problem is at most , where m is the number of origins and n is the number of destinations.
Explanation
First note that there are in all m + n constraints. We shall show that one of these is redundant so that there are in effect equation in mn variables and hence at most basic variable are there. We note… (263 more words) …
Question number: 3
» Operations Research and Reliability » LPP Computational Methods
Appeared in Year: 2015
Describe in Detail
Solve the following problem Simplex method.
Maximize Z = 8x_{1}+6x_{2}
Subject to
x_{1}+x_{2 } ≤ 10
2x_{1}+3x_{2} ≤ 25
x_{1}+5x_{2} ≤ 35
x_{1}, x_{2} ≥ 0
Explanation
The Simplex algorithm is an iterative procedure for solving LP problems in a finite number of steps. It consists of

Having a trial basic feasible solution to constraintequations

Testing whether it is an optimal solution

Improving the first trial solution by a set of rules and repeating the process till… (573 more words) …