# Queuing Theory and Transportation

 Question 1
A set of jobs A, B, C, D, E, F, G, H arrive at time t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence - first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below.

$\begin{array}{|l|l|l|l|l|l|l|l|l|}\hline \text{Job} & \text{A} & \text{B} & \text{C} & \text{D} & \text{E} & \text{F} & \text{G} & \text{H} \\ \hline \text{Turning (minutes)} & \text{2} & \text{4} &\text{8}&\text{9} &\text{7} &\text{6} &\text{5} &\text{10} \\ \hline \text{Grinding (minutes)} & \text{6} & \text{1} &\text{3} &\text{7} &\text{9}&\text{5} &\text{2} &\text{4} \\ \hline \end{array}$
If the makespan is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is
 A A-E-D-F-H-C-G-B B A-D-E-F-H-C-G-B C G-E-D-F-H-C-A-B D B-G-C-H-F-D-E-A
GATE ME 2021 SET-1   Industrial Engineering
Question 1 Explanation:
Sequencing,
$\begin{array}{|c|c|c|} \hline A & (2) & 6 \\ \hline B & 4 & (1) \\ \hline C & 8 & (3) \\ \hline D & 9 & (7) \\ \hline E & (7) & 9 \\ \hline F & 6 & (5) \\ \hline G & 5 & (2) \\ \hline H & 10 & (4) \\ \hline \end{array}$
AEDFHCGB
 Question 2
Maximize $Z=5x_{1}+3x_{2}$,
subject to
$x_{1}+2x_{2}\leq 10$ ,
$x_{1}-x_{2}\leq 8$ ,
$x_{1},x_{2}\geq 0$ ,
In the starting Simplex tableau, $x_{1}$ and $x_{2}$ are non-basic variables and the value of Z is zero. The value of Z in the next Simplex tableau is____.
 A 30 B 35 C 40 D 50
GATE ME 2017 SET-2   Industrial Engineering
Question 2 Explanation:
\begin{aligned} \operatorname{Max} . Z &=5 x_{1}+3 x_{2}+0 \times S_{1}+0 \times S_{2} \\ x_{1}+2 x_{1}+S_{1} &=10 \\ x_{1}-x_{2}+S_{2} &=8 \end{aligned}

 Question 3
A product made in two factories P and Q, is transport to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:

Factory P produces 7 units and factory Q produces 9 units of the product. Each destination required 8 units. If the north-west corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (X-Y), in Rupees, is
 A 0 B 15 C 35 D 105
GATE ME 2017 SET-2   Industrial Engineering
Question 3 Explanation:
As per GATE official answer key MTA (Marks to All)
X=105
Using penalty corner method and following modi method we get

-4 water value indicates that its optimum table, so
\begin{aligned} Y &=7 \times 7+3 \times 8+4 \\ &=49+24+4=78 \\ X-Y &=105-77=28 \end{aligned}
 Question 4
For a single with Poisson arrival and exponential service time, the arrival rate is 12 per hour. Which one of the following service rates will provide a steady state finite queue length?
 A 6 per hour B 10 per hour C 12 per hour D 24 per hour
GATE ME 2017 SET-2   Industrial Engineering
Question 4 Explanation:
$\mu>\lambda$
as $\lambda=12\text{cust/hr}$, we should go with option (D) 24/hr
 Question 5
In a single-channel queuing model, the customer arrival rate is 12 per hour and the serving rate is 24 per hour. The expected time that a customer is in queue is _______ minutes.
 A 6.5s B 2.5s C 1.8s D 2.3s
GATE ME 2016 SET-2   Industrial Engineering
Question 5 Explanation:
\begin{aligned} \lambda&=12 \mathrm{hr}^{-1} \\ u&=24 \mathrm{hr}^{-1} \\ w_{s}&=\frac{\lambda}{\mu(u-\lambda)}=\frac{12}{24 \times 12} \times 60 \\ &=2.5\text{seconds} \end{aligned}

There are 5 questions to complete.

### 1 thought on “Queuing Theory and Transportation”

1. if you can do create bookmark so that it will good for us because we can mark question for better revision.