Questions
Syllabus
Qns. By Syllabus

Semester

Subject

Year

Bachelors Level/Second Year/Fourth Semester/Science bit/fourth semester/operations research/syllabus wise questions

Bachelors In Information Technology

Institute of Science and Technology, TU

Operations Research (ORS255)

Year Asked: 2080, syllabus wise question

Decision Theory
1.
A milk salesman estimates the probability of the demand for a litre of milk is as follows: He purchases a litre of milk @ Rs. 60 and sells it @ Rs. 70. Assuming that the unsold milk has no scrap value, find (a) Find optimum quantity that would obtain Max. EMV. (b) Find the minimum value of EOL. (c) What is the value of expected profit with perfect information (EPPI)?

$\begin{array}{|c|c|c|c|c|c|}\hline \text{Demand} & 11 & 12 & 13 & 14 & 15 \\ \hline \text{Probability} & 0.10 & 0.15 & 0.30 & 0.25 & 0.20 \\ \hline \end{array}$
[10]
2.
Write short notes on: (a) Marginal analysis approach in decision making. Write short notes on: (b) Modified distribution (MODI) method. [2.5+2.5]
Networking Analysis
1.
A project consists of nine activities whose time estimates (in weeks) and other characteristics are given below: (a) Show the PERT network diagram for the project. (b) Identify the critical activities. (c) What is the expected project completing time and its variance?

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline \text{Activities} & A & B & C & D & E & F & G & H & I \\ \hline \text{Preceding activities} & - & - & - & A & A & B, D & B, D & C, F & E \\ \hline \text{Optimistic time} & 2 & 6 & 6 & 2 & 11 & 8 & 3 & 9 & 4 \\ \hline \text{Most likely time} & 4 & 6 & 12 & 5 & 14 & 10 & 6 & 15 & 10 \\ \hline \text{Pessimistic time} & 6 & 6 & 24 & 8 & 23 & 12 & 9 & 27 & 16 \\ \hline \end{array}$
[10]
2.
Draw the network diagram and identify critical path and bottleneck activities.

$\begin{array}{|c|c|c|c|c|c|c|c|}\hline \text{Activity} & A & B & C & D & E & F & G \\ \hline \text{Predecessors} & - & A & A & A & B, C & C, D & E, F \\ \hline \text{Time (in days)} & 7 & 4 & 5 & 6 & 7 & 5 & 6 \\ \hline \end{array}$
[5]
Optimization(Linear Programming I: Formulation and Graphic Solution), (Linear Programming II: Simplex Method), Transportation problem, Assignment problem
1.
Solve the given linear programming problem (LPP) by using simplex method and interpret the findings.

$\text{Maximize Z= } 4A+3B+6C $

$\text{Subject to Constraints:}$

$2A+3B+2C \leq 440$

$4A+3C \leq 470$

$2A+5B \leq 430$

$A,B,C \geq 0$
[10]
2.
The ABC company has three jobs to be done on three machines. Each job must be done on one and only one machine. The cost of each job on each machine is given in the following table. By using Hungarian method, find the job assignments which will minimize the machine cost.

$\begin{array}{|c|c|c|c|}\hline \text{Jobs\Machine} & X & Y & Z \\ \hline A & 4 & 6 & 8 \\ B & 2 & 3 & 4 \\ C & 4 & 8 & 5 \\ \hline \end{array}$
[5]
3.
Food X contains 6 units of vitamin A and 7 units of vitamin B and costs Rs. 5 per gram. Food Y contains 8 units of vitamin A and 12 units of vitamin B and costs Rs. 18 per gram. The daily minimum requirement of vitamins A and B are respectively 100 units and 138 units respectively. Formulate the problem as a LPP with the objective function minimizing the cost. [5]
4.
Find the initial solution by using Vogel’s Approximation Method (VAM).

$\begin{array}{|c|c|c|c|c|c|}\hline \text{From} & P & Q & R & S & \text{Supply} \\ \hline A & 19 & 30 & 50 & 10 & 7 \\ B & 70 & 30 & 40 & 60 & 9 \\ C & 40 & 8 & 70 & 20 & 18 \\ \hline \text{Demand} & 5 & 8 & 7 & 14 & 34 \\ \hline \end{array}$
[5]
Queuing Models
1.
Customers arrive at a bank having single counter at the rate of 25 customers per hour. Time required to serve a customer has exponential distribution and average number of customers served per hour is 30. Find the average number of customers in queue and in system as well. [5]
2.
Describe different types of queuing disciplines used in serving a customer in a queue. [5]
Theory of Games
1.
The following is the payoff matrix of a game being played by A and B. Determine the optimal strategies for the players and the value of the game.

$\begin{array}{|c|c|c|c|}\hline \text{A's strategies} & B_1 & B_2 & B_3 \\ \hline A_1 & 120 & -80 & -20 \\ A_2 & 60 & 70 & 30 \\ A_3 & -100 & 70 & 20 \\ \hline \end{array}$
[5]
2.
Describe dominance rule method for solving a problem of game theory. [5]