(SEM VIII) THEORY EXAMINATION 2017-18 OPERATIONS RESEARCH

Here is your Operations Research (NME-051) explanation in brief, clear paragraph format (not too long, not short points) based on your uploaded paper 

SECTION A (Brief Explanations)

Basic Feasible Solution of LPP
A basic feasible solution in a Linear Programming Problem is a solution that satisfies all the constraints and non-negativity conditions. It is obtained by setting some variables equal to zero and solving the remaining equations. It represents a corner point of the feasible region.

Condition for Degeneracy in LPP
Degeneracy occurs when the value of one or more basic variables becomes zero in a basic feasible solution. This may lead to cycling in the simplex method and requires special handling.

Unbalanced Transportation Problem
A transportation problem is unbalanced when total supply is not equal to total demand. To balance it, a dummy source or dummy destination is added with zero transportation cost.

Saddle Point in Game Theory
A saddle point exists when the minimum value of the row equals the maximum value of the column in a payoff matrix. It represents an equilibrium where both players use pure strategies.

EOQ Calculation
Given:
Demand (D) = 200 units/month = 2400 units/year
Ordering cost (S) = 1000
Holding cost (H) = 2% of 100 = 2 per unit per year

EOQ formula:
EOQ = √(2DS / H)
= √(2 × 2400 × 1000 / 2)
= √(2400000)
≈ 1549 units

Multi-channel Queuing Model
A multi-channel queuing model has more than one server providing service to customers. It reduces waiting time and increases service efficiency.

Applications of Network Techniques
Network techniques like CPM and PERT are used in project planning, construction scheduling, production management, and research projects.

Unbalanced Assignment Problem
An assignment problem becomes unbalanced when the number of jobs and machines are unequal. A dummy row or column is added to make it square before solving.

Pure Strategy in Game Theory
A pure strategy is a strategy where a player consistently chooses a single course of action without randomization.

Parameters of EOQ
EOQ depends on demand rate, ordering cost, and holding cost. These factors determine the most economical order quantity.

SECTION B (Brief Explanation)

Simplex Method
The simplex method is an iterative procedure used to solve linear programming problems. It starts with a basic feasible solution and moves to adjacent corner points to improve the objective function value until the optimal solution is reached.

Assignment Problem
The assignment problem aims to assign jobs to machines in such a way that total cost is minimized. It is solved using the Hungarian method by reducing rows and columns and selecting optimal zero positions.

Sequencing Problem
In sequencing problems involving two machines, Johnson’s rule is used. Jobs are arranged based on the smallest processing times to minimize total completion time.

Inventory and Types of Costs
Inventory is maintained to meet customer demand and avoid production stoppage. The main costs are ordering cost, holding cost, and shortage cost. Balancing these costs helps in determining optimal inventory levels.

SECTION C (Brief Explanation)

Sensitivity Analysis in LPP
Sensitivity analysis studies how changes in coefficients of objective function or constraints affect the optimal solution. It helps managers understand the stability of the solution and make better decisions under uncertainty.

Transportation Optimization Methods
Transportation problems are optimized using methods like North-West Corner, Least Cost Method, and Vogel’s Approximation Method for initial solution, and MODI method for optimality test.

Game Theory Terms
Pure strategy means fixed action, mixed strategy involves probability distribution over actions, saddle point indicates equilibrium, payoff matrix shows gains and losses, and zero-sum game means one player's gain equals another's loss.

Simulation and Monte Carlo Method
Simulation is a technique to imitate real-world systems using models. Monte Carlo simulation uses random numbers to solve probabilistic problems and estimate outcomes.

CPM vs PERT
CPM is used when activity times are certain and focuses on cost optimization. PERT is used when activity times are uncertain and focuses on time estimation. Free float is the time an activity can be delayed without affecting the next activity, while independent float is delay without affecting preceding or succeeding activities.

Queuing Model Problem
In a single-server system, arrival rate and service rate determine waiting time and queue length. If service rate is greater than arrival rate, the system remains stable. Adding another server reduces waiting time.