(SEM VII) THEORY EXAMINATION 2024-25 OPERATIONS RESEARCH

SECTION A — Very Short Answers (2 Marks Each)

a. Principle of Simplex Method                           Moves from one basic feasible solution to another

Improves objective function at each iteration until optimality

b. Duality in Linear Programming                        Every LPP (primal) has a corresponding dual problem

Optimal values of primal and dual are equal

c. Objective of Transportation Problem                Minimize total transportation cost

Satisfy supply and demand constraints

d. Applications of Job Sequencing                       Manufacturing scheduling

Machine utilization                                               Minimizing idle time

e. CPM vs PERT

f. Critical Path (CPM)

Longest duration path

Determines minimum project completion time

g. Mixed Strategy (Game Theory)                       Player uses probabilities to choose strategies

Applied when no saddle point exists

h. Single vs Multi-Server Queue                         Single server → one service channel

Multi-server → multiple service channels

i. EOQ (Economic Order Quantity)                      Optimal order size minimizing ordering + holding cost

j. Individual vs Group Replacement                     Individual: replace items separately

Group: replace all items together at fixed interval

SECTION B — Short Notes / Numerical Concepts (10 Marks)

a. Phases of Operations Research                       Problem formulation

Model construction                                             Solution of model

Validation                                                            Implementation

b. Transportation Problem                                  Initial solution: North-West Corner Method

Optimality test: MODI Method                         Goal: minimum transportation cost

c. Max-Flow Problem                                         Finds maximum possible flow from source (s) to sink (t)

Uses capacity constraints on edges

d. Minimax Theorem                                          Player minimizes maximum possible loss

Used in zero-sum games

e. EOQ Formula                                                  EOQ=2DSHEOQ = \sqrt{\frac{2DS}{H}}EOQ=H2DS​​

Where:
 

D = demand, S = ordering cost, H = holding cost

SECTION C — Linear Programming (10 Marks)

Graphical Method

Steps:                                                                   Formulate LPP

Plot constraints                                                    Identify feasible region

Find corner points                                               Evaluate objective function

Simplex Method Steps                                        Convert to standard form

Identify entering & leaving variables                  Perform iterations until optimality

SECTION D — Assignment & Sequencing (10 Marks)

Hungarian Method (Assignment)                       Row reduction

Column reduction                                               Zero assignment

Optimal allocation                                               Importance of Job Sequencing

Reduces total elapsed time                                 Improves machine efficiency

Minimizes idle time