(SEM VII) THEORY EXAMINATION 2018-19 OPERATIONS RESEARCH

SECTION – A

(Attempt all questions in brief – 2 × 10 = 20 marks)

(a) Role of Operations Research in Decision Making

Operations Research plays an important role in decision making by providing scientific and quantitative techniques to solve complex problems. It helps managers choose the best possible solution among many alternatives by using mathematical models, optimization techniques, and logical reasoning. OR improves efficiency, reduces cost, and supports objective decision making.

(b) Dual of a Dual is its Primal

In linear programming, every problem has a corresponding dual problem. When the dual of a dual problem is formed, it results in the original primal problem. This property shows the close relationship between primal and dual problems and ensures consistency in optimization results.

(c) Degeneracy in a Transportation Problem

Degeneracy in a transportation problem occurs when the number of allocated cells is less than (m + n − 

1), where m is the number of rows and n is the number of columns. Degeneracy may cause difficulty in reaching the optimal solution, so small artificial allocations are added to resolve it.

(d) Assignment Problem

An assignment problem is a special type of transportation problem where each resource is assigned to exactly one job. The objective is to minimize cost or maximize profit. It is commonly solved using the Hungarian method.

(e) Feasible Solution

A feasible solution is a solution that satisfies all constraints of a linear programming problem. It may or may not be optimal, but it lies within the feasible region.

(f) Optimal Solution

An optimal solution is a feasible solution that gives the best value of the objective function, either maximum profit or minimum cost.

(g) Slack Variable

A slack variable is added to a “less than or equal to” constraint to convert it into an equation. It represents unused resources.

(h) Surplus Variable

A surplus variable is subtracted from a “greater than or equal to” constraint to convert it into an equation. It represents excess resources.

(i) Linear Programming Problem

A linear programming problem involves maximizing or minimizing a linear objective function subject to linear constraints and non-negativity conditions.

(j) Critical Path

The critical path is the longest path in a project network. Activities on this path have zero float, and any delay in them delays the entire project.

SECTION – B

(Attempt any ONE – 10 marks)

(a) Transportation Problem and Its Solution

The transportation problem is a type of linear programming problem that aims to minimize the cost of transporting goods from multiple sources to multiple destinations. The solution involves finding an initial basic feasible solution using methods like North-West Corner Rule, Least Cost Method, or Vogel’s Approximation Method, followed by optimization using the MODI method. Transportation models help reduce distribution costs efficiently.

(b) Assignment Problem and Its Applications

The assignment problem ensures optimal allocation of resources to tasks such that total cost is minimized or profit is maximized. It is solved using the Hungarian method. Applications include job assignments, machine scheduling, crew assignment, and task allocation in organizations.

SECTION – C

(Attempt any ONE – 10 marks)

(a) PERT / CPM Network Analysis (Numerical Concept)

In this question, different activities are given with optimistic, most likely, and pessimistic time estimates. First, expected time for each activity is calculated using the PERT formula. A network diagram is then drawn showing activity sequences. The critical path is identified by finding the longest path in the network. The total duration of the critical path gives the minimum time required to complete the project.

This technique helps managers plan, schedule, and control projects effectively.

(b) Importance of Critical Path Method

The Critical Path Method helps identify activities that directly affect project completion time. It assists in proper planning, monitoring progress, and allocating resources efficiently. CPM is widely used in construction, production planning, and project management.