JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS Previous Question Paper (February/March - 2022 - R18)

Operations Research (OR) employs various mathematical and analytical techniques to support decision-making. Key techniques include:

• Linear Programming (LP): Used for optimizing a linear objective function subject to linear constraints. Applied in resource allocation and production planning.
• Queuing Theory: Analyzes waiting lines to optimize service levels and minimize costs. Applied in telecommunications, banking, and traffic management.
• Inventory Control Models: Determines optimal order quantities and reorder points. Applied in supply chain management and retail.
• Game Theory: Models competitive situations where outcomes depend on the actions of multiple participants. Applied in strategic marketing and corporate negotiations.
• Simulation: Uses computer models to replicate real-world processes. Applied in complex systems like logistics and manufacturing plant design.
• Network Analysis (PERT/CPM): Manages project schedules and identifies critical paths. Applied in construction and large-scale project management.

The Simplex Algorithm is an iterative algebraic procedure used to solve Linear Programming problems. The methodology follows these steps:

1. Standard Form Conversion: Convert the objective function and constraints into standard form by adding slack variables for 'less-than-or-equal' constraints and surplus/artificial variables for others.
2. Initial Basic Feasible Solution: Set up the initial simplex tableau, typically starting with the origin (all decision variables equal to zero).
3. Optimality Test: Examine the objective function row. If all coefficients are non-negative (for maximization), the current solution is optimal.
4. Pivot Column Selection: If not optimal, select the column with the most negative coefficient (entering variable).
5. Pivot Row Selection: Calculate the ratio of the right-hand side to the pivot column elements. The row with the smallest positive ratio identifies the leaving variable.
6. Tableau Update: Perform Gauss-Jordan row operations to create a new tableau with the entering variable replacing the leaving variable. Repeat steps 3-6 until optimality is reached.