OPERATIONS RESEARCH

OPERATIONS RESEARCH

1. Uses:

   • A scientific discipline focused on data-driven, optimal decision-making to improve efficiency and reduce costs.

2. MATHEMATICAL MODELS

   • classified by certainty into:
     • Simplified representations of real-world systems using mathematical expressions (variables, constraints, and objective functions).
   • PROBABILISTIC MODELS
     • Models involving risk and uncertainty, where outcomes are based on probabilities.
   • DETERMINISTIC MODELS
     • Models where all parameters and data are known with absolute certainty.
     • This model is divided between these methods:
       • LINEAR PROGRAMMING (LP)
         • aims to:
           • Maximize or minimize a linear objective function subject to linear constraints, assuming proportionality and divisibility.
         • is a specialized type of:
           • TRANSPORTATION MODEL
             • Core Framework:
               • Optimization technique to determine the lowest-cost plan for shipping goods from multiple Sources (Supply) to multiple Destinations (Demand).
                 • Decision Variables: Quantity shipped from source x to destination y.
                 • Unit Costs: Shipping cost per unit.
             • Algorithmic Phases:
               • Phase A: Initial Basic Feasible Solution
                 • Northwest Corner Rule: Fast but ignores costs.
                 • Least Cost Method: Prioritizes the cheapest routes.
                 • Vogel’s Approximation Method (VAM): Analyzes penalties; yields the best initial results.
               • Phase B: Optimal Solution
                 • MODI Method (Modified Distribution): Test empty cells to guarantee the absolute minimum cost.
             • Digital Tools:
               • Computational software used to solve large-scale transportation matrices.
                 • Examples:
                   • Excel Solver, LINGO, LINDO, CPLEX.
       • LP SOLUTION METHODS
         • Graphical Method
           • : Visual approach for problems with only 2 decision variables.
         • Simplex Method
           • Iterative algebraic algorithm for complex problems with 3 or more variables.