Pure Whole Programming

Pure Whole Programming

1. Methods

   • Comprehensive enumeration algorithm
   • Eliminate parts of the relaxed solution space that are not feasible integers
     • Branch and bound
       • Divide the problem
         • Subdivide subproblems
           • Find the optimal solution
       • Use of branching variables
     • Cutting planes
       • Use the graphic method
       • Implement the idea algebraically
       • Add cuts to the solution space
         • Produce an optimal whole product

2. Software

   • GAMS
   • LINDO
   • Excel Solver
   • PHPSimplex

3. Objetive

   • Optimize the search for an optimal solution
   • Optimization of linear models
     • Factible
     • No factible
     • Objective Function
     • Restrictions
     • Non-negative decision variables

4. Methodology

   • 1. Relax the solution space
     • PLE -> PL
     • Ignore the restriction you already have integers
   • 2. Solve by identifying the "optimal point"
   • 3. Add constraints that force integer variables
     • Iterative step

5. Generalities

   • Subset of linear programming
   • All its variables are only integers.
   • Reduce the search for the optimal solution
     • Finite solution
     • Non-negative variables

6. Applications

   • Transportation problems
     • Minimum cost plan for transportation
       • Multiple destinations
       • Multiple origins
   • Backpack problem
     • Select a subset of objects
       • Maximize the utility
       • Without exceeding the capacity of loading objects
   • Assignment problems
     • Allocate scarce resources NOT FRACTIONABLE
   • Logging
     • Production activity
     • Manpower planning
     • Inventory management
       • Only whole solutions