Branch and Bound Method Hindi/Urdu explanation Integer linear programing problem

INTEGER LINEAR PROGRAMING INTEGER LINEAR PROGRAMING In linear programming, each decision variable as well as slack and/or surplus variable is allowed to take any real or fractional value. However, there are certain real-life problems in which the fractional value of however, be obtained by rounding off the optimum value of the variables to the nearest integer value. This be working on a project or 1.6 machines will be used in a workshop. The integer solution to a problem an integer solution. This solution however may not satisfy all the given constraints. Secondly, the value if the given problem, where an integer solution is required, is solved by integer programming techniques. . An integer LP problem has important applications. Capital budgeting, construction scheduling, plant problems that demonstrate the areas of application of integer programming. 7.2 TYPES OF INTEGER PROGRAMMING PROBLEMS Linear integer programming problems can be classified into three categories: (1) Pure (all) integer programming problems in which all decision variables are restricted to integer values. (ii) Mixed integer programming problems in which some, but not all, of the decision variables are restricted to integer values. (ii) Zero-one integer programming problems in which all decision variables are restricted to integer values of either 0 or 1. The broader classification of integer LP problems and their solution methods are summarized in : (i) Gomory's cutting plane method and (ii) Branch and Bound method, for solving integer programming problems INTEGER LINEAR PROGRAMING BRANCH AND BOUND METHOD The branch and bound method was first developed by AH Land and AG Doig, and it was further studied by JDC Little et al., and other researchers. This method can be used to solve all-integer, mixed-integer and zero-one linear programming problems. The concept behind this method is to divide the entire feasible solution space of an LP problem into smaller parts called subproblems and then evaluate corner (extreme) points of each subproblem for an optimal solution. This approach is useful for solving LP problems where there is a large number of feasible solutions and so the enumeration becomes economically impractical. The branch and bound method starts by imposing bounds on the value of objective function that help to determine the subproblem to be eliminated from consideration when the optimal solution has been found. If the solution to a subproblem does not yield an optimal integer solution, a new subproblem is selected for branching. At a point where no more subproblem can be created, an optimal solution is arrived at. If you have any question related to this topic feel free to Whatsapp me on 7298312652