Operations Research or Qualitative Approach MCQ Questions and Solutions with Explanations | Management

To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are n-1. The Modified Distribution Method or MODI is an efficient method of checking the optimality of the initial feasible solution.

The Hungarian method for solving an assignment problem can also be used to solve a travelling salesman problem. The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.

If the number of assigned cells is equal to the number of rows/columns, then it is an optimal solution.

The objective functions and constraints are linear relationship between variables. This means that no variables can be multiplied with each other. This formulation is called the Standard form.

Assignment problem helps to find a maximum weight identical in nature in a weighted Bipartite graph. The assignment problem is a well-known graph optimization problem defined on weighted-bipartite graphs. The objective of the standard assignment problem is to maximize the summation of the weights of the matched edges of the bipartite graph. In the standard assignment problem, any node in one partition can be matched with any node in the other partition without any restriction. In this paper, variations of the standard assignment problem are defined with matching constraints by introducing structures in the partitions of the bipartite graph, and by defining constraints on these structures.

All the parameters in the linear programming model are assumed to be Constraints. For a problem to be a linear programming problem, the decision variables, objective function and constraints all have to be linear functions. If the all the three conditions are satisfied, it is called a Linear Programming Problem.

The solution need not be in whole numbers.

Graphic method can be applied to solve a LPP when there are only two variable. This method is used to solve a two variable linear program. If you have only two decision variables, you should use the graphical method to find the optimal solution. A graphical method involves formulating a set of linear inequalities subject to the constraints. Then the inequalities are plotted on a X-Y plane.

If the feasible region of a LPP is empty, the solution is infeasible. A linear program is infeasible if there exists no solution that satisfies all of the constraints -- in other words, if no feasible solution can be constructed. Since any real operation that you are modelling must remain within the constraints of reality, infeasibility most often indicates an error of some kind. Simplex-based LP software like lp_solve efficiently detects when no feasible solution is possible.

The variables whose coefficient vectors are unit vectors are called basic variables. The basic variables can be defined as the m variables which can take any value other than zero. Moreover, if the variables satisfy the non-negativity condition of the LP model, the basic solution created by them is called the basic feasible solution. The remaining variables are known as the non-basic variables.