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

An optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost be equal to the number of rows equal to number of columns.

While solving an assignment problem, an activity is assigned to a resource through a square with zero opportunity cost because the objective is to minimize total cost of assignment. The objective of assignment problem is to assign a number of jobs to an equal number of machines so as to minimize the total assignment cost or to minimize the total consumed time for execution of all the jobs. In the multi-objective assignment problem, the objectives alone are considered as fuzzy.

The method used for solving an assignment problem is called Hungarian method. The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal-dual methods.

The purpose of a dummy row or column in an assignment problem is to obtain balance between total activities & total resources. Dummy rows (or columns) are added in the matrix so as to complete it to form a square matrix. The dummy rows or columns will contain all costs elements as zeroes. The Hungarian method may be used to solve the problem.

If there were n workers & n jobs there would be n! solutions.

An assignment problem can be solved by Simplex method and Transportation method. The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which is a polytope) in sequence so that at each new vertex the objective function improves or is unchanged. The Transportation Method of linear programming is applied to the problems related to the study of the efficient transportation routes i.e. how efficiently the product from different sources of production is transported to the different destinations, such as the total transportation cost is minimum.

For a salesman who has to visit n cities (n-1)! is the way of his tour plan.

The assignment problem requires that only one activity be assigned to each resource, is a special case of transportation problem and can be used to maximize resources.

An assignment problem is a special case of transportation problem, where Number of rows equals number of columns, all rim conditions are 1and values of each decision variable is either 0 or 1.

Every basic feasible solution of a general assignment problem, having a square pay-off matrix of order, n should have assignments equal to 2n-1.