Assignment Problem special type of linear programming problem known as assignment problem will be introduced. The assignment problem deals in allocating the various resources (items) to various activities (receivers) on a one to one basis in such a way that the resultant effectiveness is optimized. These types of problems are linear programming applications that can be solved using the simplex method. Assignment problems can also be solved by transportation method. But simpler and more efficient methods were developed by Hungarian mathematician D.Konig (known as Hungarian method) for getting the solution of assignment problems.

            There are number of decision making situations where assignment technique can be successfully used. For Example. Assignment of available sales force to different regions; vehicles to routes products to factories contracts to bidders machines to jobs development engineers to several construction sites and so on. Management generally makes assignment on a one-to-one basis in such a manner that the group maximizes the revenue from the sales the vehicles are deployed to various routes in such a way that the transportation cost in minimum and so on.

ASSIGNMENT MODELS

            The assignment problem is a special case of the transportation problem. In assignment problems supply ineach row represents the availability of a resource such as a man vehicle product salesman etc and demand in each column represents different activities to be performed such as jobs routes factories areas etc for each of which only one man or vechicle or product or salesman respectively is required. Entries in the square being costs, times or distances the essential characteristics of the assignment problem is n resources are to be assigned to n activities such that each resource is allocated to each activity and each activity is performed by one resource only. The allocation is to be done in such a way so as to maximize the resultant effectiveness.

            The assignment problem may be stated as follows.

With information about the number of assignment i, ( I = 1,2,3,…….,n) performing the same number of jobs j. (j=1,2,3,….,) and the pay off measure c_ij available for each assignment the objective is to determine the strategy that maximizes the total cost or maximizes the total utility.

The assignment problem can conveniently be represented in the form of n x n matrix [c_ij]nxn known as cost or effectiveness; where x_ij represent assignment of jth person to ith job and c_ij is the cost associated of assigning ith facility (person) to the jth job.

Further, it is assumed that

            X_ij = 1, if ith person is assigned to the jth job and x_ij =0, otherwise, the mathematical formulation of the assignment problem is given as follows:

                                               N           n

Minimize (Total cost) = z =  ?            ?          c_ij x_ij

                                              I=1         j=1

Subject to the constraints

(i)                 Each person should be assigned to one and only one job, i.e.,

X_ij + x_i2 +…..+ x_in = 1 ; I = 1,2,…,n

(ii)               Each jon must be assigned to one and only person, i.e.,

X_ij + x_2j + …. + x_nj = 1; j = 1,2,…,n

(iii)             X_ij = 0 or 1 for all i.j.

This problem is a special case of the transportation problem where each ai = 1 and bj =1. Thus every assignment problem can be solved by the transportation in method but solution by assignment method will be more efficient and requires less computation time.

Remark. Every basic feasible solution of a general assignment problem having a square pay off matrix (say n x n) should have (n+n-1) assignment cells. But due to the special structure of the assignment problem, any solution of such a problem cannot have more than assignment cells. Thus the assignment problem is inherently degenerate’. If the given pay off matrix is not a square matrix, we can convert it to a square matrix by adding dummy row or column. This concept of unbalanced assignment problem will be discussed later.

Assignment Models Assignment Help - Assignment Problems Homework Help

The special case of transportation problem can be solved by assignment models. The problems under assignment models are quite interesting and difficult somehow for students. For solving assignment problems, an assignment models introduced. It makes complex transportation problems easy by some particular method. We at Expertsmind.com offer assignment models homework help, assignment models based assignment help, assignment problem's solutions and live assistance with online tutors. Get solved assignment models questions in operation research with step by step answers which may help you in solving same kind of problems in future.