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Zhang and Bard  studied a multi-period assignment problem that arises as part of a weekly planning problem at mail processing and distribution centres. The Assignment Problem Suppose we have n resources to which we want to assign to n tasks on a one-to-one basis. We define the cost matrix to be the n × n matrix An assignment is a set of n entry positions in the cost matrix, no two of which lie in the same row or column.Suppose also that we know the cost of assigning a given resource to a given task. The sum of the n entries of an assignment is its cost.
Step 3: Draw lines through appropriate rows and columns so that all the zero entries of the cost matrix are covered and the minimum number of such lines is used. (2011) Adaptation and Fine-Tuning of the Weighted Sum Method on Personnel Assignment Problem with Hierarchical Ordering and Team Constraints.Step 4: Test for Optimality: i) If the minimum number of covering lines is n, an optimal assignment of zeros is possible and we are finished. and De Causmaecker, P., Eds., Practice and Theory of Automated Timetabling IV, Vol. (2007) Workforce Optimization: Identification and Assignment of Professional Workers Using Constraint Programming. 26th International Symposium on Computer and Information Sciences, London, 26-28 September 2011, 571-576.ii) If the minimum number of covering lines is less than n, an optimal assignment of zeros is not yet possible. Step 5: Determine the smallest entry not covered by any line. Penalty method (Proposed Heuristic Method) The algorithm for n × n cost matrix using the proposed heuristic method is as shown below. 2740, Lecture Notes in Computer Science, Springer Berlin, Heidelberg, 113-119. IBM Journal of Research and Development, Business Optimization Archive, 51, 263-279. Turkish Armed Forces assign thousands of personnel to vacant positions every year, and want to utilize the personnel to a maximum extent by assigning the right person to the right job, while taking into consideration the hierarchy constraint, Cimen  .Toroslu and Arslanoglu  , presented variations of the standard assignment problem with matching constraints by introducing structures in the partitions of the bipartite graph, and by defining constraints on these structures.  presented a novel solution designed to bridge the gap between the need for high-quality matches and the need for timeliness.By applying constraint programming, a subfield of artificial intelligence, the authors dealt successfully with the complex constraints encountered in the field and reach near-optimal assignments that take into account all resources and positions in the pool.Katta and Jay  presented the problem of allocating a set of indivisible objects to agents in a fair and efficient manner. Mathematical Model Let be the cost of assigning the ith resource to the jth task.Hungarian Method The following algorithm applies the above theorem to a given n × n cost matrix to find an optimal assignment.Step 1: Subtract the smallest entry in each row from all the entries of its row.However, the computational time and convergence rate of the proposed method showed much less time than that of the Hungarian method. As a member, you'll also get unlimited access to over 79,000 lessons in math, English, science, history, and more.