Modeling and Solution for Assignment Problem

In this paper, the mixed-integer linear programming (MILP) of minimax assignment is formed, and a solution called Operations on Matrix is presented and compared with the solutions of exhaustion and MILP. Theoretical analyses and numerical tests show that the operations on matrix are efficient well-implied enumeration for both minimax and global-minimum assignment problems. Keywords—Assignment problem, method of exhaustion, mixed-integer linear programming (MILP), operations on matrix. I. INTRODUCTION HE global-minimum assignment problem is described, see, e.g. (1), by language as: There are n people and n tasks. Each person completes and only completes a task. The payment in each person for a task is given. The problem is, which person completes which task such that the total payment is minimum? Let ij x be the 2 n 0-1 decision variables, where 1 ij x = represents person i for task j , and 0 ij x = , otherwise. The