Decomposition Method for Solving a Three-Index Planar Assignment Problem

Abstract

The classical assignment problem is considered. A third index is introduced, which can characterize, for example, the location of the work carried out. An iterative decomposition algorithm is proposed. At each step, a problem is solved with three constraints from different groups of conditions and with one connecting variable. The triples of problems are also solved with one restriction, and according to certain rules, the coefficients of the objective functions change. The iterative process that is monotonic in the objective function either arrives at the exact optimum solution of the original problem or indicates the nonuniqueness of the solution. In the latter case, a simple procedure finds the optima.