SettingsAn Intelligent Assignment Problem Using Novel Heuristic: The Dhouib-Matrix-AP1 (DM-AP1)
Souhail Dhouib
Abstract
The assignment problem is one of the most popular optimization problems where the main objective is to find the total minimal cost for assigning n objects to n other objects. This paper presents an original heuristic, named Dhouib-Matrix-AP1, to generate an initial basic feasible solution for the classical assignment problem in very easy and fast steps. The proposed method Dhouib-Matrix-AP1 finds the optimal or a near optimal solution for the assignment problem after just n iterations with only three easy steps in each one. The first step consists in computing the total cost by rows and columns using an original formula (Sum -(Min * n /2)). The second step looks for selecting the greatest value (Z) from these total costs. Finally, the third step is based on choosing the minimal row or column matrix element which corresponds to the value Z. For this purpose, we generate a detailed step by step process application based on 4x4 dimensional sample. Moreover, a stepwise application of the Dhouib-Matrix-AP1 method is presented with details for three examples. Besides, the results of a set of fifteen literature examples with different dimensions are discussed. The outcomes of the study show that the proposed method provides the optimal or near optimal solutions in easier and faster manner.