Novel optimization method for unbalanced assignment problems with multiple jobs: The Dhouib-Matrix-AP2

Abstract

This paper introduces a new stochastic constructive heuristic entitled Dhouib-Matrix-AP2 (DM-AP2) in order to optimize a variant of the Unbalanced Assignment Problem with constraint on agents. This problem aims to limit the maximal number of tasks affected to agents. It is more suitable for real-live situations where the number of resources (agents) are limited and less than the number of demands (tasks). This problem is solved by modifying the formulation of the assignment matrix cost through adding the minimal processing cost for each column and then by applying DM-AP2 with its two lists (Fictional-Agents and Real-Agents) and the Sum metric function. In fact, DM-AP2 is executed without any parameter, just three simple steps and a stochastic selection in an iterative structure until no improvement of the solution. To clarify the proposed DM-AP2 method, a stepwise application is presented in details. Obviously, the experimental results show the efficiency of the novel technique DM-AP2 by comparing its results with several other methods such as Genetic Algorithm, Ant Colony Optimization, Modified Hungarian Method and Classical Hungarian Algorithm with Simple Textbook Formulation. Moreover, DM-AP2 is coded with Python programming language and using Matplotlib and Numpy standard libraries.