Solving the trapezoidal fuzzy assignment problem using the novel Dhouib-Matrix-AP1 heuristic

Abstract

The assignment problem is a famous problem in combinatorial optimization where several objects (tasks) are assigned to different entities (workers) with the goal of minimizing the total assignment cost. In real life, this problem often arises in many practical applications with uncertain data. Hence, this data (the assignment cost) is usually presented as fuzzy numbers. In this paper, the assignment problem is considered with trapezoidal fuzzy parameters and solved using the novel Dhouib-Matrix-AP1 (DM-AP1) heuristic. In fact, this research work presents the first application of the DM-AP1 heuristic to the fuzzy assignment problem, and a step-by-step application of DM-AP1 is detailed for more clarity. DM-AP1 is composed of three simple steps and repeated only once in n iterations. Moreover, DM-AP1 is enhanced with two techniques: a ranking function to order the trapezoidal fuzzy numbers and the min descriptive statistical metric to navigate through the research space. DM-AP1 is developed under the Python programming language and generates a convivial assignment network diagram plan.