Minimization of total task tardiness using a ranking-based method with sorting rules

Abstract

This paper proposes a model of general tardiness in task execution based on a graph G, in which each vertex corresponds to a task, and each edge (i, j) is characterized by a weight Tj = max(0, Cj − dj), where Cj denotes the completion time and dj denotes the execution time of task j. A distinctive feature of this problem is that the weights of the graph’s edges emanating from an arbitrary vertex Ji are not constant values but depend on the order in which the vertices leading to vertex Ji are traversed, since this determines the value of Cj, which is defined as the sum of the durations of the operations preceding the execution of operation Ji. This problem can be reduced to finding the shortest Hamiltonian path in the graph. A method is proposed to solve this problem based on randomly determining the initial order of the vertices in the graph.