A general variable neighborhood search for single-machine total tardiness scheduling problem with step-deteriorating jobs

TL;DR

This paper introduces a general variable neighborhood search algorithm for a complex single-machine scheduling problem with step-deteriorating jobs, demonstrating superior solutions compared to existing methods through extensive experiments.

Contribution

It proposes a novel GVNS algorithm with a perturbation procedure for the NP-hard total tardiness scheduling problem with step deterioration.

Findings

GVNS outperforms CPLEX and standard VNS in solution quality

Proposed heuristics find near-optimal solutions efficiently

Extensive tests validate the effectiveness of the new algorithm

Abstract

In this article, we study a single-machine scheduling problem of minimizing the total tardiness for a set of independent jobs. The processing time of a job is modeled as a step function of its starting time and a specific deteriorating date. A mixed integer programming model was applied to the problem and validated. Since the problem is known to be NP-hard, we proposed a heuristic named simple weighted search procedure (SWSP) and a general variable neighborhood search algorithm (GVNS). A perturbation procedure with 3-opt is embedded within the GVNS process in order to explore broader spaces. Extensive numerical experiments are carried out on some randomly generated test instances so as to investigate the performance of the proposed algorithms. By comparing to the results of the CPLEX optimization solver, the heuristic SWSP and the standard variable neighborhood search, it is shown that the proposed GVNS algorithm can provide better solutions within a reasonable running time.