Scheduling step-deteriorating jobs to minimize the total weighted tardiness on a single machine

TL;DR

This paper investigates the complex problem of scheduling step-deteriorating jobs on a single machine to minimize total weighted tardiness, proving its NP-hardness and proposing exact and heuristic solutions with computational validation.

Contribution

It is the first to prove the problem's strong NP-hardness and develops a mixed integer programming model along with seven heuristic procedures for large instances.

Findings

The problem is strongly NP-hard.

Heuristic procedures achieve near-optimal solutions.

Computational results demonstrate the effectiveness of the proposed methods.

Abstract

This paper addresses the scheduling problem of minimizing the total weighted tardiness on a single machine with step-deteriorating jobs. With the assumption of deterioration, the job processing times are modeled by step functions of job starting times and pre-specified job deteriorating dates. The introduction of step-deteriorating jobs makes a single machine total weighted tardiness problem more intractable. The computational complexity of this problem under consideration was not determined. In this study, it is firstly proved to be strongly NP-hard. Then a mixed integer programming model is derived for solving the problem instances optimally. In order to tackle large-sized problems, seven dispatching heuristic procedures are developed for near-optimal solutions. Meanwhile, the solutions delivered by the proposed heuristic are further improved by a pair-wise swap movement. Computational results are presented to reveal the performance of all proposed approaches.