Scheduling step-deteriorating jobs to minimize the total weighted tardiness on a single machine
Peng Guo, Wenming Cheng, Yi Wang

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.…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Supply Chain and Inventory Management · Assembly Line Balancing Optimization
