Abstract
This paper addresses job-shop scheduling problems with deteriorating jobs, i.e. jobs whose processing times are an increasing function of their starting time. A simple linear deterioration is assumed and our objective is makespan minimization. We provide a complete analysis of the complexity of flow-shops, open-shops and job-shop problems. We introduce a polynomial-time algorithm for the two-machine flow-shop, and prove NP-hardness when an arbitrary number of machines (three and above) is assumed. Similarly, we introduce a polynomial-time algorithm for the two-machine open-shop, and prove NP-hardness when an arbitrary number of machines (three and above) is assumed. Finally, we prove NP-hardness of the job-shop problem even for two machines.
| Original language | English |
|---|---|
| Pages (from-to) | 195-209 |
| Number of pages | 15 |
| Journal | Discrete Applied Mathematics |
| Volume | 117 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - 15 Mar 2002 |
Bibliographical note
Funding Information:I want to thank Dina Sher for preparing the graphs. This paper was supported in part by the Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.
Keywords
- Deteriorating jobs
- Deterministic scheduling
- Flow-shop
- Job-shop
- Open-shop