Skip to main content

Minimizing Freshwater Usage in Batch Process Scheduling: S-Graph Approach


Water is one of the most important natural resources of life. While it is considerably cheap and vastly available currently, except for extreme locations, this is not guaranteed in the future. Being provident with water has multitude of advantages in both short and long term. Using less clean water not only brings immediate financial benefits, it simultaneously reduces wastewater production, related treatment costs, and the impact on the environment. Reducing the water footprint of a batch system is not a trivial task, as water sources and sinks need to be matched not only in quantity and quality, but in time as well. In this paper, the S-graph scheduling framework is extended to address simultaneous scheduling and water minimization in batch processing systems. The proposed approach tackles truly batch processes with a single contaminant, and allows only a single water source to be reused for each sink. The presented algorithm and S-graph extension have been implemented and tested on various case studies from the literature. The results of this paper provide an opportunity for further extensions to address a wider range of problems with multiple contaminants, semi-continuous behavior, cyclic operations, etc.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18


Download references


Supported by the ÚNKP-19-3 New National Excellence Program of the Ministry for Innovation and Technology.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Olivér Ősz.

Ethics declarations

Conflict of Interest

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ősz, O., Foo, D.C.Y. & Hegyháti, M. Minimizing Freshwater Usage in Batch Process Scheduling: S-Graph Approach. Process Integr Optim Sustain 5, 31–42 (2021).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Wastewater minimization
  • Water reuse
  • Scheduling
  • S-graph