A two-stage LP-NLP methodology for the least-cost design and operation of water distribution systems

Mengning Qiu, Mashor Housh, Avi Ostfeld

Research output: Contribution to journalArticlepeer-review


This paper presents a two-stage method for simultaneous least-cost design and operation of looped water distribution systems (WDSs). After partitioning the network into a chord and spanning trees, in the first stage, a reformulated linear programming (LP) method is used to find the least cost design of a WDS for a given set of flow distribution. In the second stage, a non-linear programming (NLP) method is used to find a new flow distribution that reduces the cost of the WDS operation given the WDS design obtained in stage one. The following features of the proposed two-stage method make it more appealing compared to other methods: (1) the reformulated LP stage can consistently reduce the penalty cost when designing a WDS under multiple loading conditions; (2) robustness as the number of loading conditions increases; (3) parameter tuning is not required; (4) the method reduces the computational burden significantly when compared to meta-heuristic methods; and (5) in oppose to an evolutionary "black box" based methodology such as a genetic algorithm, insights through analytical sensitivity analysis, while the algorithm progresses, are handy. The efficacy of the proposed methodology is demonstrated using two WDSs case studies.

Original languageEnglish
Article number1364
Pages (from-to)1-21
JournalWater (Switzerland)
Issue number5
StatePublished - 1 May 2020

Bibliographical note

Funding Information:
Funding: This research was funded by the Israel Science Foundation (grant No. 555/18) and the Israeli Water Authority grant number 4501687498.

Publisher Copyright:
© 2020 by the author.


  • Linear programming
  • Non-linear programming
  • Two-stage
  • Water distribution system
  • Water distribution system design
  • Water distribution system operation

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Biochemistry
  • Aquatic Science
  • Water Science and Technology


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