Computational and Applied Mathematics

, Volume 36, Issue 1, pp 159–184 | Cite as

An intelligent water drop algorithm to identical parallel machine scheduling with controllable processing times: a just-in-time approach

  • Vahid Kayvanfar
  • M. ZandiehEmail author
  • Ehsan Teymourian


Identical parallel machine scheduling problem with controllable processing times is investigated in this research. In such an area, our focus is mostly motivated by the adoption of just-in-time (JIT) philosophy with the objective of minimizing total weighted tardiness and earliness as well as job compressions/expansion cost simultaneously. Also the optimal set amounts of job compressions/expansion plus the job sequence are determined on each machine. It is assumed that the jobs processing times can vary within a given interval, i.e., it is permitted to compress or expand in return for compression/expansion cost. A mixed integer linear programming (MILP) model for the considered problem is firstly proposed and thereafter the optimal jobs set amounts of compression and expansion processing times in a known sequence are determined via parallel net benefit compression–net benefit expansion called PNBCNBE heuristic. An intelligent water drop (IWD) algorithm, as a new swarm-based nature-inspired optimization one, is also adopted to solve this multi-criteria problem. A heuristic method besides three meta-heuristic algorithms is then employed to solve small- and medium- to large-size sample-generated instances. Computational results reveal that the proposed IWDNN outperforms the other techniques and is a trustable one which can solve such complicated problems with satisfactory consequences.


Controllable processing times Earliness and tardiness Intelligent water drops algorithm Identical parallel machines 

Mathematics Subject Classification

Primary 90B35 Secondary 68M20 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2015

Authors and Affiliations

  1. 1.Department of Industrial EngineeringAmirkabir University of TechnologyTehranIran
  2. 2.Department of Industrial Management, Management and Accounting FacultyShahid Beheshti University, G.C.TehranIran
  3. 3.Department of Industrial EngineeringMazandaran University of Science and TechnologyBabolIran

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