Two-machine flowshop scheduling with flexible operations and controllable processing times

Zeynep Uruk, Hakan Gultekin*, M. Selim Akturk

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


We consider a two-machine flowshop scheduling problem with identical jobs. Each of these jobs has three operations, where the first operation must be performed on the first machine, the second operation must be performed on the second machine, and the third operation (named as flexible operation) can be performed on either machine but cannot be preempted. Highly flexible CNC machines are capable of performing different operations. Furthermore, the processing times on these machines can be changed easily in albeit of higher manufacturing cost by adjusting the machining parameters like the speed and/or feed rate of the machine. The overall problem is to determine the assignment of the flexible operations to the machines and processing times for each operation to minimize the total manufacturing cost and makespan simultaneously. For such a bicriteria problem, there is no unique optimum but a set of nondominated solutions. Using ε-constraint approach, the problem could be transformed to be minimizing total manufacturing cost for a given upper limit on the makespan. The resulting single criterion problem can be reformulated as a mixed integer nonlinear problem with a set of linear constraints. We use this formulation to optimally solve small instances of the problem while a heuristic procedure is constructed to solve larger instances in a reasonable time.

Original languageEnglish
Pages (from-to)639-653
Number of pages15
JournalComputers and Operations Research
Issue number2
Publication statusPublished - Feb 2013


  • Controllable processing times
  • Flexible manufacturing system
  • Flowshop
  • Scheduling

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research


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