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

This paper considers a two-machine flowshop scheduling problem with fuzzy processing times and flexible operations to minimise makespan. The jobs have three operations, one of which is a flexible operation that can be processed on one of the machines. The flexible operation should be assigned to one of the machines. Moreover, the processing times on the machines are not fixed but fuzzy processing times which are assumed to have triangular possibility distributions. Firstly, a possibilistic mathematical model is proposed with fuzzy processing times and then it is converted to an auxiliary crisp model using the weighted average defuzzification method. For the large cases where the exact algorithm may not be efficient, a heuristic algorithm is proposed. [Received: 24 May 2022; Accepted: 18 October 2022]