A heuristic algorithm for mean flowtime objective in flowshop scheduling

Scope and Purpose—A permutation flowshop consists of serial machines that process a given number of jobs in the same order. In this permutation flowshop, a sequence of jobs that optimizes performance measures such as makespan and mean flowtime should be determined. These scheduling problems are known as the NP-complete problem in the area of combinatorial optimization. The purpose of this paper is to develop a heuristic algorithm by modifying the characteristics in the existing algorithms known as good heuristics, and to show improvement with respect to mean flowtime. Based on a job insertion method, a heuristic algorithm is developed to reduce the mean flowtime in a permutation flowshop environment. Simulation experiments are performed to evaluate effectiveness of the proposed algorithm against the existing heuristic methods. The simulation results show that the proposed algorithm generates more accurate solutions than other heuristics, especially when ratio of the number of jobs and the number of machines is greater than or equal to two.