Optimal Results and Numerical Simulations for Flow Shop Scheduling Problems

Abstract

This paper considers the m-machine flow shop problem with two objectives: makespan with release dates and total quadratic completion time, respectively. For F$m\left|r_j\right|{\text{C}}_{max}$, we prove the asymptotic optimality for any dense scheduling when the problem scale is large enough. For F$m{\Vert \Sigma \text{C}}_j^2$, improvement strategy with local search is presented to promote the performance of the classical SPT heuristic. At the end of the paper, simulations show the effectiveness of the improvement strategy.