Minimizing the makespan in the permutation flowshop problem with minimal and maximal time lags

In this paper, we investigate the m-machine permutation flowshop scheduling problem where minimal and maximal time lags are required between consecutive operations of each job. Such problem has not been studied extensively in the scheduling literature. The objective is to minimize the makespan. We propose a mathematical formulation for this problem; it is solved by running commercial software CPLEX using many instances randomly generated. Then, we propose a Genetic Algorithm and we perform a computational analysis. The results of numerical experiments show that our proposed Genetic algorithm performs very well.