modeling and scheduling no-idle hybrid flow shop problems

Although several papers have studied no-idle scheduling problems, they all focused on flow shops, assuming one processor at each working stage. but, companies commonly extend to hybrid flow shops by duplicating machines in parallel in stages. this paper considers the problem of scheduling no-idle hybrid flow shops. a mixed integer linear programming model is first developed to mathematically formulate the problem. using commercial software, the model can solve small instances to optimality. then, two metaheuristics, based on variable neighborhood search and genetic algorithms, are developed to solve larger instances. using numerical experiments, the performance of the model and algorithms are evaluated.