The no-idle flowshop scheduling problem with discounted weight

This paper discusses the no-idle permutation flowshop scheduling problem, whose objective function is the weighted total completion time with discounted factor. Optimal algorithms for four special cases are discussed. The first problem assumes an increasing series of dominant machines. The second problem assumes a decreasing series of dominant machines. The third problem assumes a decreasing then increasing series of dominant machines. The last problem assumes an increasing–decreasing series of dominant machines.