Research on no-idle permutation flowshop scheduling with time-dependent learning effect and deteriorating jobs

This note considers no-idle permutation flowshop scheduling problems with time-dependent learning effect and deteriorating jobs. The objective functions are to minimize the makespan and the total (weighted) completion time, respectively. Low and Lin [1], showed that an optimal sequence for these problems can be solved in polynomial time. We demonstrate these results to be incorrect by counter-examples for the no-idle permutation flowshop scheduling problems with an increasing series of dominating machines (idm), then introduce new exact solution algorithms that polynomially solve these problems.