Novel properties along with solution methods for permutation owshop scheduling

This paper deals with permutation ow shop scheduling to minimize makespan. some novel, useful definitions and properties are established. then, the paper proposes novel solution methods. particular attention is paid to algorithms based on the orderings of pairs of jobs. the first algorithm is for three-machine problems; it gives an optimal solution in a certain strict sense in the case of the ordering of two jobs. moreover, the paper extends the three-machine johnson's rule to the general case of m-machine problems.