Minimization of total absolute flow time deviation in single and multiple machine scheduling

In this note, single machine scheduling and minimizing absolute flow time deviation (TAFD) are considered. The relationship between this problem and the mean absolute deviation of job completion times about a common due date (MAD) is discussed. Based on the MAD problem optimal solutions of the TAFD problem are given. Furthermore, the generalization of the problem to the multiple machine case is discussed and an efficient algorithm for generating many optimal solutions of the problem, in the multi-machine case, is given.