AN ADJACENT PAIRWISE APPROACH TO THE MEAN FLOW-TIME SCHEDULING PROBLEM.

In this paper, sufficient conditions to decide the precedence relation between neighboring two jobs are presented by means of an adjacent pairwise interchage method for minimizing mean flow·time in flow-shop scheduling. On the bases of the sufficient conditions, a computational algorithm is proposed for an optimal or near optimal solution. The mean flow-time by this algorithm puts 90% of the optimal value as an average of over one hundred problems. The algorithm can be executed even by manual calculations within the time proportional to nxm2 , where n and m are the number of jobs and machines respectively. Ever so muc h research [I 'V 9] has been devoted to f low-shop scheduling, yet relatively few results exist for performance measures other than maximal flow-time. For instance, Nabeshima [5] presented an algorithm based on the sufficient conditions to minimize maximal flow-time in flow-shop scheduling where no passing is allowed. The same approach, however, has not been applied to the mean flow-time problem, which is as significant a performance measure as the maximal flow-time. In this paper, the sufficient conditions are given to decide the preced­ ence relation between neighboring two jobs to minimize the mean flow-time in flow-shop scheduling problem. An algorithm based on the sufficient conditions is also presented for an optimal or near optimal solution. The computational experience shows that the approximation ratio between obtained solutions and the optimal ones indicates 90 % as an average of over one hundred problems. Moreover, it shows that the algorithm can be executed even by manual calculations within the time proportional to (the number of jobs) x (the number of machines) 2 .