Abstract
This paper deals with the problem of minimizing the weighted mean flow-time in n/m flow-shop scheduling where no passing is allowed. Analysis, through the adjacent pairwise interchange method, leads to a condition for determining the precedence relation between adjacent jobs. The condition consists of inequalities, the number of which equals the square of the number of machines. An algorithm based on these inequalities is proposed to obtain the optimal or near optimal solution. The numerical examples show that the algorighm can produce a solution which has an average approximation ratio of 91.4 percent over 160 problems. The three factors: the number of jobs, the number of machines and the range of weights do not affect the approximation ratio of the tested problems. The computational time required to obtain a solution through the proposed algorithm is proportional to (the number of jobs) x (the number of machines)^2 . As a result, the CPU time needed to solve a seven job and six machine problem through TOSBAC 5600/120 is 0.25sec.
