an optimum algorithm for single machine with early/tardy cost

the problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. production systems like jit are one of the many applications of the problem. this problem is studied in special cases and their optimal solutions are introduced with simple orders. in general, some effective conditions for neighboring jobs have been developed and the dominant set for the optimal solution is determined. branch and bound (bb) method is also used for this problem. the strong upper and lower limits are introduced in bb, resulting in optimal solutions to a lot of problems in short time periods. to show the effectiveness of the suggested solution methods, as many as 720 problems in different sizes, with 5 to 100 jobs, have been randomly generated and solved.