Optimal scheduling for a single machine to minimize the sum of maximum earliness and tardiness considering idle insert

This paper presents the optimal scheduling in a single machine by considering idle insert. The objective function is to minimize the sum of maximum earliness and tardiness. This scheduling problem can be applied in different production systems such as just in time (JIT) systems. Special case of common due date is presented and the associated optimal solution is reported. In general case of a single machine scheduling, a number of effective lemmas regarding idle insert (n/1/OI/ETmax) are also developed. In order to show the efficiency of the proposed algorithm, 1020 problems with different job sizes, ranging from 7 to 1000 jobs, are generated at random and then the idle insert algorithm is applied to solve these problems.