An algorithm for insertion of idle time in the single-machine scheduling problem with convex cost functions

An improved earliness–tardiness timing algorithm

“…= 1, the event (13,4,4,2) is inserted, (14, 3, 3, 3, 1) is removed. = 0, (13,4,4,2) is removed, (12, 3, 3, 1) is inserted. At the end of the iteration = −2, thus (13, 4, 3, 2) is inserted.…”

“…In our presentation, we are going to use the elegant reduction of the isotonic regression problem to our problem, which was proposed by Pan and Shi [8]. Finally, we mention another, also recent, algorithm by Colin and Quinino [13], which is useful when cost functions are not piecewise linear. The complexity of their algorithm depends on the time horizon.…”

Production scheduling with history‐dependent setup times

“…If the sequences of the jobs are predetermined, then other timing issues may be considered. When the sequences are fixed and the cost of each job is a convex function of its completion time, the idle time insertion problem to minimize the total cost can be considered; a pseudopolynomial time algorithm for finding a solution within some tolerance of the optimality space has been proposed [8]. A single machine scheduling problem with a fixed sequence of n jobs to minimize the makespan subject to time-lag restrictions, that is,…”

A Mixed Integer Linear Programming Solution for Insertion of Idle Time in the Jobs Scheduling

“…Unrelated parallel machine scheduling is widely applied in manufacturing environments [1]. In addition, idle time insertion arises in JIT environments where costs associated with early completion time of jobs are relevant [2]. As a result, it has drawn attention of numerous researchers.…”