A unified heuristic and an annotated bibliography for a large class of earliness–tardiness scheduling problems

Abstract

This work proposes a unified heuristic algorithm for a large class of earliness-tardiness (E-T) scheduling problems. We consider single/parallel machine E-T problems that may or may not consider some additional features such as idle time, setup times and release dates. In addition, we also consider those problems whose objective is to minimize either the total (average) weighted completion time or the total (average) weighted flow time, which arise as particular cases when the due dates of all jobs are either set to zero or to their associated release dates, respectively. The developed local search based metaheuristic framework is quite simple, but at the same time relies on sophisticated procedures for efficiently performing local search according to the characteristics of the problem. We present efficient move evaluation approaches for some parallel machine problems that generalize the existing ones for single machine problems. The algorithm was tested in hundreds of instances of several E-T problems and particular cases. The results obtained show that our unified heuristic is capable of producing high quality solutions when compared to the best ones available in the literature that were obtained by specific methods. Moreover, we provide an extensive annotated bibliography on the problems related to those considered in this work, where we not only indicate the approach(es) used in each publication, but we also point out the characteristics of the problem(s) considered. Beyond that, we classify the existing methods in different categories so as to have a better idea of the popularity of each type of solution procedure.

Scheduling jobs with release dates on identical parallel machines by minimizing the total weighted completion time

“…In all our tests, all exact methods have been provided with an initial valid upper bound given by the iterated local search (ILS) metaheuristic proposed by Kramer and Subramanian (2019). With the aim on quickly obtaining a valid upper bound, in our experiments we ran the ILS algorithm with a time limit of n/5 seconds or for at least one complete iteration of the inner local search phase, which is performed by a randomized variable neighborhood descent procedure.…”

Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines

“…In general words, the ILS by Kramer and Subramanian (2017) is composed by constructive, local search and perturbation phases. We modified the construction and local search phases to take into account that in the P || w j C j all machine schedules follow the WSPT rule.…”

Mixed integer formulations using natural variables for single machine scheduling around a common due date

“…These problems have been treated by several approaches: with heuristics (e.g. [5], [16]), with branch-and-bound algorithms (e.g. [23]), and with dynamic programming methods (e.g.…”