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.

We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical formulations, some of which require the implementation of tailored branch-and-price methods. In our work, we solve the problem instead by means of new arc-flow formulations, by first representing it on a capacitated network and then invoking a mixed integer linear model with a pseudo-polynomial number of variables and constraints. According to our computational tests, existing formulations from the literature can solve to proven optimality benchmark instances with up to 100 jobs, whereas our most performing arc-flow formulation solves all instances with up to 400 jobs and provides very low gap for larger instances with up to 1000 jobs.

This paper addresses the parallel machine scheduling problem with family dependent setup times and total weighted completion time minimization. In this problem, when two jobs j and k are scheduled consecutively on the same machine, a setup time is performed between the finishing time of j and the starting time of k if and only if j and k belong to different families. The problem is strongly N P-hard and is commonly addressed in the literature by heuristic approaches and by branch-and-bound algorithms. Achieving proven optimal solution is a challenging task even for small size instances. Our contribution is to introduce five novel mixed integer linear programs based on concepts derived from onecommodity, arc-flow and set covering formulations. Numerical experiments on more than 10000 benchmark instances show that one of the arc-flow models and the set covering model are quite efficient, as they provide on average better solutions than state-of-the-art approaches with shorter computation times, and solve to proven optimality a large number of open instances from the literature.

This paper addresses the well-known dynamic berth allocation problem (DBAP), which finds numerous applications at container terminals aiming to allocate and schedule incoming container vessels into berthing positions along the quay. Due to its impact on ports' performance, having efficient DBAP formulations is of great importance, especially for determining optimal schedules in quick time as well as aiding managers and developers in the assessment of solution strategies and approximate approaches. In this work, we propose two novel formulations, a time-indexed formulation and an arc-flow one, to efficiently tackle the DBAP. Additionally, to improve computational performance, we propose problem-based modeling enhancements and a variable-fixing procedure that allows to discard some variables by considering their reduced costs. By means of these contributions, we improve the models' performance for those instances where the optimal solutions were already known, and we solve to optimality for the first time other instances from the literature.