Dominance-Based Heuristics for One-Machine Total Cost Scheduling Problems

International audienceWe study the one-machine scheduling problem with release dates and we look at several objective functions including total (weighted) tardiness and total (weighted) completion time. We describe dominance rules for these criteria, as well as techniques for using these dominance rules to build heuristic solutions. We use them to improve certain well-known greedy heuristic algorithms from the literature. Finally, we introduce a Tabu Search method with a neighborhood based on our dominance rules. Experiments show the effectiveness of our techniques in obtaining very good solutions for all studied criteria

One Benders cut to rule all schedules in the neighbourhood

Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose tighter dual bounds, its application to resource-constrained scheduling remains less explored. Given a position-based Mixed-Integer Linear Programming (MILP) formulation for scheduling on unrelated parallel machines, we notice that certain $k-$OPT neighbourhoods could implicitly be explored by regular local search operators, thus allowing us to integrate Local Branching into Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining their local optima - hence, proving that they are suboptimal - a local branching cut (applied as a Benders cut) eliminates all their solutions at once, thus avoiding an overload of the master problem with thousands of Benders cuts. However, to guarantee convergence to optimality, the constructed neighbourhood should be exhaustively explored, hence this time-consuming procedure must be accelerated by domination rules or selectively implemented on nodes which are more likely to reduce the optimality gap. In this study, the realisation of this idea is limited on the common 'internal (job) swaps' to construct formulation-specific $4$-OPT neighbourhoods. Nonetheless, the experimentation on two challenging scheduling problems (i.e., the minimisation of total completion times and the minimisation of total tardiness on unrelated machines with sequence-dependent and resource-constrained setups) shows that the proposed methodology offers considerable reductions of optimality gaps or faster convergence to optimality. The simplicity of our approach allows its transferability to other neighbourhoods and different sequencing optimisation problems, hence providing a promising prospect to improve Branch-and-Check methods

Scheduling with processing set restrictions : a survey

2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Combining column generation and Lagrangean relaxation : an application to a single-machine common due date scheduling problem

Column generation has proved to be an effective technique for solving the linear programming relaxation of huge set covering or set partitioning problems, and column generation approaches have led to state-of-the-art so-called branch-and-price algorithms for various archetypical combinatorial optimization problems. Usually, if Lagrangean relaxation is embedded at all in a column generation approach, then the Lagrangean bound serves only as a tool to fathom nodes of the branch-and-price tree. We show that the Lagrangean bound can be exploited in more sophisticated and effective ways for two purposes: to speed up convergence of the column generation algorithm and to speed up the pricing algorithm. Our vehicle to demonstrate the effectiveness of teaming up column generation with Lagrangean relaxation is an archetypical single-machine common due date scheduling problem. Our comprehensive computational study shows that the combined algorithm is by far superior to two existing purely column generation algorithms: it solves instances with up to 125 jobs to optimality, while purely column generation algorithm can solve instances with up to only 60 jobs

Hybrid genetic algorithm for assembly flow-shop scheduling problem with sequence-dependent setup and transportation times

Ovaj rad prikazuje hibridni genetski algoritam za planiranje poslova montaže na tekućoj traci s vremenima za montiranje i transport ovisnima o redoslijedu odvijanja poslova. Objektivna funkcija upotrijebljena u ovom istraživanju sastoji se od smanjenja zbroja ukupno procijenjenih zakašnjenja na kvadrat, vremena potrebnog za izradu (makespan), ukupno procijenjenih ranije obavljenih poslova na kvadrat i broja zakašnjelih poslova. Da bi se potvrdio predloženi model, korišten je program Lingo 8.0. Usporedba rezultata dobivenih pomoću Lingo 8.0 i hibridnog genetskog algoritma pokazuje da kod većih problema (ako je n >10, gdje je n broj poslova) Lingo ne daje odgovarajuću efikasnost i ne može se usporediti s predloženim hibridnim genetskim algoritmom u odnosu na vrijeme izračuna i devijaciju od minimalne objektivne funkcije. Rezultati ispitivanja daju se za veliki broj slučajeva.This paper presents a hybrid genetic algorithm for assembly flow-shop scheduling problem with sequence-dependent setup and transportation times. The used objective function in this research consists of minimizing of the sum of total weighted squared tardiness, makespan, total weighted squared earliness and number of tardy job. Since the problem is NP-hard, we solved this problem by hybrid genetic algorithm. To validate the proposed model, the Lingo 8.0 software was used. Comparison between the results of the Lingo 8.0 and hybrid genetic algorithm shows that in larger problems (if n >10, where n is the number of jobs) the results obtained by Lingo do not have adequate efficiency and cannot be compared with the proposed hybrid genetic algorithm in terms of computational time and deviation from the minimum objective function. Test results are provided for a wide range of problem instances

Factory level preventive maintenance in Turkish air force

Cataloged from PDF version of article.In this thesis, we study the Factory Level Preventive Maintenance Problem (FLPM) experienced by Turkish Air Force (TUAF). This problem is a specific case of Nonpreemptive Resource Constrained Multiple Project Scheduling with Mode Selection (NRCMPSMS); allocation of limited resources to competing activities of multiple project of different types in which the duration of an activity is determined by the mode selection and the activity flow is dependent on the type of the project. The objective is to determine the start (finish) time and the mode of each project’s each activity so that the minimal total weighted tardiness and total incurred cost are obtained. We proposed a heuristic for this problem definition which is composed of two phases and apply it to a real life problem experienced by TUAF. In the first phase, the aim is to construct an initial schedule with minimum total weighted tardiness and in the second phase, this schedule is improved in terms of total incurred cost by the mode selection exchanges. Since the activity due date information is not available but required in prioritization of the activities, we develop five FLPM specific activity due date estimation methods. We run the proposed heuristic for three different weight figures which are determined by the Analytic Hierarchy Process and the one being used by TUAF. In addition, we study the influence of the release and the due dates of the aircrafts on the objective functions. We propose a determination method for each of the release and the due dates that aims finding the tightness levels of these two parameters. The release date determination method that we propose relates the arrival rate of the aircrafts with the utilization of the bottleneck resource whereas the due date determination method that we propose relates the due dates of the aircrafts with the fraction of the number of tardy jobs in percentages. We investigate the performance of the activity due date estimation methods in terms of the objective functions and the computational effort required by the tightness levels of the release and the due date that are found by the determination methods that we propose.Ünlü, NuriyeM.S

A strong preemptive relaxation for weighted tardiness and earliness/tardiness problems on unrelated parallel machines

Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total weighted tardiness (TWT) and total weighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lower bound. Moreover, it offers a near-optimal partition of the jobs to the machines. We then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem. We demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs