Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

Single-machine scheduling with stepwise tardiness costs and release times

We study a scheduling problem that belongs to the yard operations component of the railroad planning problems, namely the hump sequencing problem. The scheduling problem is characterized as a single-machine problem with stepwise tardiness cost objectives. This is a new scheduling criterion which is also relevant in the context of traditional machine scheduling problems. We produce complexity results that characterize some cases of the problem as pseudo-polynomially solvable. For the difficult-to-solve cases of the problem, we develop mathematical programming formulations, and propose heuristic algorithms. We test the formulations and heuristic algorithms on randomly generated single-machine scheduling problems and real-life datasets for the hump sequencing problem. Our experiments show promising results for both sets of problems

Multi-Period Cell Loading and Job Sequencing in a Cellular Manufacturing System

In this paper, a multi-period cell loading problem is addressed, where the objectives are to minimise the number of tardy jobs (nT) in a multi-period planning horizon and optimise the scheduling of tardy jobs. Three cell loading and job scheduling strategies are proposed and tested with two newly developed mixed integer programming models. Additionally, three types of due dates (tight, medium and loose) and three different demand levels were considered. Finally, two tardy job assignment methods were proposed to observe the impact on nT. Case problems were solved based on minimising nT, Tmax and total tardiness (TT) objectives and cost sensitivity analysis was performed. Results indicated that, the first strategy, (early start allowance and tardy job assignment after each period) performed better in terms of nT. For the secondary objectives, tradeoffs were observed among different strategies depending on the type of due date, demand level and tardy job assignment method

Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times – A polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in O(Tfeas(n) log n) time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Algorithms for two scheduling problems

We describe algorithms for solving the following two scheduling problems on identical pa.rallel processors. Each job requires unit processing time, has a release date and a weight. The first problem also involves the existence of dea.dlines and consists of minimizing the weighted sum of tardy jobs. The second consists of minimizing the weighted sum of completion times. The proposed algorithms run in time 0((1 + log m)n² /m) and O((log n + n/m)n), respectively.Descrevemos algoritmos para resolver os dois problemas de escalonamento envolvendo processadores paralelos idênticos, que se seguem. Cada tarefa necessita de uma unidade de tempo de processamento, tem uma data de chegada e um peso associados. O primeiro problema também envolve a existência de prazos e consiste em minimizar o somatório ponderado das tarefas tardias. Já o segundo problema consiste em se minimizar o somatório ponderado dos tempos de término das tarefas. Os algoritmos propostos rodam em tempos O((1+log m)n² /m) e O((log n+n/m)n), respectivamente

Some topics on deterministic scheduling problems

Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case