The Complexity of Mean Flow Time Scheduling Problems with Release Times

We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.Comment: Subsumes and replaces cs.DS/0412094 and "Complexity of mean flow time scheduling problems with release dates" by P.B, S.

A Note on NP-Hardness of Preemptive Mean Flow-Time Scheduling for Parallel Machines

In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, D\"urr, Kravchenko and Sourd, the authors claimed to prove strong NP-hardness of the scheduling problem $P|pmtn,r_j|\sum C_j$, namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong NP-hardness for this problem

The robust single machine scheduling problem with uncertain release and processing times

In this work, we study the single machine scheduling problem with uncertain release times and processing times of jobs. We adopt a robust scheduling approach, in which the measure of robustness to be minimized for a given sequence of jobs is the worst-case objective function value from the set of all possible realizations of release and processing times. The objective function value is the total flow time of all jobs. We discuss some important properties of robust schedules for zero and non-zero release times, and illustrate the added complexity in robust scheduling given non-zero release times. We propose heuristics based on variable neighborhood search and iterated local search to solve the problem and generate robust schedules. The algorithms are tested and their solution performance is compared with optimal solutions or lower bounds through numerical experiments based on synthetic data

New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems

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

Parallel machine scheduling with precedence constraints and setup times

This paper presents different methods for solving parallel machine scheduling problems with precedence constraints and setup times between the jobs. Limited discrepancy search methods mixed with local search principles, dominance conditions and specific lower bounds are proposed. The proposed methods are evaluated on a set of randomly generated instances and compared with previous results from the literature and those obtained with an efficient commercial solver. We conclude that our propositions are quite competitive and our results even outperform other approaches in most cases

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan

Scheduling of non-repetitive lean manufacturing systems under uncertainty using intelligent agent simulation

World-class manufacturing paradigms emerge from specific types of manufacturing systems with which they remain associated until they are obsolete. Since its introduction the lean paradigm is almost exclusively implemented in repetitive manufacturing systems employing flow-shop layout configurations. Due to its inherent complexity and combinatorial nature, scheduling is one application domain whereby the implementation of manufacturing philosophies and best practices is particularly challenging. The study of the limited reported attempts to extend leanness into the scheduling of non-repetitive manufacturing systems with functional shop-floor configurations confirms that these works have adopted a similar approach which aims to transform the system mainly through reconfiguration in order to increase the degree of manufacturing repetitiveness and thus facilitate the adoption of leanness. This research proposes the use of leading edge intelligent agent simulation to extend the lean principles and techniques to the scheduling of non-repetitive production environments with functional layouts and no prior reconfiguration of any form. The simulated system is a dynamic job-shop with stochastic order arrivals and processing times operating under a variety of dispatching rules. The modelled job-shop is subject to uncertainty expressed in the form of high priority orders unexpectedly arriving at the system, order cancellations and machine breakdowns. The effect of the various forms of the stochastic disruptions considered in this study on system performance prior and post the introduction of leanness is analysed in terms of a number of time, due date and work-in-progress related performance metrics

Dynamic scheduling in a multi-product manufacturing system

To remain competitive in global marketplace, manufacturing companies need to improve their operational practices. One of the methods to increase competitiveness in manufacturing is by implementing proper scheduling system. This is important to enable job orders to be completed on time, minimize waiting time and maximize utilization of equipment and machineries. The dynamics of real manufacturing system are very complex in nature. Schedules developed based on deterministic algorithms are unable to effectively deal with uncertainties in demand and capacity. Significant differences can be found between planned schedules and actual schedule implementation. This study attempted to develop a scheduling system that is able to react quickly and reliably for accommodating changes in product demand and manufacturing capacity. A case study, 6 by 6 job shop scheduling problem was adapted with uncertainty elements added to the data sets. A simulation model was designed and implemented using ARENA simulation package to generate various job shop scheduling scenarios. Their performances were evaluated using scheduling rules, namely, first-in-first-out (FIFO), earliest due date (EDD), and shortest processing time (SPT). An artificial neural network (ANN) model was developed and trained using various scheduling scenarios generated by ARENA simulation. The experimental results suggest that the ANN scheduling model can provided moderately reliable prediction results for limited scenarios when predicting the number completed jobs, maximum flowtime, average machine utilization, and average length of queue. This study has provided better understanding on the effects of changes in demand and capacity on the job shop schedules. Areas for further study includes: (i) Fine tune the proposed ANN scheduling model (ii) Consider more variety of job shop environment (iii) Incorporate an expert system for interpretation of results. The theoretical framework proposed in this study can be used as a basis for further investigation