Minimizing the number of tardy jobs with precedence constraints and agreeable due dates

AbstractMinimizing the number of precedence constrained, unit-time tardy jobs is strongly NP-hard on a single machine. We study a special case of the problem where a job is tardy if it is finished more than a fixed K time units after its earliest possible completion time under the precedence constraints. We prove that the problem remains strongly NP-hard even with these special due dates. We also present polynomial time solutions for the weighted version of the problem if the precedence constraints are out-forests or interval orders. In the process, we also present a polynomial time solution for a special case of the minimum weight hitting set problem

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

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

A new mathematical model for single machine batch scheduling problem for minimizing maximum lateness with deteriorating jobs

This paper presents a mathematical model for the problem of minimizing the maximum lateness on a single machine when the deteriorated jobs are delivered to each customer in various size batches. In reality, this issue may happen within a supply chain in which delivering goods to customers entails cost. Under such situation, keeping completed jobs to deliver in batches may result in reducing delivery costs. In literature review of batch scheduling, minimizing the maximum lateness is known as NP-Hard problem; therefore the present issue aiming at minimizing the costs of delivering, in addition to the aforementioned objective function, remains an NP-Hard problem. In order to solve the proposed model, a Simulation annealing meta-heuristic is used, where the parameters are calibrated by Taguchi approach and the results are compared to the global optimal values generated by Lingo 10 software. Furthermore, in order to check the efficiency of proposed method to solve larger scales of problem, a lower bound is generated. The results are also analyzed based on the effective factors of the problem. Computational study validates the efficiency and the accuracy of the presented model

Stronger Lagrangian bounds by use of slack variables: applications to machine scheduling problems

Lagrangian relaxation is a powerful bounding technique that has been applied successfully to manyNP-hard combinatorial optimization problems. The basic idea is to see anNP-hard problem as an easy-to-solve problem complicated by a number of nasty side constraints. We show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds. The trick is widely applicable, but we focus on a broad class of machine scheduling problems for which it is particularly useful. We provide promising computational results for three problems belonging to this class for which Lagrangian bounds have appeared in the literature: the single-machine problem of minimizing total weighted completion time subject to precedence constraints, the two-machine flow-shop problem of minimizing total completion time, and the single-machine problem of minimizing total weighted tardiness

Scheduling problems for logistic platforms with fixed staircase component arrivals and various deliveries hypotheses

International audienceThis paper studies the scheduling problem within a logistic platform node. It corresponds to the last node in the supply chain located just before the final customers. In this node, customer orders are prepared using known quantities of components received from the suppliers. For upstream flows, trucks deliver known component quantities at fixed times. For downstream flows, optimized customer delivery tours are planned at fixed times except the last one which will be done at a flexible time corresponding to the end of the schedule. We consider a simplified case of one bottleneck-assembling machine. Several sub cases are considered depending on the number of the fixed and flexible deliveries and also on the chosen criteria. For each sub case, upper and lower bounds are proposed and compared experimentally on heterogeneous instance families. All the ingredients are therefore available to design a branch and bound for these new scheduling problems

A common framework and taxonomy for multicriteria scheduling problems with Interfering and competing Jobs: Multi-agent scheduling problems

Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a uni ed view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear de nition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an uni ed framework providing a common de nition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic