Single machine due-date scheduling of jobs with decreasing start-time dependent processing times

Published version at http://dx.doi.org/10.1111/j.1475-3995.2005.501_1.xAuthor name used in this publication: T. C. E. ChengAuthor name used in this publication: L. Y. KangAuthor name used in this publication: C. T. Ng2005-2006 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Single machine scheduling with general positional deterioration and rate-modifying maintenance

We present polynomial-time algorithms for single machine problems with generalized positional deterioration effects and machine maintenance. The decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule in order to minimize the overall makespan. We deal with general non-decreasing functions to represent deterioration rates of job processing times. Another novel extension of existing models is our assumption that a maintenance activity does not necessarily fully restore the machine to its original perfect state. In the resulting schedules, the jobs are split into groups, a particular group to be sequenced after a particular maintenance period, and the actual processing time of a job is affected by the group that job is placed into and its position within the group

A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of $O(n \log n)$ for both cases, where $n$ is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR-library.Comment: Book Chapter 22 page

Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud this paper. As this research is guided by a real problem in industry, the flowshop\ud considered has considerable flexibility, which stimulated the development of an\ud innovative methodology for this research. Each stage of the flowshop currently has\ud one or several identical machines. However, the manufacturing company is planning\ud to introduce additional machines with different capabilities in different stages in the\ud near future. Thus, the algorithm proposed and developed for the problem is not only\ud capable of solving the current flow line configuration but also the potential new\ud configurations that may result in the future. A meta-heuristic search algorithm based\ud on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud different initial solution finding mechanisms are proposed. A carefully planned\ud nested split-plot design is performed to test the significance of different factors and\ud their impact on the performance of the different algorithms. To the best of our\ud knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud problem with the concern for future developments

Common Due-Date Problem: Exact Polynomial Algorithms for a Given Job Sequence

This paper considers the problem of scheduling jobs on single and parallel machines where all the jobs possess different processing times but a common due date. There is a penalty involved with each job if it is processed earlier or later than the due date. The objective of the problem is to find the assignment of jobs to machines, the processing sequence of jobs and the time at which they are processed, which minimizes the total penalty incurred due to tardiness or earliness of the jobs. This work presents exact polynomial algorithms for optimizing a given job sequence or single and parallel machines with the run-time complexities of $O(n \log n)$ and $O(mn^2 \log n)$ respectively, where $n$ is the number of jobs and $m$ the number of machines. The algorithms take a sequence consisting of all the jobs $(J_i, i=1,2,\dots,n)$ as input and distribute the jobs to machines (for $m>1$) along with their best completion times so as to get the least possible total penalty for this sequence. We prove the optimality for the single machine case and the runtime complexities of both. Henceforth, we present the results for the benchmark instances and compare with previous work for single and parallel machine cases, up to $200$ jobs.Comment: 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computin

Minimizing weighted total earliness, total tardiness and setup costs

The paper considers a (static) portfolio system that satisfies adding-up contraints and the gross substitution theorem. The paper shows the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables to investigate the impact of simultaneous changes in interest rates on the asset demands.

How Unsplittable-Flow-Covering helps Scheduling with Job-Dependent Cost Functions

Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private cost function, and one seeks to schedule the jobs to minimize the total sum of these costs. The framework captures many important scheduling objectives such as weighted flow time or weighted tardiness. Still, the general case as well as the mentioned special cases are far from being very well understood yet, even for only one machine. Aiming for better general understanding of this problem, in this paper we focus on the case of uniform job release dates on one machine for which the state of the art is a 4-approximation algorithm. This is true even for a special case that is equivalent to the covering version of the well-studied and prominent unsplittable flow on a path problem, which is interesting in its own right. For that covering problem, we present a quasi-polynomial time $(1+\epsilon)$-approximation algorithm that yields an $(e+\epsilon)$-approximation for the above scheduling problem. Moreover, for the latter we devise the best possible resource augmentation result regarding speed: a polynomial time algorithm which computes a solution with \emph{optimal }cost at $1+\epsilon$ speedup. Finally, we present an elegant QPTAS for the special case where the cost functions of the jobs fall into at most $\log n$ many classes. This algorithm allows the jobs even to have up to $\log n$ many distinct release dates.Comment: 2 pages, 1 figur