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

Shop scheduling with availability constraints

Scheduling Theory studies planning and timetabling of various industrial and human activities and, therefore, is of constant scientific interest. Being a branch of Operational Research, Theory of Scheduling mostly deals with problems of practical interest which can be easily (from a mathematical point of view) solved by full enumeration and at the same time usually require enormous time to be solved optimally. Therefore, one attempts to develop algorithms for finding optimal or near optimal solutions of the problems under consideration in reasonable time. If the output of an algorithm is not always an optimal solution then the worst-case analysis of this algorithm is undertaken in order to estimate either a relative error or an absolute error that holds for any given instance of the problem. Scheduling problems which are usually considered in the literature assume that the processing facilities are constantly available throughout the planning period. However, in practice, the processing facility, e.g. a machine, a labour, etc. can become non-available due to various reasons, e.g. breakdowns, lunch breaks, holidays, maintenance work, etc. All these facts stimulate research in the area of scheduling with non-availability constraints. This branch of Scheduling Theory has recently received a lot of attention and a considerable number of research papers have been published. This thesis is fully dedicated to scheduling with non-availability constraints under various assumptions on the structure of the processing system and on the types of non-availability intervals

Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags

Algorithmic And Mathematical Programming Approaches To Scheduling Problems With Energy-Based Objectives

This dissertation studies scheduling as a means to address the increasing concerns related to energy consumption and electricity cost in manufacturing enterprises. Two classes of problems are considered in this dissertation: (i) minimizing the makespan in a permutation flow shop with peak power consumption constraints (the PFSPP problem for short) and (ii) minimizing the total electricity cost on a single machine under time-of-use tariffs (the SMSEC problem for short). We incorporate the technology of dynamic speed scaling and the variable pricing of electricity into these scheduling problems to improve energy efficiency in manufacturing.The challenge in the PFSPP problem is to keep track of which jobs are running concurrently at any time so that the peak power consumption can be properly taken into account. The challenge in the SMSEC problem is to keep track of the electricity prices at which the jobs are processed so that the total electricity cost can be properly computed. For the PFSPP problem, we consider both mathematical programming and combinatorial approaches. For the case of discrete speeds and unlimited intermediate storage, we propose two mixed integer programs and test their computational performance on instances arising from the manufacturing of cast iron plates. We also examine the PFSPP problem with two machines and zero intermediate storage, and investigate the structural properties of optimal schedules in this setting. For the SMSEC problem, we consider both uniform-speed and speed-scalable machine environments. For the uniform-speed case, we prove that this problem is strongly NP-hard, and in fact inapproximable within a constant factor, unless P = NP. In addition, we propose an exact polynomial-time algorithm for this problem when all the jobs have the same work volume and the electricity prices follow a so-called pyramidal structure. For the speed-scalable case, in which jobs can be processed at an arbitrary speed with a trade-off between speed and energy consumption, we show that this problem is strongly NP-hard and that there is no polynomial time approximation scheme for this problem. We also present different approximation algorithms for this case and test the computational performance of these approximation algorithms on randomly generated instances

Four decades of research on the open-shop scheduling problem to minimize the makespan

One of the basic scheduling problems, the open-shop scheduling problem has a broad range of applications across different sectors. The problem concerns scheduling a set of jobs, each of which has a set of operations, on a set of different machines. Each machine can process at most one operation at a time and the job processing order on the machines is immaterial, i.e., it has no implication for the scheduling outcome. The aim is to determine a schedule, i.e., the completion times of the operations processed on the machines, such that a performance criterion is optimized. While research on the problem dates back to the 1970s, there have been reviving interests in the computational complexity of variants of the problem and solution methodologies in the past few years. Aiming to provide a complete road map for future research on the open-shop scheduling problem, we present an up-to-date and comprehensive review of studies on the problem that focuses on minimizing the makespan, and discuss potential research opportunities