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

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

Clips: a capacity and lead time integrated procedure for scheduling.

We propose a general procedure to address real life job shop scheduling problems. The shop typically produces a variety of products, each with its own arrival stream, its own route through the shop and a given customer due date. The procedure first determines the manufacturing lot sizes for each product. The objective is to minimize the expected lead time and therefore we model the production environment as a queueing network. Given these lead times, release dates are set dynamically. This in turn creates a time window for every manufacturing order in which the various operations have to be sequenced. The sequencing logic is based on a Extended Shifting Bottleneck Procedure. These three major decisions are next incorporated into a four phase hierarchical operational implementation scheme. A small numerical example is used to illustrate the methodology. The final objective however is to develop a procedure that is useful for large, real life shops. We therefore report on a real life application.Model; Models; Applications; Product; Scheduling;

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

Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

Capacity Planning and Leadtime management

In this paper we discuss a framework for capacity planning and lead time management in manufacturing companies, with an emphasis on the machine shop. First we show how queueing models can be used to find approximations of the mean and the variance of manufacturing shop lead times. These quantities often serve as a basis to set a fixed planned lead time in an MRP-controlled environment. A major drawback of a fixed planned lead time is the ignorance of the correlation between actual work loads and the lead times that can be realized under a limited capacity flexibility. To overcome this problem, we develop a method that determines the earliest possible completion time of any arriving job, without sacrificing the delivery performance of any other job in the shop. This earliest completion time is then taken to be the delivery date and thereby determines a workload-dependent planned lead time. We compare this capacity planning procedure with a fixed planned lead time approach (as in MRP), with a procedure in which lead times are estimated based on the amount of work in the shop, and with a workload-oriented release procedure. Numerical experiments so far show an excellent performance of the capacity planning procedure