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Scheduling : Theory, Algorithms, and Systems / M. Pinedo
The problem of scheduling several tasks over time, including the topics of measures of performance, single-machine sequencing, flow shop scheduling, the job shop problem, and priority dispatching. Integer programming, dynamic programming, and heuristic approaches to various problems are presented.
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Mathematical challenges in scheduling theory
Journal of Scheduling
Scheduling is the allocation of resources over time to execute a set of tasks that belong-in most applications-to computational and manufacturing processes. During execution, the tasks compete for required resources. Resources can be of different categories, e.g. manpower, money, processors (machines), energy, tools, transportation (by truck, robot, drone, etc.). There is a limited quantity of resources and the scheduler determines how to allocate the resources to tasks over time to complete them. The quality of a schedule is mostly determined by attributes of the tasks. These attributes may include release times, due dates, priority weights, functions describing task processing in relation to allotted resources, technical restrictions, economical limitations or temporal restrictions. A scheduler must design a schedule that satisfies the specified restrictions while optimizing one or more goals that evaluate the quality of the generated solution. There
Peter Brucker, ,Scheduling Algorithms fourth ed. (2003) Osnabrück University,Springer
2006
Chapter 9 is also an academic paper that attempts to reflect on the processes of carrying out ''soft'' OR with senior management teams. The main intention of this paper is to enhance learning from the many of the authorsÕ experience of over 200 interventions using ''soft'' OR. Chapter 10 presents the status of models in defence systems engineering. This is a theoretical paper that shows the limitations of ''classical'' systems engineering in the modern defence area. Finally, Chapter 11 is a paper written by practitioners focusing on the use of ''complementary'' in Ministry of Defence OR practice. The result is that every study of necessity employs a mix of models and methods that must form a complementary and coherent whole capable withstanding expert professional scrutinity by scientists, military and policy staffs. 3. Discussion During the last years, the academic OR community has dedicated a lot of work to extend and strength our discipline in various directions. The main four research areas has been:
Some Common Performance Measures in Scheduling Problems: Review Article
2009
In this Study, we discussed 29 different scheduling criteria. We developed mathematical expressions for all the criteria considered. Each of the criteria was expressed as a function of either the completion time of job or the given parameters. This will assist researchers to easily compute the value of any of the scheduling criteria considered in this study.
Fifty years of scheduling: a survey of milestones
Journal of the Operational Research Society, 2009
Scheduling has become a major field within operational research with several hundred publications appearing each year. This paper explores the historical development of the subject since the mid 1950s when the landmark publications started to appear. A discussion of the main topics of scheduling research for the past five decades is provided, highlighting the key contributions that helped shape the subject. The main topics covered in the respective decades are combinatorial analysis, branch and bound, computational complexity and classification, approximate solution algorithms, and enhanced scheduling models.
2-Cover Definition for a Coupled-Tasks Scheduling Problem
2009
This paper introduces a scheduling problem with coupledtasks in presence of a compatibility graph on a single processor. We investigate a specific configuration, in which the coupled-tasks possess an idle time equal to 2. The complexity of these problems will be studied according to the presence or absence of triangles in the compatibility graph. As an extended matching, we propose a polynomialtime algorithm which consists in minimizing the number of non-covered vertices, by covering vertices with edges or paths of length two in the compatibility graph. This type of covering will be denoted by 2-cover technique. According on the compatibility graph type, the 2-cover technique provides a polynomial-time ρ-approximation algorithm with ρ = 13 12 (resp. ρ = 10 9) in absence (resp. presence) of triangles.