The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. In this paper we survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. We indicate some problems for future research and include a selective bibliography.

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Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey

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Sequencing and scheduling: algorithms and complexity

Publisher Summary This chapter discusses different types of sequencing and scheduling problems, and describes different types of algorithms and the concepts of complexity theory. A class of deterministic machine scheduling problems has been introduced in the chapter. The chapter also deals with the single machine, parallel machine and multi-operation problems in this class, respectively. The two generalizations of the deterministic machine-scheduling model have been presented in the chapter. A deterministic scheduling model may give rise to various stochastic counterparts, as there is a choice in the parameters that are randomized, in their distributions, and in the classes of policies that can be applied. A characteristic feature of these models is that the stochastic parameters are regarded as independent random variables with a given distribution and that their realization occurs only after the scheduling decision has been made. In the deterministic model, one has perfect information, and capitalizing on it in minimizing the realization of a performance measure may require exponential time.

Chapter 9 Sequencing and scheduling: Algorithms and complexity

The scheduling of computer and manufacturing systems has been the subject of extensive research for over forty years. In addition to computers and manufacturing, scheduling theory can be applied to many areas including agriculture, hospitals and transport. The main focus is on the efficient allocation of one or more resources to activities over time. Adopting manufacturing terminology, a job consists of one or more activities, and a machine is a resource that can perform at most one activity at a time. We concentrate on deterministic machine scheduling for which it is assumed that all data that define a problem instance are known with certainty.

A Review of Machine Scheduling: Complexity, Algorithms and Approximability

The theory of deterministic sequencing and scheduling has expanded rapidly during the past years. We survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory. Special cases considered are single machine scheduling, identical, uniform and unrelated parallel machine scheduling, and open shop, flow shop and job shop scheduling. This paper is a revised version of the survey by Graham et al. (Ann. Discrete Math. 5(1979) 287–326) , with emphasis on recent developments.

Recent Developments in Deterministic Sequencing and Scheduling: A Survey

The problem of preemptively scheduling a set of n independent jobs on an m processor open shop is discussed. An algorithm to construct preemptive schedules with minimum-maximum finishing time is presented. The worst case time complexity is 0(r + min {m4, n4, r2}), where r is the number of nonzero tasks. The maximum number of preemptions introduced is 0(min {rn, rm, n3, m3}). The algorithm is best possible for open shops with a fixed number of processors or jobs. In this case the maximum number of preemptions introduced is bounded by some fixed constant.

Gonzalez

Papers

A Note on Open Shop Preemptive Schedules