Sequencing and scheduling : algorithms and complexity
01 Jan 1993-Vol. 4, pp 445
TL;DR: A survey of deterministic machine scheduling can be found in this article, where complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops are presented.
Abstract: Sequencing and scheduling as a research area is motivated by questions that arise in production planning, in computer control, and generally in all situations in which scarce resources have to be allocated to activities over time. In this survey, we concentrate on the area of deterministic machine scheduling. We review complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops. We also pay attention to two extensions of this area: resource-constrained project scheduling and stochastic machine scheduling.
Citations
More filters
TL;DR: A comprehensive review of the literature on scheduling problems involving setup times (costs) classifies scheduling problems into batch and non-batch, sequence-independent and sequence-dependent setup, and categorizes the literature according to the shop environments of single machine, parallel machines, flowshops, and job shops.
Abstract: The majority of scheduling research assumes setup as negligible or part of the processing time. While this assumption simplifies the analysis and/or reflects certain applications, it adversely affects the solution quality for many applications which require explicit treatment of setup. Such applications, coupled with the emergence of production concepts like time-based competition and group technology, have motivated increasing interest to include setup considerations in scheduling problems. This paper provides a comprehensive review of the literature on scheduling problems involving setup times (costs). It classifies scheduling problems into batch and non-batch, sequence-independent and sequence-dependent setup, and categorizes the literature according to the shop environments of single machine, parallel machines, flowshops, and job shops. The suggested classification scheme organizes the scheduling literature involving setup considerations, summarizes the current research results for different problem types, and finally provides guidelines for future research.
899 citations
TL;DR: The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs; each job is to be processed by exactly one machine; processing jobj on machinei requires timepij and incurs a cost ofcij; each machinei is available forTi time units, and the objective is to minimize the total cost incurred.
Abstract: The generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs. Each job is to be processed by exactly one machine; processing jobj on machinei requires timep
ij
and incurs a cost ofc
ij
; each machinei is available forT
i
time units, and the objective is to minimize the total cost incurred. Our main result is as follows. There is a polynomial-time algorithm that, given a valueC, either proves that no feasible schedule of costC exists, or else finds a schedule of cost at mostC where each machinei is used for at most 2T
i
time units. We also extend this result to a variant of the problem where, instead of a fixed processing timep
ij
, there is a range of possible processing times for each machine—job pair, and the cost linearly increases as the processing time decreases. We show that these results imply a polynomial-time 2-approximation algorithm to minimize a weighted sum of the cost and the makespan, i.e., the maximum job completion time. We also consider the objective of minimizing the mean job completion time. We show that there is a polynomial-time algorithm that, given valuesM andT, either proves that no schedule of mean job completion timeM and makespanT exists, or else finds a schedule of mean job completion time at mostM and makespan at most 2T.
761 citations
TL;DR: A framework is provided to illustrate how models for this class of machine scheduling problems have been generalized from the classical scheduling theory, and a complexity boundary is presented for each model.
603 citations
TL;DR: This paper presents a hybrid genetic algorithm for the job shop scheduling problem that is based on random keys and tested on a set of standard instances taken from the literature and compared with other approaches.
577 citations
TL;DR: A job shop consists of a set of different machines that perform operations on jobs, each job is composed of an ordered list of operations each of which is determined by the machine required and the processing time on it.
548 citations