Results 1 
8 of
8
Complexity Results for SingleMachine Problems with Positive FinishStart TimeLags
 Computing
, 1998
"... In a singlemachine problem with timelags a set of jobs has to be processed on a single machine in such a way that certain timing restrictions between the finishing and starting times of the jobs are satisfied and a given objective function is minimized. We consider the case of positive finishstart ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
In a singlemachine problem with timelags a set of jobs has to be processed on a single machine in such a way that certain timing restrictions between the finishing and starting times of the jobs are satisfied and a given objective function is minimized. We consider the case of positive finishstart timelags l ij which mean that between the finishing time of job i and the starting time of job j the minimal distance l ij has to be respected. New complexity results are derived for singlemachine problems with constant positive timelags l ij = l which also lead to new results for flowshop problems with unit processing times and job precedences. Key words: complexity results, timelags, single machine, flowshop problem Supported by the Deutsche Forschungsgemeinschaft, Project `Komplexe MaschinenSchedulingprobleme ' 1 Introduction In a singlemachine problem a set of jobs j = 1; : : : ; n has to be processed without preemption on a single machine in such a way that at most one jo...
Identical Parallel Machines Vs UnitTime Shops And Preemptions Vs Chains In Scheduling Complexity
 European Journal of Operational Research
, 2000
"... . This paper surveys, analyses and establishes new polynomialtime reductions among scheduling problems that connect identical parallel machines with unittime shops and the preemption facility with chainlike precedence constraints in equal machine environments. The reductions turn out to be une ..."
Abstract

Cited by 13 (7 self)
 Add to MetaCart
(Show Context)
. This paper surveys, analyses and establishes new polynomialtime reductions among scheduling problems that connect identical parallel machines with unittime shops and the preemption facility with chainlike precedence constraints in equal machine environments. The reductions turn out to be unexpectedly fruitful in clarifying the complexity status of many scheduling problems that were open before. New complexity results in the paper are devoted to identical parallel machines, ow shops and open shops. 1. Introduction Recently found mass polynomialtime reductions between scheduling problems on identical parallel machines and shop scheduling problems with nonpreemptive unit processing time operations proved to be very eective in studying their complexity. The latter problems we simply call unittime shops. Reductions of unittime shops to identical parallel machines we call parallelizings, and the inverse reductions, i.e., of identical parallel machines to unittime shops, we c...
A PolynomialTime Algorithm For The TwoMachine UnitTime ReleaseDate JobShop ScheduleLength Problem
 Discrete Appl. Math
, 1997
"... . We consider a polynomialtime algorithm for the following scheduling problem: Given two machines, where each machine can process at most one job at a time; a set of jobs, where each job can start on or after its release date and consists of a chain of unittime operations such that the machines ..."
Abstract

Cited by 9 (8 self)
 Add to MetaCart
(Show Context)
. We consider a polynomialtime algorithm for the following scheduling problem: Given two machines, where each machine can process at most one job at a time; a set of jobs, where each job can start on or after its release date and consists of a chain of unittime operations such that the machines have to process them by turn begining with a given machine; nd a schedule minimizing the maximum job completion time. Formerly, only pseudopolynomialtime algorithms have been proposed for this problem. Key words and phrases. Jobshop scheduling, unittime operations, release dates, due dates, schedule length, maximum lateness, polynomialtime algorithm. 1. Introduction The mmachine unittime releasedate jobshop schedulelength problem, Jmjr j ; p ij = 1jC max , can be formulated as follows. Given m machines M 1 ; :::; Mm , where m is xed and each machine can process at most one job at a time; n jobs J 1 ; :::; J n , where J j ; j = 1; :::; n, can start on or after release date r ...
On Preemption Redundancy in Scheduling Unit Processing Time Jobs on Two Parallel Machines
, 2000
"... McNaughton's theorem (1959) states that preemptions in scheduling arbitrary processing time jobs on identical parallel machines to minimize the total weighted completion time are redundant. Du, Leung and Young (1991) proved that this remains true even though the jobs have precedence constraints ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
McNaughton's theorem (1959) states that preemptions in scheduling arbitrary processing time jobs on identical parallel machines to minimize the total weighted completion time are redundant. Du, Leung and Young (1991) proved that this remains true even though the jobs have precedence constraints in the form of chains. There are known simple counterexamples showing that other extensions of McNaughton's theorem to other criteria or more general precedence constraints such as intrees or outtrees, or different release dates of jobs, or different speeds of machines, are not true even for equal weights of jobs. In this paper we show that in the case of two machines and unit processing times, preemptions are still advantageous for intrees or machines with different speeds even for equal weights, or outtrees for different weights, but become redundant for outtrees and equal weights even for different release dates. We also conjecture that the latter statement is actually true for any number of machines.
On Scheduling Cycle Shops: Classification, Complexity And Approximation
"... . This paper considers problems of finding nonperiodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but so ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
. This paper considers problems of finding nonperiodic and periodic schedules in a cycle shop which is a special case of a job shop but an extension of a flow shop. The cycle shop means the machine environment where all jobs have to pass the machines over the same route like in a flow shop but some of the machines in the route can be met more than once. We propose a classification of cycle shops and show that recently studied reentrant flow shops, robotic flow shops, loop reentrant flowshops and V shops are special cases of cycle shops. Problems solvable in polynomial time, pseudopolynomial time, NPhard problems and performance guarantee approximations are presented. Related earlier results are surveyed. 1.
Scheduling UnitTime Operation Jobs On Identical Parallel Machines And In A Flow Shop: Complexity And Correlation
, 1998
"... . This paper considers the complexity and the correlation of scheduling unittime jobs on identical parallel machines and unittime flowshop scheduling under precedence constraints. It is shown that, in the case of chainlike precedence constraints, the nonpreemptive parallelmachines problem and t ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. This paper considers the complexity and the correlation of scheduling unittime jobs on identical parallel machines and unittime flowshop scheduling under precedence constraints. It is shown that, in the case of chainlike precedence constraints, the nonpreemptive parallelmachines problem and the flowshop problem to minimize maximum or total completion time can be solved in polynomial time, and their optimal schedules can be constructed from each other by simple transformations. We show that adding different release dates of jobs leaves the parallelmachines problem solvable in polynomial time, whereas the related flowshop problem remains so only in the twomachine case. For general precedence constraints and treelike precedence constraints with different release dates of jobs, it is shown a polynomialtime reduction from the preemptive parallelmachines problems to the flowshop problems to minimize maximum completion time. The latter are proved to be strongly NPhard because ...
How To Make Brucker's Algorithm Polynomial: Scheduling By Periodization
, 1999
"... This paper introduces scheduling by periodization as a new approach to the design and analysis of efficient algorithms finding compactly specified schedules. The approach is demonstrated in application to the twomachine maximumlateness unittime jobshop scheduling problem. Earlier, Brucker propos ..."
Abstract
 Add to MetaCart
(Show Context)
This paper introduces scheduling by periodization as a new approach to the design and analysis of efficient algorithms finding compactly specified schedules. The approach is demonstrated in application to the twomachine maximumlateness unittime jobshop scheduling problem. Earlier, Brucker proposed the largestlagfirst algorithm which is of pseudopolynomial time proportional to the total number of operations in jobs. We show that by using periodization Brucker's algorithm can be elaborated to solve the problem in polynomial time. The result represents a rare example of when a pseudopolynomial algorithm can be brought to a polynomial algorithm which, in addition, proves to have the best presently known time and space requirements. In comparison with an earlier algorithm of Timkovsky with time and space requirements both O(n&sup2;), where n is the number of jobs, the algorithm in this paper has time and space requirements O(n&sup2;) and O(n), respectively.