A heap of pieces model for the cyclic job shop problem (original) (raw)

The time varying cyclic job shop problem

2016

In classical scheduling, a set of tasks is executed once while the determined schedule optimizes objective functions such as the makespan or earliness-tardiness. In contrast, cyclic scheduling means performing a set of generic tasks infinitely often while minimizing the time between two occurrences of the same task.Cyclic scheduling has several applications, e.g. in robotic industry, in manufacturing systems or multiprocessor computing. It has been studied from multiple perspectives, since there exist several possible representations of the problem such as graph theory, mixed integer linear programming, Petri nets or (max, +) algebra. An overview about cyclic scheduling problems and the different approaches can be found in [Hanen and Munier, 1995a] and [Brucker and Kampmeyer, 2008]. However, few works have tackled the robust version of this problem although the literature for robust classical scheduling problem is large. In this paper, we consider a subset of tasks that have variabl...

An efficient algorithm for finding ideal schedules

Acta Informatica, 2012

We study the problem of scheduling unit execution time (UET) jobs with release dates and precedence constraints on two identical processors. We say that a schedule is ideal if it minimizes both maximum and total completion time simultaneously. We give an instance of the problem where the min-max completion time is exceeded in every preemptive schedule that minimizes total completion time for that instance, even if the precedence constraints form an intree. This proves that ideal schedules do not exist in general when preemptions are allowed. On the other hand, we prove that, when preemptions are not allowed, then ideal schedules do exist for general precedence constraints, and we provide an algorithm for finding ideal schedules in O(n 3 ) time, where n is the number of jobs. In finding such ideal schedules we resolve a conjecture of Baptiste and Timkovsky [1]. Further, our algorithm for finding min-max completion-time schedules requires only O(n 3 ) time, while the most efficient solution to date has required O(n 9 ) time.

Scheduling with Concurrency-Based Constraints

Journal of Algorithms, 1995

This paper considers scheduling problems with timing constraints of the forms: < (precedence), (no later than), and : = (concurrence). Scheduling unit-time jobs subject to < and : = constraints, and scheduling unit-time jobs subject to constraints, are proved NP-complete for xed k 3 processors. (This contrasts with the case of just < constraints, which is a famous open problem.) We then show that a modi ed version of Gabow's linear time 2-processor scheduling algorithm can optimally handle all three types of constraints. Linear time and NC algorithms for optimally scheduling with any subset of f<; ; : =g constraints are thus obtained for k = 2 processors. Approximation results for k 3 processors are also obtained. Finally, we consider a problem that arises in practice on the Tera architecture, proving an NP-Completeness result and providing an approximation algorithm.

Scheduling jobs of equal length: compleixty, facets and computational results

The following problem was originally motivated by a question arising in the automated assembly of printed circuit boards. Given are n jobs, which have to be performed on a single machine within a xed timespan 0; T ], subdivided into T unit-length subperiods. The processing time (or length) of each job equals p, p 2 I N . The processing cost of each job is an arbitrary function of its start-time. The problem is to schedule all jobs so as to minimize the sum of the processing costs.

On the geometry, preemptions and complexity of multiprocessor and shop scheduling

Annals of Operations Research, 2008

In this paper we study multiprocessor and open shop scheduling problems from several points of view. We explore a tight dependence of the polynomial solvability/intractability on the number of allowed preemptions. For an exhaustive interrelation, we address the geometry of problems by means of a novel graphical representation. We use the so-called preemption and machine-dependency graphs for preemptive multiprocessor and shop scheduling problems, respectively. In a natural manner, we call a scheduling problem acyclic if the corresponding graph is acyclic. There is a substantial interrelation between the structure of these graphs and the complexity of the problems. Acyclic scheduling problems are quite restrictive; at the same time, many of them still remain NP-hard. We believe that an exhaustive study of acyclic scheduling problems can lead to a better understanding and give a better insight of general scheduling problems.

Single machine scheduling with precedence constraints and positionally dependent processing times

Computers & Operations Research, 2012

In many real-life situations the processing conditions in scheduling models cannot be viewed as given constants since they vary over time thereby affecting actual durations of jobs. We consider single machine scheduling problems of minimizing the makespan in which the processing * Corresponding author, e-mail address: gordon@newman.bas-net.by, tel: +375 17 2842125, fax: +375 17 3318403.

Scheduling with processing set restrictions: A survey

International Journal of Production Economics, 2008

Scheduling problems with processing set restrictions have been studied extensively by computer scientists and operations researchers under different names. These include "scheduling typed task systems," "multi-purpose machine scheduling," "scheduling with eligibility constraints," "scheduling with processing set restrictions," and "semimatchings for bipartite graphs." In this paper we survey the state of the art of these problems. Our survey covers offline and online problems, as well as nonpreemptive and preemptive scheduling environments. Our emphasis is on polynomial-time algorithms, complexity issues, and approximation schemes. While our main focus is on the makespan objective, other performance criteria are also discussed.