In computing, scheduling is the action of assigning resources to perform tasks. The resources may be processors, network links or expansion cards. The tasks may be threads, processes or data flows.
In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. Precisely, a topological sort is a graph traversal in which each node v is visited only after all its dependencies are visited. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time. Topological sorting has many applications, especially in ranking problems such as feedback arc set. Topological sorting is possible even when the DAG has disconnected components.
Uniform machine scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m different machines. The goal is to minimize the makespan - the total time required to execute the schedule. The time that machine i needs in order to process job j is denoted by pi,j. In the general case, the times pi,j are unrelated, and any matrix of positive processing times is possible. In the specific variant called uniform machine scheduling, some machines are uniformly faster than others. This means that, for each machine i, there is a speed factor si, and the run-time of job j on machine i is pi,j = pj / si.
Single-machine scheduling or single-resource scheduling is an optimization problem in computer science and operations research. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on a single machine, in a way that optimizes a certain objective, such as the throughput.
Optimal job scheduling is a class of optimization problems related to scheduling. The inputs to such problems are a list of jobs and a list of machines. The required output is a schedule – an assignment of jobs to machines. The schedule should optimize a certain objective function. In the literature, problems of optimal job scheduling are often called machine scheduling, processor scheduling, multiprocessor scheduling, or just scheduling.
Interval scheduling is a class of problems in computer science, particularly in the area of algorithm design. The problems consider a set of tasks. Each task is represented by an interval describing the time in which it needs to be processed by some machine. For instance, task A might run from 2:00 to 5:00, task B might run from 4:00 to 10:00 and task C might run from 9:00 to 11:00. A subset of intervals is compatible if no two intervals overlap on the machine/resource. For example, the subset {A,C} is compatible, as is the subset {B}; but neither {A,B} nor {B,C} are compatible subsets, because the corresponding intervals within each subset overlap.
The Shifting Bottleneck Heuristic is a procedure intended to minimize the time it takes to do work, or specifically, the makespan in a job shop. The makespan is defined as the amount of time, from start to finish, to complete a set of multi-machine jobs where machine order is pre-set for each job. Assuming that the jobs are actually competing for the same resources (machines) then there will always be one or more resources that act as a 'bottleneck' in the processing. This heuristic, or 'rule of thumb' procedure minimises the effect of the bottleneck. The Shifting Bottleneck Heuristic is intended for job shops with a finite number of jobs and a finite number of machines.
The genetic algorithm is an operational research method that may be used to solve scheduling problems in production planning.
Job-shop scheduling, the job-shop problem (JSP) or job-shop scheduling problem (JSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length of the schedule. In the specific variant known as job-shop scheduling, each job consists of a set of operationsO1, O2, ..., On which need to be processed in a specific order. Each operation has a specific machine that it needs to be processed on and only one operation in a job can be processed at a given time. A common relaxation is the flexible job shop, where each operation can be processed on any machine of a given set.
Flow-shop scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan – the total length of the schedule. In the specific variant known as flow-shop scheduling, each job contains exactly m operations. The i-th operation of the job must be executed on the i-th machine. No machine can perform more than one operation simultaneously. For each operation of each job, execution time is specified.
Open-shop scheduling or open-shop scheduling problem (OSSP) is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job-scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines with varying processing power, while trying to minimize the makespan - the total length of the schedule. In the specific variant known as open-shop scheduling, each job consists of a set of operationsO1, O2, ..., On which need to be processed in an arbitrary order. The problem was first studied by Teofilo F. Gonzalez and Sartaj Sahni in 1976.
The Coffman–Graham algorithm is an algorithm for arranging the elements of a partially ordered set into a sequence of levels. The algorithm chooses an arrangement such that an element that comes after another in the order is assigned to a lower level, and such that each level has a number of elements that does not exceed a fixed width bound W. When W = 2, it uses the minimum possible number of distinct levels, and in general it uses at most 2 − 2/W times as many levels as necessary.
In the mathematical modeling of job shop scheduling problems, disjunctive graphs are a way of modeling a system of tasks to be scheduled and timing constraints that must be respected by the schedule. They are mixed graphs, in which vertices may be connected by both directed and undirected edges. The two types of edges represent constraints of two different types:
Truthful job scheduling is a mechanism design variant of the job shop scheduling problem from operations research.
Stochastic scheduling concerns scheduling problems involving random attributes, such as random processing times, random due dates, random weights, and stochastic machine breakdowns. Major applications arise in manufacturing systems, computer systems, communication systems, logistics and transportation, and machine learning, among others.
Parallel task scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. In a general job scheduling problem, we are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m machines while trying to minimize the makespan - the total length of the schedule. In the specific variant known as parallel-task scheduling, all machines are identical. Each job j has a length parameter pj and a size parameter qj, and it must run for exactly pj time-steps on exactly qj machines in parallel.
In computer science, multiway number partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets, such that the sums of the subsets are as similar as possible. It was first presented by Ronald Graham in 1969 in the context of the identical-machines scheduling problem. The problem is parametrized by a positive integer k, and called k-way number partitioning. The input to the problem is a multiset S of numbers, whose sum is k*T.
Identical-machines scheduling is an optimization problem in computer science and operations research. We are given n jobs J1, J2, ..., Jn of varying processing times, which need to be scheduled on m identical machines, such that a certain objective function is optimized, for example, the makespan is minimized.
Unrelated-machines scheduling is an optimization problem in computer science and operations research. It is a variant of optimal job scheduling. We need to schedule n jobs J1, J2, ..., Jn on m different machines, such that a certain objective function is optimized. The time that machine i needs in order to process job j is denoted by pi,j. The term unrelated emphasizes that there is no relation between values of pi,j for different i and j. This is in contrast to two special cases of this problem: uniform-machines scheduling - in which pi,j = pi / sj, and identical-machines scheduling - in which pi,j = pi.
Fractional job scheduling is a variant of optimal job scheduling in which it is allowed to break jobs into parts and process each part separately on the same or a different machine. Breaking jobs into parts may allow for improving the overall performance, for example, decreasing the makespan. Moreover, the computational problem of finding an optimal schedule may become easier, as some of the optimization variables become continuous. On the other hand, breaking jobs apart might be costly.
