Single-machine scheduling

About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.

Competitive algorithms from competitive equilibria: non-clairvoyant scheduling under polyhedral constraints

Abstract: We introduce and study a general scheduling problem that we term the Packing Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes; a scheduler can process job j at rate xj, subject to arbitrary packing constraints over the set of rates (x) of the outstanding jobs. The PSP framework captures a variety of scheduling problems, including the classical problems of unrelated machines scheduling, broadcast scheduling, and scheduling jobs of different parallelizability. It also captures scheduling constraints arising in diverse modern environments ranging from individual computer architectures to data centers. More concretely, PSP models multidimensional resource requirements and parallelizability, as well as network bandwidth requirements found in data center scheduling. In this paper, we design non-clairvoyant online algorithms for PSP and its special cases -- in this setting, the scheduler is unaware of the sizes of jobs. Our results are summarized as follows. • For minimizing total weighted completion time, we show a O(1)-competitive algorithm. Surprisingly, we achieve this result by applying the well-known Proportional Fairness algorithm (PF) to perform allocations each time instant. Though PF has been extensively studied in the context of maximizing fairness in resource allocation, we present the first analysis in adversarial and general settings for optimizing job latency. Our result is also the first O(1)-competitive algorithm for weighted completion time for several classical non-clairvoyant scheduling problems. •For minimizing total weighted flow time, for any constant e > 0, any O(n1---e)-competitive algorithm requires extra speed (resource augmentation) compared to the offline optimum. We show that PF is a O(log n)-speed O(log n)-competitive non-clairvoyant algorithm, where n is the total number of jobs. We further show that there is an instance of PSP for which no non-clairvoyant algorithm can be O(n1---e)-competitive with o(√log n) speed. •For the classical problem of minimizing total flow time for unrelated machines in the non-clairvoyant setting, we present the first online algorithm which is scalable ((1 + e)-speed O(1)-competitive for any constant e > 0). No non-trivial results were known for this setting, and the previous scalable algorithm could handle only related machines. We develop new algorithmic techniques to handle the unrelated machines setting that build on a new single machine scheduling policy. Since unrelated machine scheduling is a special case of PSP, when contrasted with the lower bound for PSP, our result also shows that PSP is significantly harder than perhaps the most general classical scheduling settings. Our results for PSP show that instantaneous fair scheduling algorithms can also be effective tools for minimizing the overall job latency, even when the scheduling decisions are non-clairvoyant and constrained by general packing constraints.

Single-machine scheduling with simple linear deterioration to minimize earliness penalties

Abstract: We consider a single-machine scheduling problem with deteriorating jobs in which the due dates are determined by the equal slack method. In this model, the processing time of a job is defined as a simple linear function of its starting time. The objective is to minimize the total weighted earliness penalty subject to no tardy jobs. We prove that two special cases of the problem remain polynomially solvable. The first case is the problem with equally weighted monotonous penalty objective function and the other case is the problem with weighted linear penalty objective function.

Scheduling jobs under increasing linear machine maintenance time

Abstract: Although scheduling problems with machine availability have attracted many researchers' attention, most of the past studies are mainly focused on one or several prefixed machine maintenance activities. In this research, we assume that the time needed to perform one maintenance activity is an increasing linear function of the total processing time of the jobs that are processed after the machine's last maintenance activity. We consider two scheduling problems with such maintenance requirement in this paper. The first problem is a parallel machine scheduling problem where the length of the time interval between any two consecutive maintenance activities is between two given positive numbers. The objective is to minimize the maintenance makespan, i.e., the completion time of the last finished maintenance. The second problem is a single machine scheduling problem where the length of the time interval between any two consecutive maintenance activities is fixed and the objective is to minimize the makespan, i.e., the completion time of the last finished job. We propose two approximation algorithms for the considered problems and analyze their performances.

Single Machine Scheduling with Precedence Constraints of Dimension 2

Abstract: Consider the set of tasks that are partially ordered by precedence constraints. The tasks are to be sequenced so that a given objective function will assume its optimal value over the set of feasible solutions. A subset of tasks is called feasible, if for every task in the subset, all of its predecessors are also in the subset. We present a dynamic programming solution to the problem, when the constraining partial order has a dimension ≤2. This is done by definining a “compact” labeling scheme and an efficient enumerative procedure for all the feasible subsets. In this process a new characterization is given for 2-dimensional partial orders.