The Complexity of Mean Flow Time Scheduling Problems with Release Times

We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can be solved in polynomial time using linear programming. Our algorithm can also be applied to the open-shop problem with release times and unit processing times. For the general case (when processing times are arbitrary), we show that the problem is unary NP-hard.Comment: Subsumes and replaces cs.DS/0412094 and "Complexity of mean flow time scheduling problems with release dates" by P.B, S.

Preemptive Multi-Machine Scheduling of Equal-Length Jobs to Minimize the Average Flow Time

We study the problem of preemptive scheduling of n equal-length jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. Recently, Brucker and Kravchenko proved that the optimal schedule can be computed in polynomial time by solving a linear program with O(n^3) variables and constraints, followed by some substantial post-processing (where n is the number of jobs.) In this note we describe a simple linear program with only O(mn) variables and constraints. Our linear program produces directly the optimal schedule and does not require any post-processing

Optimal Specially Structured N X 2 Flow Shop Scheduling to Minimize Total Waiting Time of Jobs Including Job Block Concept with Processing Time Separated From Set up Time

In the present state of affairs the current engineering and manufacturing built- up units are facing mishmash of problems in a lot of aspects such as man power, machining time, raw material, electricity and customer’s constraints. The flow-shop scheduling is one of the most significant manufacturing behaviors particularly in manufacturing planning. The creation of every time admirable schedules has verified to be enormously complicated. This paper involves the fortitude of the order of processing of m jobs on 2 machines. This paper proposes the specially structured Flow Shop Scheduling problem separated from set up time assuming that maximum of the equivalent processing time on first machine is less than or equal to the minimum of equivalent processing time on second machine with the objective of getting the optimal sequence of jobs for total waiting time of jobs using the heuristic algorithm by taking two of the jobs as a group job. The proposed technique is followed by numerical example

Non-clairvoyant Scheduling Games

In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy -- the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these so-called non-clairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules the jobs in parallel using time-multiplexing, assigning each job an equal fraction of CPU time

On-line scheduling with delivery time on a single batch machine

AbstractWe consider a single batch machine on-line scheduling problem with jobs arriving over time. A batch processing machine can handle up to B jobs simultaneously as a batch, and the processing time for a batch is equal to the longest processing time among the jobs in it. Each job becomes available at its arrival time, which is not known in advance, and its characteristics, such as processing time and delivery time, become known at its arrival. Once the processing of a job is completed we deliver it to the destination. The objective is to minimize the time by which all jobs have been delivered. In this paper, we deal with two variants: the unbound model where B is sufficiently large and the bounded model where B is finite. We provide on-line algorithms with competitive ratio 2 for the unbounded model and with competitive ratio 3 for the bounded model. For when each job has the same processing time, we provide on-line algorithms with competitive ratios (5+1)/2, and these results are the best possible

Sublinear Approximation Schemes for Scheduling Precedence Graphs of Bounded Depth

We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth h. Our goal is to minimize the maximum completion time. We focus on developing approximation algorithms that use only sublinear space or sublinear time. We develop the first one-pass streaming approximation schemes using sublinear space when all jobs\u27 processing times differ no more than a constant factor c and the number of machines m is at most 2nϵ3hc. This is so far the best approximation we can have in terms of m, since no polynomial time approximation better than 43 exists when m=n3 unless P=NP. %the problem cannot be approximated within a factor of 43 when m=n3 even if all jobs have equal processing time. The algorithms are then extended to the more general problem where the largest αn jobs have no more than c factor difference. % for some constant