Optimal online algorithm for scheduling on two identical machines with machine availability constraints

2002 ◽  
Vol 83 (6) ◽  
pp. 323-329 ◽  
Author(s):  
Zhiyi Tan ◽  
Yong He
Keyword(s):  
Online Algorithm ◽  
Machine Availability ◽  
Availability Constraints ◽  
Identical Machines

ONLINE SCHEDULING OF MIXED CPU-GPU JOBS

2014 ◽  
Vol 25 (06) ◽  
pp. 745-761 ◽  
Author(s):  
LIN CHEN ◽  
DESHI YE ◽  
GUOCHUAN ZHANG
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Competitive Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Identical Machines ◽  
The One

We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and the GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. For the balanced case, we first provide a simple 3-competitive algorithm, and then a better algorithm with competitive ratio of 2.732 is derived. For the one-sided case, a 3-competitive algorithm is given.

ONLINE ALGORITHMS FOR SCHEDULING WITH MACHINE ACTIVATION COST

2007 ◽  
Vol 24 (02) ◽  
pp. 263-277 ◽  
Author(s):  
YONG HE ◽  
SHUGUANG HAN ◽  
YIWEI JIANG
Keyword(s):  
Lower Bound ◽  
Online Algorithms ◽  
Competitive Ratio ◽  
Online Algorithm ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problem ◽  
Identical Machines ◽  
Parallel Machine Scheduling Problem

In this paper, we consider a variant of the classical parallel machine scheduling problem. For this problem, we are given m potential identical machines to non-preemptively process a sequence of independent jobs. Machines need to be activated before starting to process, and each machine activated incurs a fixed machine activation cost. No machines are initially activated, and when a job is revealed the algorithm has the option to activate new machines. The objective is to minimize the sum of the makespan and activation cost of machines. We first present two optimal online algorithms with competitive ratios of 3/2 and 5/3 for m = 2, 3 cases, respectively. Then we present an online algorithm with a competitive ratio of at most 2 for general m ≥ 4, while the lower bound is 1.88.

scholarly journals Comparison of Multiobjective Evolutionary Algorithms for Operations Scheduling under Machine Availability Constraints

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
M. Frutos ◽  
M. Méndez ◽  
F. Tohmé ◽  
D. Broz
Keyword(s):  
Buffer Capacity ◽  
Job Shop ◽  
Production Systems ◽  
Pareto Frontier ◽  
Multiobjective Evolutionary Algorithms ◽  
Machine Availability ◽  
Operations Scheduling ◽  
Performance Indexes ◽  
Availability Constraints ◽  
Multiobjective Algorithms

Many of the problems that arise in production systems can be handled with multiobjective techniques. One of those problems is that of scheduling operations subject to constraints on the availability of machines and buffer capacity. In this paper we analyze different Evolutionary multiobjective Algorithms (MOEAs) for this kind of problems. We consider an experimental framework in which we schedule production operations for four real world Job-Shop contexts using three algorithms, NSGAII, SPEA2, and IBEA. Using two performance indexes, Hypervolume and R2, we found that SPEA2 and IBEA are the most efficient for the tasks at hand. On the other hand IBEA seems to be a better choice of tool since it yields more solutions in the approximate Pareto frontier.

MAKESPAN MINIMIZATION WITH MACHINE AVAILABILITY CONSTRAINTS

2009 ◽  
Vol 01 (02) ◽  
pp. 141-151 ◽  
Author(s):  
BIN FU ◽  
YUMEI HUO ◽  
HAIRONG ZHAO
Keyword(s):  
Processing Time ◽  
A Priori ◽  
Total Processing Time ◽  
Makespan Minimization ◽  
Machine Maintenance ◽  
Machine Availability ◽  
Negative Function ◽  
Availability Constraints ◽  
Subset Sum ◽  
One Machine

We investigate the problems of scheduling n jobs to m machines with availability constraints. We consider two different models of availability constraints: the preventive model where the unavailability is due to preventive machine maintenance, and the fixed job model where the unavailability is due to a priori assignment of some of the n jobs to certain machines at certain times. In both models, the objective is to minimize the makespan. We assume that m is a constant, and if a job is interrupted by the unavailable interval, it can be resumed after the machine becomes available. For fixed job model, we show there is an FPTAS. For the preventive model, we show that if at least one machine is always available, then the PTAS for Multiple Subset Sum problem given by Kellerer can be applied to get a PTAS; otherwise, every machine has some unavailable intervals, we show that if (m - 1) machines each of which has unavailable intervals with total length bounded by α(n) · P sum /m where P sum is the total processing time of all jobs and α(n) can be any non-negative function, we can develop a (1 + α(n) + ∊)-approximation algorithm for any constant 0 < ∊ < 1; further we show that there does not exist any polynomial time (1 + α(n) - o(1))-approximation unless P = NP.

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