We investigate an online version of a basic scheduling problem where a set of jobs has to be scheduled on a number of identical machines so as to minimize the makespan. The job processing times are known in advance and preemption of jobs is allowed. Machines are non-continuously available, i.e., they can break down and recover at arbitrary time instances not known in advance. New machines may b...

Parallel machine scheduling, also known as parallel task scheduling, involves the assignment of multiple tasks onto the system architecture’s processing components (a bank of machines in parallel). A basic model involving m machines and n independent jobs is the foundation of more complex models. Here, the jobs are allocated according to resource availability following some allocation rule. The...

In this paper, we consider the problem of scheduling a given set of n jobs on two identical parallel machines with a single server. Each job must be processed on one of the machines. Prior to processing, the server has to set up the relevant machine. The objective is to minimize the makespan. For this unary NP-hard problem two fast algorithms with a complexity of O(n

A heuristic algorithm that uses iteratively LPT and MF approaches on different job and machine sets constructed by using the current solution is developed to solve a classical multiprocessor scheduling problem with the objective of minimizing the makespan. Computational results indicate that the proposed algorithm is very competitive with respect to well-known constructive algorithms for a larg...

For example, in job scheduling problems, one often thinks of the jobs as arriving online (i.e., one-by-one), with a new job needing to be scheduled on some machine immediately. Or in a graph problem, perhaps the vertices of a graph show up one by one (with whatever edges are incident to previously arriving vertices). Thus the meaning of “one piece at a time” varies with the problem, but it many...

This paper considers the minimization of makespan in unrelated parallel batch processing machines scheduling problem with considering non-identical job size and dynamic ready time. The considered have different capacity speed. Each machine processes a number jobs as at same time so that machine’s is not exceeded. are equal to largest batch, respectively. In this paper, Mixed Integer Linear Prog...

Consider scheduling of unit jobs with release times and deadlines on m identical machines with the objective to maximize the number of jobs completed before their deadlines. We prove a new lower bound for online algorithms with immediate decision. This means that the jobs arrive over time and the algorithm has to decide the schedule of each job immediately upon its release. Our lower bound tend...

In 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. To date this has remained the best algorithm, and whether it can or cannot be improved has become a major open problem in scheduling theory. We address this problem by establishing a...