We study scheduling problemswhen jobs can be split and a setup is required before processing each part, to minimize the weighted sum of completion times. Using a simple splitting strategy and a reduction to an orders scheduling problem we derive a 2-approximation algorithm for the case with uniform weights and setups, improving upon previouswork.We extend this idea to the general identical mach...

Scheduling with assignment restrictions is an important special case of scheduling unrelated machines which has attracted much attention in the recent past. While a lower bound on approximability of 3/2 is known for its most general setting, subclasses of the problem admit polynomialtime approximation schemes. This note provides a PTAS for tree-like hierarchical structures, improving on a recen...

This paper presents a genetic algorithm for a scheduling problem frequent in printed circuit board manufacturing: a hybrid flowshop with unrelated machines, sequence dependent setup time and machine availability constraints. The proposed genetic algorithm is a modified version of previously proposed genetic algorithms for the same problem. Experimental results show the advantages of using new c...

We consider the unrelated parallel machines scheduling problem where jobs have earliness and tardiness penalties and a common due date. We formulate this problem and some of its variants as 0-1 programs with quadratic objective function subject to linear constraints. The main contribution of this paper is to use and develop different convex reformulations to solve exactly the quadratic programs...

Maintenance is important to manufacturing process with a view to sustaining production efficiency. In this study scheduling of unrelated parallel machines with effects of learning and aging and multi maintenance activities is considered. The objective is to find the optimal maintenance periods, optimal maintenance frequencies and optimal job sequences such that the makespan of all jobs are mini...

Here, we consider approximation algorithms for the Graph Balancing problem which is a special case of the job scheduling on unrelated parallel machines to minimize the makespan. We present an interpretation of the 2approximation LP-rounding algorithm given by Lenstra et al. to the special case of graph balancing. We then show how the approximation guarantee can be improved by the technique of a...

The paper suggests a stochastic approximate solution to scheduling problems with unrelated parallel machines. The presented method is based on neurodynamic programming (reinforcement learning and feed-forward artificial neural networks). For various scheduling environments (static-dynamic, deterministicstochastic) different variants of episodic Q-learning rules are proposed. A way to improve th...

In this work we study the unrelated parallel machines problem with the objective of the minimization of the maximum completion time or makespan (Cmax). We propose some metaheuristics based on a size-reduction of the original assignment problem. The idea is to consider only a few of the best possible machine assignments for the jobs and not all of them. We test the proposed simple algorithms wit...

Setup operations on machines usually need of tooling and/or personnel to be carried out. Therefore, the length of the setup might not only depend on the machine and job sequence, but also on the number of resources assigned. This situation is common in real problems arising in several industries where setup operations in production lines are frequent. These operations are indeed setups whose le...