This short paper studies a parallel machines scheduling problem with the consideration of resources. Each job needs a number of resources at each machine for its completion. The objective studied is the minimization of the makespan. We model this problem by means of two integer linear programming problems. One of them is based on a model previously proposed in the literature, whereas the other ...

We consider the problem of minimizing general delay costs on unrelated machines. In this problem, we are given a set of m machines and a set of n jobs. Each job j has a machine dependent processing time of pij on machine i, and a release time rij . Further, we are also given a non-decreasing function fj(t) which gives the cost of completing the job j at time t. Our goal is to assign each job to...

<abstract><p>We consider a basic preemptive scheduling problem where $ n non-simultaneously released jobs are to be processed by m unrelated parallel machines so as minimize maximum job completion time. An optimal LP-solution has been used construct an schedule for simultaneously in time O(n^3) $. We propose fast O(m) algorithm that finds case the above possesses "small enough" numb...

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In this paper we deal with the problem of assigning a set of n jobs, with release dates and tails, to either one of two unrelated parallel machines and scheduling each machine so that the makespan is minimized. This problem will be denoted by R2jri; qijCmax. The model generalizes the problem on one machine 1jri; qijCmax, for which a very ecient algorithm exists. In this paper we describe a Bra...

This paper presents an investigation of scheduling procedures to seek the minimum of a positively weighted convex sum of makespan and the number of tardy jobs in a static flexible flow shop scheduling environment. The flexible flow shop problem is a scheduling of jobs in a flow shop environment consisting of series of production stages, some of which may have only one machine, but at least one ...

Abstract: Research on due date oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study, we leverage on our previous work on the single machine total we...

We developed mixed integer programming (MIP) models and hybrid genetic-local search algorithms for the scheduling problem of unrelated parallel machines with job sequence and machine-dependent setup times and with job splitting property. The first contribution of this paper is to introduce novel algorithms which make splitting and scheduling simultaneously with variable number of subjobs. We pr...

We have a set J of n jobs, and a set M of m machines. The processing time of job i is pij on machine j. Let f : J ←M be a function that assigns each job to exactly one machine. The makespan of f is max1≤j≤m ∑ i:f(i)=j pij , where ∑ i:f(i)=j pij is the total processing time of the jobs that are assigned to machine j. In the Scheduling on Unrelated Parallel Machines problem, the goal is to find a...

A novel scheduling problem that results from the addition of resource-assignable setups is presented in this paper. We consider an unrelated parallel machine problem with machine and job sequencedependent setup times. The new characteristic is that the amount of setup time does not only depend on the machine and job sequence but also on the amount of resources assigned, which can vary between a...