We consider the problem of scheduling jobs that arrive online in the unrelated machine model to minimize `k norms of weighted flowtime. In the unrelated setting, the processing time and weight of a job depends on the machine it is assigned to, and it is perhaps the most general machine model considered in scheduling literature. Chadha et al. [10] obtained a recent breakthrough result in obtaini...

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequenceand machinedependent setup times are given. The objective is to find a schedule that minimizes a positively weighted convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0-1 m...

The flexible flowshop problem is a well known and common challenge. Extended with unrelated parallel machines and especially with the dynamic aspect of distributed release times, the problem gets very ‘close to reality’. Triggered by the growing complexity of logistic systems, the paradigm of central planning is being shifted to decentralised control. As part of this, an autonomous control conc...

We investigate a difficult scheduling problem in a semiconductor manufacturing process that seeks to minimize the number of tardy jobs and makespan with sequence-dependent setup time, release time, due dates and tool constraints. We propose a mixed integer programming (MIP) formulation which treats tardy jobs as soft constraints so that our objective seeks the minimum weighted sum of makespan a...

Each of n jobs is to be processed without interruption on one of m unrelated parallel machines. The objective is to minimize the maximum completion time. A heuristic method is presented, the first stage of which uses linear programming to form a partial schedule leaving at most m 1 jobs unscheduled: the second stage schedules these m1 jobs using an enumerative method. For m 2 3, it is shown tha...

This paper addresses a scheduling problem with unrelated parallel machines, sequence dependent setups and due dates. The problem is based on a real case and the objective is to minimise the sum of the makespan and the weighted delays. A mixed integer linear programming model is proposed and since the model considers realistic constraints, a metaheuristic based on GRASP is used as a solution met...

We consider the problem of scheduling jobs that arrive online in the unrelated machine model to minimize `k norms of weighted flowtime. In the unrelated setting, the processing time and weight of a job depends on the machine it is assigned to, and it is perhaps the most general machine model considered in scheduling literature. Chadha et al. [10] obtained a recent breakthrough result in obtaini...

Job scheduling has always been a challenging task in modern manufacturing and the most real life scheduling problems which involves multi-criteria and multi-machine environments. In this research our direction is largely motivated by the adoption of the Just-In-Time (JIT) philosophy in parallel machines system, where processing times of jobs are controllable. The goal of this paper is to minimi...

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 ...

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees sm...