W consider both branch-and-cut and column-generation approaches for the problem of finding a minimumcost assignment of jobs with release dates and deadlines to unrelated parallel machines. Results are presented for several variants both with and without constraint programming. Among the variants, the most effective strategy is to combine a tight and compact, but approximate, mixed integer progr...

This work deals with the problem of scheduling n independent jobs on m unrelated parallel machines with the objective of minimizing the makespan (the total elapsed time from the start of execution until all jobs have been completed). Preemption is not allowed. This way a job, once assigned to a particular machine, may not be removed until it has finished its execution. All the machines start wo...

We consider several parallel machine scheduling settings with the objective to minimize the schedule makespan. The most general of these settings is unrelated parallel machine scheduling. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource. A given amount of that resource, e.g. workers, can be distributed...

This paper studies a scheduling problem with non-identical job sizes, arbitrary ready times, and incompatible family constraints for unrelated parallel batch processing machines, where the batches are limited to jobs from same family. The objective is minimize maximum completion time (makespan). important has wide applications in semiconductor manufacturing industries. study proposes mixed inte...

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...

This paper studies the customer order scheduling problem in context of additive manufacturing. The study discusses an integrated involving nesting parts as well batches nested onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from literature, that integrates different materials and sequence-dependent setup times. Additionally, a met...

In this work we propose new randomized rounding algorithms for matroid intersection and matroid base polytopes. We prove concentration inequalities for polynomial objective functions and constraints that has numerous applications and can be used in approximation algorithms for Minimum Quadratic Spanning Tree, Unrelated Parallel Machines Scheduling and Scheduling with Time Windows and Nonlinear ...