In this paper, the unrelated parallel batch processing machine (UPBPM) scheduling problem is addressed to minimize total energy consumption (TEC) and makespan. Firstly, a mixed-integer line programming model (MILP) of UPBPM presented. Secondly, self-adaptive multiobjective differential evolution (AMODE) algorithm put forward. Since parameter value can affect performance greatly, an adaptive con...

Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worst-case ratio between the makespan of an optimal nonpreemptive and that of an optimal preemptive schedule, is at least 4. This matches the upper bound proposed in Lin and Vitt...

We consider a scheduling problem on unrelated parallel machines with the objective to minimize the makespan. In addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource, e.g. workers. A given amount of that resource can be distributed over the jobs in process at any time. The more of the resource is allocated to a job, the small...

We consider a time-indexed formulation for the unrelated parallel machine scheduling problem. show that all polyhedral knowledge known from single problem (in particular, valid inequalities) is applicable to this formulation. present new facet-inducing inequalities and preprocessing technique involving fixing variables based on reduced costs. combine both techniques in basic cutting-plane algor...

appropriate scheduling and sequencing of tasks on machines is one of the basic and significant problems that a shop or a factory manager encounters; this is why in recent decades extensive studies have been done on scheduling issues. one type of scheduling problems is just-in-time (jit) scheduling and in this area, motivated by jit manufacturing, this study investigates a mathematical model for...

A new unrelated parallel machine scheduling problem with deteriorating 26 effect and the objective of makespan minimization is presented in this paper. The 27 deterioration of each machine (and therefore of the job processing times) is a function of the 28 sequence of jobs that have been processed by the machine and not (as considered in the 29 literature) by the time at which each job is assig...