Uniform parallel machine scheduling problems with fixed machine cost

Abstract

This paper considers two uniform parallel machine scheduling problems with fixed machine cost under the background of cloud manufacturing. The goal is to minimize the makespan with a given budget of total cost, \(\hat{U}\). All the jobs are homogeneous, i.e., the processing times of the jobs are identical. Non-preemptive and preemptive problems are studied. For the non-preemptive problem, we give a \(2[1+1{/}(h-1)]\)-approximation algorithm, where h is the number of the machine which can not be selected the first time. For the preemptive problem, we give an algorithm whose worst-case bound equals to \(1+1{/}(h-1)\). Preliminary experimental results indicate that the proposed algorithms are reasonably accurate compared with the lower bounds.