Some Single Machine Scheduling Problems with Resource Dependent Set-up and Processing Times

Abstract

In the paper, we consider a single machine scheduling problem with set-up times and job processing times given as linear functions dependent on some continuously divisible resources. The scheduling objective is to find the optimal sequence of the jobs and the allocation of limited resources, which minimize the maximum completion time (makespan). A dual problem is also considered, i.e. the problem, in which the objective is to find a sequence of jobs and an allocation of resources, which minimize the total resource consumption, under a given constraint on maximum completion time. Based on the problems properties, we present polynomial time solution algorithms. We conclude the paper by outlining some possible directions for future research.