Single-Machine Scheduling with Learning Effect, Deteriorating Jobs and Convex Resource Dependent Processing Times

Abstract

This paper considers single-machine scheduling with learning effect, deteriorating jobs and convex resource dependent processing times, i.e., the processing time of a job is a function of its starting time, its position in a sequence and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately to minimize a cost function containing makespan, total completion (waiting) time, total absolute differences in completion (waiting) times and total resource cost. It is proved that the problem can be solved in polynomial time.