Single Machine Scheduling with Precedence Constrains, Release and Delivery Times

Abstract

The goal of this paper is to propose algorithms for scheduling problem, where set of jobs performed on a single processor. Each job has a release time, when it becomes available for processing, a processing time and a delivery time. We study the case in which there exist precedence constrains among jobs and preemption is not allowed. The objective is to minimize the time, by which all jobs are delivered. The single machine scheduling problem is one of the classic NP-hard optimization problems, and it is useful in solving flowshop and jobshop scheduling problems. We develop branch and bound algorithm for the problem. We propose an approximation algorithm to find an upper bound, solve the preemptive version of the problem to provide a lower bound and use a binary branching rule, where at each branch node, a complete schedule is generated. To illustrate the effectiveness of our algorithms we tested them on randomly generated set of jobs.