Parallel machine scheduling with earliness–tardiness penalties and additional resource constraints

Abstract

This research considers the problem of scheduling jobs on parallel machines with noncommon due dates and additional resource constraints. The objective is to minimize the total absolute deviation of job completion times about the corresponding due dates. All job processing times are assumed to be the same. This problem is motivated by restrictions that occur in the handling and processing of jobs in certain phases of semiconductor manufacturing and other production systems. We examine two special cases. For the first of these, the number of additional resource types and the resource requirements per job are arbitrary. The problem is formulated as a zero–one integer linear program and the Lagrangian relaxation approach is used to obtain tight lower bounds. In the second case, there exist one single type of additional resource and the resource requirements per job are zero or one. This problem is shown to be equivalent to the asymmetric assignment problem. Scope and purpose This paper considers the problem of scheduling jobs on parallel machines where jobs have different due dates and may require, besides machines, certain additional limited resources for their handling and processing. The objective is to minimize the total absolute deviation of job completion times about the corresponding due dates. This objective function is consistent with the just-in-time production philosophy which espouses the notion that earliness as well as tardiness should be penalized. Two problems are addressed. In the first of these, the number of different types of additional resources and resource requirements per job are arbitrary. The problem is formulated as a zero–one integer linear program and the Lagrangian relaxation approach is used. In the second problem, there exists one single type of additional resource and the resource requirements per job are zero or one. This problem can be reformulated as an assignment problem.