A PTAS for common due window scheduling with window penalty on identical machines

Abstract

We study the problem with a set of independent jobs to be processed on some identical parallel machines. Jobs should be completed as close as possible to the common due window, but the window location is a decision variable with linear penalty. The objective is to find a schedule to minimize the sum of earliness and tardiness penalties together with window location cost. Since it is strongly NP-complete, polynomial time approximation schemes are firstly proposed.