Erratum to: Scheduling jobs on parallel machines to minimize a regular step total cost function

Abstract

Our paper entitled “Scheduling jobs on parallel machines to minimize a regular step total cost function” appeared online in Journal of Scheduling. It is an extension from the conference article (Detienne et al. 2009). In these works, we missed two studies considering stepwise cost functions in scheduling problems, in which the authors refer to the optimization criterion as stepwise tardiness. Curry and Peters (2005) investigates a rescheduling problem in a parallel machine environment. The authors examine the tradeoff between schedule stability and tardiness cost, using simulation. A job can be on time or late for 1, 2, 3 or 4 days, thus yielding a stepwise cost function. They also consider machine reassignment costs. Within the simulation, the rescheduling problem is solved using a branch-andprice algorithm. They propose an Integer Linear Program-