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

This paper deals with a parallel machine scheduling problem whose objective is to minimize a regular step total cost function. A real world application of the problem is presented, and Mixed Integer Linear Programming models are described for the cases with and without release dates, as well as a dedicated constraint generation procedure. Experimental results are reported and discussed to evaluate the relevance of the different approaches on well‐known special cases and the general case.