Improved rolling schedules for the dynamic single-level lot-sizing problem

A major argument for favoring simple lot-sizing heuristics – like the Silver/Meal or Groff's heuristic – to solve instances of the dynamic single-level uncapacitated lot-sizing problem (SLLSP) instead of exact algorithms – like those of Wagner/Whitin or Federgruen/Tzur – is that exact algorithms applied in a rolling horizon environment are heuristics too and may be outperformed by simple heuristics. This article shows how to modify the model of the SLLSP by looking beyond the planning horizon. Extensive tests within a rolling horizon environment have demonstrated that the modified model solved by an exact algorithm now performs at least as well as well-known heuristics and is fairly insensitive to the length of the planning horizon. Furthermore, our principal idea of improving rolling schedules by considering only a portion of the fixed cost related to a decision with an impact on periods beyond the planning horizon is applicable to a wide range of decision models.