Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows

Abstract

In this paper a new time-oriented decomposition heuristic is proposed to solve the dynamic multi-item multilevel lot-sizing problem in general product structures with single and multiple constrained resources as well as setup times. While lot-sizing decisions are made sequentially within an internally rolling planning interval (or lot-sizing window), capacities are always considered over the entire planning horizon. For each submodel a model formulation based on the “Simple Plant Location” representation is developed. These mixed-integer linear submodels are solved by standard mathematical programming software even for relatively large test instances. Extensive computational tests show that the heuristic proposed provides a better solution quality than a well-known special purpose heuristic.

Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems

“…Where comparable, the CPU times appear to be of the same order of magnitude as those in state-of-the-art heuristics such as Stadtler (2003), even though differences between the problem instances and platforms make a precise comparison impossible.…”

“…State-of-the-art solution methods include, in addition to the bc-prod system mentioned in §1 Wolsey 2000, 2001), those of Stadtler (2003) and Suerie and Stadtler (2003). Interestingly, these methods all apply variants of the (EH) heuristic: In the "fix-and-relax" heuristic, each consecutive problem instance expands the horizon of the previous instance by appending the same number of periods to its tail.…”

“…Interestingly, these methods all apply variants of the (EH) heuristic: In the "fix-and-relax" heuristic, each consecutive problem instance expands the horizon of the previous instance by appending the same number of periods to its tail. The "internally rolling schedule heuristics" in Stadtler (2003) and Suerie and Stadtler (2003) use constant interval increments . In each problem instance, instead of imposing boundary conditions that are necessary and sufficient for a feasible extension until the end of the full planning horizon, the authors include the periods beyond the end of the current interval, however, with all binary variables in these periods treated either as continuous variables (bc-prod) or set equal to one (Stadtler 2003, Suerie andStadtler 2003).…”

“…The "internally rolling schedule heuristics" in Stadtler (2003) and Suerie and Stadtler (2003) use constant interval increments . In each problem instance, instead of imposing boundary conditions that are necessary and sufficient for a feasible extension until the end of the full planning horizon, the authors include the periods beyond the end of the current interval, however, with all binary variables in these periods treated either as continuous variables (bc-prod) or set equal to one (Stadtler 2003, Suerie andStadtler 2003). The heuristics in the latter two papers substitute all cost parameters for the afterthe-interval periods by zero, with the possible exception of variable overtime cost rates, in case the capacity constraints may be violated by scheduling overtime.…”

Polynomial-Time Algorithms for Stochastic Uncapacitated Lot-Sizing Problems

“…This fundamental model, first introduced by Wagner and Whitin (1958), is embedded within many practical production planning problems. It is easily seen to be fixed-charge flow problem in a network composed of a directed path and a dummy production node, and understanding and exploiting this structure has been essential in developing approaches to complicated, real-world problems (see, for example, Tempelmeier and Derstroff (1996), Belvaux and Wolsey (2000), Belvaux and Wolsey (2001), Stadtler (2003), and many others).…”