Progressive Hedging Innovations for a Stochastic Spare Parts Support Enterprise Problem.

Progressive hedging (PH) is a scenario-based decompositio n technique well-suited to solving stochastic mixed-integer programs. While PH has been successfully applied to a number of problems, a variety of issues arise when implem enting PH in practice, especially when dealing with large-scale problems. In part icular, decisions must be made regarding the value of the perturbation parameter, ρ, criteria for convergence, and techniques for accelerating convergence. We investiga te these issues in the context of a large-scale, real-world stochastic mixed-intege r problem for minimizing the procurement costs associated with spare-parts support ent erprises. We introduce a mathematically-based heuristic for setting the ρ parameter, novel techniques for convergence acceleration, and methods for detecting and recov ering from oscillatory behavior. The efficacy of these techniques is empirically asse s ed on two categories of test problems: those in which only spare-parts procurement levels are considered, and those that additionally consider procurement of repair-re lated resources. The latter class of problem represents a significant open challenge in t he literature, which we show to be efficiently and effectively solved via our PH imple mentations. Additionally, we demonstrate that variable-specific ρ values are more effective than traditional fixed ρ values, and that the PH algorithm can serve as a very effectiv e heuristic even when the mathematical conditions for convergence are not re spected.