We make interact here 2 Knapsack players, which may be related to energy management or robot cooperation. We first discuss the setting of this problem and provide it with an ILP formulation. Next we deal with it through Dynamic Programming and deduce from this DP a Polynomial Time Approximation Scheme.

The emergence of H2energy produced through photolysis makes appear a new generation of local energy players, which are at the same time producers and consumers. This raises the question of synchronizing H2production, which deeply depends on the time, and its consumption through some transportation activity. We deal here with this issue, in the context of an experimental H2production platform, through dynamic programming augmented with ad hoc filtering devices.

Synchronizing heterogeneous processes remains a difficult issue in Scheduling area.Related ILP models are in trouble.So we propose here a pipe-line collaboration of a dynamic programming process for energy production and consumption scheduling.

Abstract In this article, we consider the k‐edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch‐and‐Cut algorithm and present some computational results. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010