A Model‐Based Approach and Analysis for Multi‐Period Networks

The aim of this contribution is to address a general class of network problems, very common in process systems engineering, where spoilage on arcs and storage in nodes are inevitable as time changes. Having a set of capacities, so‐called horizon capacity which limits the total flow passing arcs over all periods, the min‐cost flow problem in the discrete‐time model with time‐varying network parameters is investigated. While assuming a possibility of storage or and spoilage, we propose some approaches employing polyhedrals to obtain optimal solutions for a pre‐specified planning horizon. Our methods describe some reformulations based on polyhedrals that lead to LP problems comprising a set of sparse subproblems with exceptional structures. Considering the sparsity and repeating structure of the polyhedrals, algorithmic approaches based on decomposition techniques of block‐angular and block‐staircase cases are proposed to handle the global problem aiming to reduce the computational resources required.