We discuss four solution methods for problems in general network production environments. After presenting some background and motivation, in Section 13.1, we cover (1) preprocessing and tightening methods, in Section 13.2; (2) reformulations, in Section 13.3; (3) an approach to formulate models that employ multiple discrete time grids, in Section 13.4; and (4) a three-stage algorithm that employs both a discrete and continuous time models, in Section 13.5. For simplicity, we do not consider shared utilities nor special processing features such as storage in processing units and multiple material transfers. The methods presented in Section 13.2 and Section 13.3 are applicable to both discrete and continuous time models, but to keep the presentation short, we apply them to discrete time models, though we comment on their application to their continuous counterparts. The reader can study each section, after Section 13.1, independently, that is, Section 13.2 is not prerequisite for Section 13.3, and so on.

The goal of the present chapter, as well as Chapter 13, is to illustrate how problem features can be exploited to develop more efficient models and/or specialized algorithms. We start, in the present chapter, with solution methods for problems in sequential environments. Specifically, we discuss four methods: (1) a decomposition approach, in Section 12.1; (2) preprocessing algorithms and tightening constraints, in Section 12.2; (3) a reformulation and tightening constraints based on time windows, in Section 12.3; and (4) a two-step algorithm, combining the advantages of discrete and continuous time models, in Section 12.4. While all presented methods can be applied to a wide range of problems, we present them for a subset of problems for the sake of brevity. Also, all methods can be applied to problems under different processing features, but to keep the presentation simple, we discuss problems with no shared utilities and no storage constraints.