On the Model and Solution Methods for Multi-Facility Capacity Expansion Problem

Capacity expansion problem is a hard combinatorial problem to solve because it must treat many scheduling subproblems within a multi-facility framework. It is classified into a category of general Investment & Operation planning problems. This paper presents a basic model for a certain class of capacity expansion problem applicable to the generation expansion problem in power systems, and proposes several mathematical methods for the model. In the field of Operational Research, Dynamic Programming (DP) has been the most popular method under multistage dynamic environments. It is however made clear in the paper that the model cannot be exactly solved by standard DPs. Consequently, another representative methods such as Lagrangian Relaxation, Branch-and-Bound and Heuristics are also tailored as alternatives for DP and compared with each other. Computational experiments by all proposed methods yielded promising suboptima with quality guarantee, among others Branch-and-Bound and Lagrangian Relaxation methods are recommended as suitable ones for the model.