A Tutorial on Multi-time Scale Optimization Models and Algorithms

TL;DR

This tutorial introduces multi-time scale optimization models, reviews algorithms for solving them, and discusses their benefits through an illustrative capacity expansion planning example.

Contribution

It provides a comprehensive overview of multi-time scale optimization models, introduces the Value of the Multi-scale Model metric, and offers practical algorithmic insights and an example.

Findings

VMM quantifies benefits of multi-scale models

Algorithms enable efficient solutions for complex models

Illustrative example demonstrates practical application

Abstract

Systems across different industries consist of interrelated processes and decisions in different time scales including long-time decisions and short-term decisions. To optimize such systems, the most effective approach is to formulate and solve multi-time scale optimization models that integrate various decision layers. In this tutorial, we provide an overview of multi-time scale optimization models and review the algorithms used to solve them. We also discuss the metric Value of the Multi-scale Model (VMM) introduced to quantify the benefits of using multi-time scale optimization models as opposed to sequentially solving optimization models from high-level to low-level. Finally, we present an illustrative example of a multi-time scale capacity expansion planning model and showcase how it can be solved using some of the algorithms (https://github.com/li-group/MultiScaleOpt-Tutorial.git). This tutorial serves as both an introductory guide for beginners with no prior experience and a high-level overview of current algorithms for solving multi-time scale optimization models, catering to experts in process systems engineering.